Download the Top 25 CAT DILR Sets with Solutions PDF and get one step closer to mastering this crucial section and boosting your CAT 2024 score!
Top 25 CAT DILR Sets with Solutions PDF
Cracku's specially curated Top 25 CAT DILR Sets is designed to elevate your preparation and sharpen your skills in tackling Data Interpretation and Logical Reasoning (DILR) sections. These carefully chosen sets encompass a range of essential DILR problems and are perfect for honing your approach to complex scenarios often encountered in the CAT exam.
Why Practice with the Top 25 DILR Sets for CAT 2024?
The CAT DILR section is known for its unpredictability and challenging nature. Regular practice with high-quality sets can make a significant difference in your performance. Here’s why this Top 25 DILR Sets PDF is a must-have:
Enhances your ability to interpret data quickly and accurately
Improves logical reasoning skills essential for solving intricate problems
Provides practice with a diverse range of questions that reflect the real CAT exam difficulty
With the provided solutions, you will gain insights into effective problem-solving strategies. Each set includes detailed explanations to ensure you understand how to approach even the most complex DILR challenges.
An online Bus Ticket booking service GoBaba is used by customers to book and pay for the bus tickets all over India. GoBaba has a wallet where they maintain a Virtual currency GoCash coins. One has to compulsorily use these coins in the next transactions instead of paying Rupees. Each GoCash coin is equal to one rupee, but the GoCash coins expire at the end of each month.
For the month of May, GoBaba released five coupon codes to give discounts to their users. Each coupon code can be applied once a month. A user can apply only one coupon for a transaction.
The following table gives the details of the coupon codes:
Cashback is the GoCash coins provided by the company after the complete payment of the transaction in the form of rupees. In the case of the discount, a user has to pay a reduced amount for a ticket.
A Cashback or a Discount is applicable to the transaction amount after subtracting the GoCash coins i.e the amount paid in the form of Rupees. Minimum transaction is also defined in terms of the amount paid in Rupees.
A minimum of 1 ticket has to be booked for a transaction and each transaction can have multiple tickets.
Question 1
Aman wanted to book two tickets in the month of May, both of Rs 1200. What is the minimum amount(rupees) he has to pay to buy the tickets?
Show Answer
Solution
The following table gives the details of the coupon codes:
Aman wanted to book two tickets in the month of May, both of Rs 1200.
The promo code DISCOBUS will not be applicable to a single ticket. If he buys both the tickets in a single transaction to apply DISCOBUS then the GoCash coins are not useful.
As we apply Cashback option for the first ticket, we have to pay less for the second ticket. Thus the coupons as G40 and FLAT 500 cannot be applied to the next ticket due to the Minimum Transaction criteria.
He should apply either the discount coupons to both the tickets or Cash coupons to the first ticket. These cases are possible:
1. SUMMER BUS on the first ticket and GOBABA25 on the second ticket.
2. GO40 on the first ticket and FLAT500 on the second.
Case 1:
SUMMER BUS on the first ticket will return 50% of Rs 1200 i.e. coins worth Rs 600 on the wallet.
For the next ticket, he has to pay Rs 1200- Rs 600= Rs 600.
GOBABA25 will give a 25% discount, thus he has to pay 75% of 600 i.e Rs 450.
A total of 1200+450= Rs1650.
Case 2:
GO40 on the first ticket will give a discount of 40%. i.e. 40% of Rs 1200 = Rs 480.
Aman has to pay Rs 1200-480= Rs 720.
FLAT500 will give Rs 500 discount, thus he has to pay 1200-500= Rs 700
A total of 720+700= Rs1420.
Rs 1420 will be the minimum amount Aman has to pay.
correct answer:-
1420
Instruction for set :
An online Bus Ticket booking service GoBaba is used by customers to book and pay for the bus tickets all over India. GoBaba has a wallet where they maintain a Virtual currency GoCash coins. One has to compulsorily use these coins in the next transactions instead of paying Rupees. Each GoCash coin is equal to one rupee, but the GoCash coins expire at the end of each month.
For the month of May, GoBaba released five coupon codes to give discounts to their users. Each coupon code can be applied once a month. A user can apply only one coupon for a transaction.
The following table gives the details of the coupon codes:
Cashback is the GoCash coins provided by the company after the complete payment of the transaction in the form of rupees. In the case of the discount, a user has to pay a reduced amount for a ticket.
A Cashback or a Discount is applicable to the transaction amount after subtracting the GoCash coins i.e the amount paid in the form of Rupees. Minimum transaction is also defined in terms of the amount paid in Rupees.
A minimum of 1 ticket has to be booked for a transaction and each transaction can have multiple tickets.
Question 2
Bala has to buy a total of 4 tickets such that each ticket cost Rs 1400 in the month of May, what is the minimum amount (rupees) he has to pay?
Show Answer
Solution
The following table gives the details of the coupon codes:
The actual value of tickets for Bala in total = 4*1400= Rs 5600
DISCOBUS gives the highest percentage of cashback.
DISCOBUS: Cashback of 75% on the whole amount is of no avail as the GoCash will expire at the end of the month.
Thus he should do a partial transaction with the promo code DISCOBUS.
Case 1. DISCOBUS on 3 tickets and 1 ticket bought with the GoCash coins.
Amount paid = 3*1400= Rs 4200
GoCash recieved= 75% of 4200= Rs 3150 or Rs 2000 (minimum value of the two)
The fourth ticket can be bought with the GoCash in the wallet.
Total amount paid= Rs 4200.
Case 2. DISCOBUS on 2 tickets and 2 tickets bought with the GoCash coins.
Amount paid = 2*1400= Rs 2800
GoCash recieved= 75% of 2800= Rs 2100 or Rs 2000 (minimum value of the two).
The wallet will have Rs 2000 worth of GoCash.
For the next two tickets total value of the ticket= 2* Rs1400= Rs 2800.
The GoCash can be utilised of Rs 2000
Rupees= 2800-2000= Rs 800
Apply promo code GoBABA25 and get 25% discount.
i.e. 25% of 800= Rs 200
Rupees he has to pay = 800-200= Rs 600
The total amount he has to pay:
Rs 2800+ Rs 600 = Rs 3400
correct answer:-
3400
Instruction for set :
An online Bus Ticket booking service GoBaba is used by customers to book and pay for the bus tickets all over India. GoBaba has a wallet where they maintain a Virtual currency GoCash coins. One has to compulsorily use these coins in the next transactions instead of paying Rupees. Each GoCash coin is equal to one rupee, but the GoCash coins expire at the end of each month.
For the month of May, GoBaba released five coupon codes to give discounts to their users. Each coupon code can be applied once a month. A user can apply only one coupon for a transaction.
The following table gives the details of the coupon codes:
Cashback is the GoCash coins provided by the company after the complete payment of the transaction in the form of rupees. In the case of the discount, a user has to pay a reduced amount for a ticket.
A Cashback or a Discount is applicable to the transaction amount after subtracting the GoCash coins i.e the amount paid in the form of Rupees. Minimum transaction is also defined in terms of the amount paid in Rupees.
A minimum of 1 ticket has to be booked for a transaction and each transaction can have multiple tickets.
Question 3
Hari bought a ticket of x Rs such that he got the same discount on using the promo codes GO40 and GOBABA25. What is the value of x?
Show Answer
Solution
The following table gives the details of the coupon codes:
GO40 gives a discount of 40% till Rs 1000.
GOBABA25 gives a discount of 25% till Rs 2000.
The maximum discount which GO40 can give is Rs1000.
Thus x*25/100 =1000
x= Rs 4000
On Rs 4000 both the coupon codes will give a discount of Rs 1000.
correct answer:-
1
Instruction for set :
An online Bus Ticket booking service GoBaba is used by customers to book and pay for the bus tickets all over India. GoBaba has a wallet where they maintain a Virtual currency GoCash coins. One has to compulsorily use these coins in the next transactions instead of paying Rupees. Each GoCash coin is equal to one rupee, but the GoCash coins expire at the end of each month.
For the month of May, GoBaba released five coupon codes to give discounts to their users. Each coupon code can be applied once a month. A user can apply only one coupon for a transaction.
The following table gives the details of the coupon codes:
Cashback is the GoCash coins provided by the company after the complete payment of the transaction in the form of rupees. In the case of the discount, a user has to pay a reduced amount for a ticket.
A Cashback or a Discount is applicable to the transaction amount after subtracting the GoCash coins i.e the amount paid in the form of Rupees. Minimum transaction is also defined in terms of the amount paid in Rupees.
A minimum of 1 ticket has to be booked for a transaction and each transaction can have multiple tickets.
Question 4
Vidya wanted 20 bus tickets each of Rs 200 if she wanted to buy the tickets in two transactions, what is the minimum amount she has to pay if she had applied only one promo code?
Show Answer
Solution
The following table gives the details of the coupon codes:
Vidya applied only one promo code thus she should use DISCOBUS in order to maximise the discount.
Case 1
If she applied the coupon for 10 tickets, the transaction amount will be= 10*200= Rs2000
Cashback will be 75 % of the total. Thus 75/100*2000= Rs1500
For the next transaction, she has to pay = 2000-1500= Rs500
Total amount=2000+500= Rs2500
Case 2
If she applied the coupon for 11 tickets, the transaction amount will be= 11*200= Rs2200
Cashback will be 75 % of the total. Thus 75/100*2200= Rs1650
For the next transaction, she has to pay = 1800-1650= Rs150
Total amount=2200+150= Rs2350
Case 3
If she applied the coupon for 12 tickets, the transaction amount will be= 12*200= Rs2400
Cashback will be 75 % of the total. Thus 75/100*2000= Rs1800
For the next transaction, she has to pay = 1600-1800= -200
Total amount= Rs 2400
Case 2 is the minimum.
correct answer:-
2
Instruction for set :
Four friends Veena, Reena, Bablu and Babila, met after a very long time and told each other about the cars owned by them. They made four statements each regarding the color, cost and brand of the car owned by each of them. It is known that atleast one among them is truthteller who always speaks the truth, a liar who always lies and an alternator who alternates between truth and a lie starting with either truth or a lie. Note that a friend can be none of these 3 and can say lie or truth in any order.
Each of them owns exactly one of the car brands among Renault, Volvo, BMW or Bentley. The colors of the cars are black, blue, red, violet such that no two cars are of the same colour.
Reena:
1: Veena's car is 37 lakhs.
2: Colour of Bablu's car is neither Black nor blue.
3: Babila owns a red coloured car.
4: Bablu is a liar.
Bablu:
1: Only one among us has the same first letter of the colour of the car, the car brand and the name of the person who owns that car.
2: I own the most expensive car.
3: Blue coloured car is owned by Veena, which is not the cheapest.
4: Reena is a liar.
Veena:
1: When the price of any car is divided by 1 lakh, the digits are prime numbers when considered individually or together.
2: Bablu is an alternator.
3: Babila is neither truthteller nor alternator.
4: The price of Babila's car is 73 lakh.
Babila:
1: I own a red coloured car whose price is 23 lakh.
2: Sum of the price of my car and Veena's car is not 76 lakh.
3: The person whose first letter in their name, the car bran and the colour of their car is same is Bablu.
4: Veena is an alternator.
It is known that exactly one among them had the same starting letter in their name, car brand and the car colour.
The prices of the four cars are 23 lakhs, 37 lakhs, 53 lakhs and 73 lakhs in some order.
Question 5
Who among the friends is truthteller?
Show Answer
Solution
Case 1:Let us consider Reena as Truthteller
Bibila's car is Red coloured.
Bablu's car is neither Black nor Blue: Red /Violet
Since Red is Babila's car, Bablu's car is violet coloured
Reena and Veena will own Black/Blue coloured car in any order, which will negate the condition that for one among them the colour of the car, brand and name starts with the same letter.
Case 2:Let us consider Veena as Truthteller
When the prices are divided by 100000, possible values 2,3,5,7, and since the prices are a 7-digited prime number, Only possible values are 23,37,53,73,97.
Bablu is an alternator.
Babila is neither truthteller nor alternator. So Babila can be either Liar/None.
Reena can be liar/Alternator/truthteller/none
Bablu's car price is not 7300000.
Bablu's first statement is true So if he is alternator the sequence of statements (T, F, T, F)
Bablu's car price can be 23/37/53.
Veena owns a blue coloured car which can be priced 37/53/73.
From Bablu's 4th statement, Reena cannot be a liar.
Since there has to be atleast one liar among them, Babila is the liar.
Let's consider Babila's statements.
$$2^{nd}$$ statement says Veena +Babila cars prices sums to 76 which is not possible.
Hence our initial consideration that Veena is truthteller is false.
Case 3:Lets consider Babila as truthteller.
Babila owns a red coloured car of price 23000000
Veena is an alternator who owns a car priced 53000000
If Veena is an alternator and her $$1^{st}$$ statement is true so the sequence should be (T, F, T, F)
$$3^{rd}$$ statement says Babila is neither truthteller nor alternator which contradicts our assumption.
Case 4: Bablu is truthteller.
Bablu's car price is 7300000
Veena owns a Blue coloured car whose price may be 37/53 lakhs.
Reena is a liar.
From Reena's 1st statement, Veena's car price is 53 lakh.
Bablu's car is either Blue or black. Since Veena owns a Blue car, Bablu's car is Black.
Babila owns Violet coloured car. Reena owns Red coloured car.
Since Veena's first statement is true, the second statement is false, and the fourth statement is false Veena
Veena can be an alternator or none.
If Veena is an alternator.
Babila is None among them, i.e. her statements can be any order.
The following cases are possible.
Since Babila's first statement is false fourth statement is true.
So second third statements can be either (FT),(FF),(TT)
when Second, third statements are F, T
when Second third statements are F,F
When second,third statements are TT
~Renault means, Reena doesnt own renault.
When Veena is None, and Babila is an alternator.
Babila cannot be an alternator because her fourth statement is False, which means her first statement should be true but which is false.
Hence contradictory.
We can see that Bablu is truthteller.
A is the correct answer.
correct answer:-
1
Instruction for set :
Four friends Veena, Reena, Bablu and Babila, met after a very long time and told each other about the cars owned by them. They made four statements each regarding the color, cost and brand of the car owned by each of them. It is known that atleast one among them is truthteller who always speaks the truth, a liar who always lies and an alternator who alternates between truth and a lie starting with either truth or a lie. Note that a friend can be none of these 3 and can say lie or truth in any order.
Each of them owns exactly one of the car brands among Renault, Volvo, BMW or Bentley. The colors of the cars are black, blue, red, violet such that no two cars are of the same colour.
Reena:
1: Veena's car is 37 lakhs.
2: Colour of Bablu's car is neither Black nor blue.
3: Babila owns a red coloured car.
4: Bablu is a liar.
Bablu:
1: Only one among us has the same first letter of the colour of the car, the car brand and the name of the person who owns that car.
2: I own the most expensive car.
3: Blue coloured car is owned by Veena, which is not the cheapest.
4: Reena is a liar.
Veena:
1: When the price of any car is divided by 1 lakh, the digits are prime numbers when considered individually or together.
2: Bablu is an alternator.
3: Babila is neither truthteller nor alternator.
4: The price of Babila's car is 73 lakh.
Babila:
1: I own a red coloured car whose price is 23 lakh.
2: Sum of the price of my car and Veena's car is not 76 lakh.
3: The person whose first letter in their name, the car bran and the colour of their car is same is Bablu.
4: Veena is an alternator.
It is known that exactly one among them had the same starting letter in their name, car brand and the car colour.
The prices of the four cars are 23 lakhs, 37 lakhs, 53 lakhs and 73 lakhs in some order.
Question 6
Who among the friends owns the cheapest car?
Show Answer
Solution
Case 1:Let us consider Reena as Truthteller
Bibila's car is Red coloured.
Bablu's car is neither Black nor Blue: Red /Violet
Since Red is Babila's car, Bablu's car is violet coloured
Reena and Veena will own Black/Blue coloured car in any order, which will negate the condition that for one among them the colour of the car, brand and name starts with the same letter.
Case 2:Let us consider Veena as Truthteller
When the prices are divided by 100000, possible values 2,3,5,7, and since the prices are a 7-digited prime number, Only possible values are 23,37,53,73,97.
Bablu is an alternator.
Babila is neither truthteller nor alternator. So Babila can be either Liar/None.
Reena can be liar/Alternator/truthteller/none
Bablu's car price is not 7300000.
Bablu's first statement is true So if he is alternator the sequence of statements (T, F, T, F)
Bablu's car price can be 23/37/53.
Veena owns a blue coloured car which can be priced 37/53/73.
From Bablu's 4th statement, Reena cannot be a liar.
Since there has to be atleast one liar among them, Babila is the liar.
Let's consider Babila's statements.
$$2^{nd}$$ statement says Veena +Babila cars prices sums to 76 which is not possible.
Hence our initial consideration that Veena is truthteller is false.
Case 3:Lets consider Babila as truthteller.
Babila owns a red coloured car of price 23000000
Veena is an alternator who owns a car priced 53000000
If Veena is an alternator and her $$1^{st}$$ statement is true so the sequence should be (T, F, T, F)
$$3^{rd}$$ statement says Babila is neither truthteller nor alternator which contradicts our assumption.
Case 4: Bablu is truthteller.
Bablu's car price is 7300000
Veena owns a Blue coloured car whose price may be 37/53 lakhs.
Reena is a liar.
From Reena's 1st statement, Veena's car price is 53 lakh.
Bablu's car is either Blue or black. Since Veena owns a Blue car, Bablu's car is Black.
Babila owns Violet coloured car. Reena owns Red coloured car.
Since Veena's first statement is true, the second statement is false, and the fourth statement is false Veena
Veena can be an alternator or none.
If Veena is an alternator.
Babila is None among them, i.e. her statements can be any order.
The following cases are possible.
Since Babila's first statement is false fourth statement is true.
So second third statements can be either (FT),(FF),(TT)
when Second, third statements are F, T
when Second third statements are F,F
When second,third statements are TT
~Renault means, Reena doesnt own renault.
When Veena is None, and Babila is an alternator.
Babila cannot be an alternator because her fourth statement is False, which means her first statement should be true but which is false.
Hence contradictory.
The person who owns cheapest car cannot be certainly determined.
D is the correct answer.
correct answer:-
4
Instruction for set :
Four friends Veena, Reena, Bablu and Babila, met after a very long time and told each other about the cars owned by them. They made four statements each regarding the color, cost and brand of the car owned by each of them. It is known that atleast one among them is truthteller who always speaks the truth, a liar who always lies and an alternator who alternates between truth and a lie starting with either truth or a lie. Note that a friend can be none of these 3 and can say lie or truth in any order.
Each of them owns exactly one of the car brands among Renault, Volvo, BMW or Bentley. The colors of the cars are black, blue, red, violet such that no two cars are of the same colour.
Reena:
1: Veena's car is 37 lakhs.
2: Colour of Bablu's car is neither Black nor blue.
3: Babila owns a red coloured car.
4: Bablu is a liar.
Bablu:
1: Only one among us has the same first letter of the colour of the car, the car brand and the name of the person who owns that car.
2: I own the most expensive car.
3: Blue coloured car is owned by Veena, which is not the cheapest.
4: Reena is a liar.
Veena:
1: When the price of any car is divided by 1 lakh, the digits are prime numbers when considered individually or together.
2: Bablu is an alternator.
3: Babila is neither truthteller nor alternator.
4: The price of Babila's car is 73 lakh.
Babila:
1: I own a red coloured car whose price is 23 lakh.
2: Sum of the price of my car and Veena's car is not 76 lakh.
3: The person whose first letter in their name, the car bran and the colour of their car is same is Bablu.
4: Veena is an alternator.
It is known that exactly one among them had the same starting letter in their name, car brand and the car colour.
The prices of the four cars are 23 lakhs, 37 lakhs, 53 lakhs and 73 lakhs in some order.
Question 7
If Babila lies more number of times than she says the truth, then who owns the car of brand Volvo?
Show Answer
Solution
Case 1:Let us consider Reena as Truthteller
Bibila's car is Red coloured.
Bablu's car is neither Black nor Blue: Red /Violet
Since Red is Babila's car, Bablu's car is violet coloured
Reena and Veena will own Black/Blue coloured car in any order, which will negate the condition that for one among them the colour of the car, brand and name starts with the same letter.
Case 2:Let us consider Veena as Truthteller
When the prices are divided by 100000, possible values 2,3,5,7, and since the prices are a 7-digited prime number, Only possible values are 23,37,53,73,97.
Bablu is an alternator.
Babila is neither truthteller nor alternator. So Babila can be either Liar/None.
Reena can be liar/Alternator/truthteller/none
Bablu's car price is not 7300000.
Bablu's first statement is true So if he is alternator the sequence of statements (T, F, T, F)
Bablu's car price can be 23/37/53.
Veena owns a blue coloured car which can be priced 37/53/73.
From Bablu's 4th statement, Reena cannot be a liar.
Since there has to be atleast one liar among them, Babila is the liar.
Let's consider Babila's statements.
$$2^{nd}$$ statement says Veena +Babila cars prices sums to 76 which is not possible.
Hence our initial consideration that Veena is truthteller is false.
Case 3:Lets consider Babila as truthteller.
Babila owns a red coloured car of price 23000000
Veena is an alternator who owns a car priced 53000000
If Veena is an alternator and her $$1^{st}$$ statement is true so the sequence should be (T, F, T, F)
$$3^{rd}$$ statement says Babila is neither truthteller nor alternator which contradicts our assumption.
Case 4: Bablu is truthteller.
Bablu's car price is 7300000
Veena owns a Blue coloured car whose price may be 37/53 lakhs.
Reena is a liar.
From Reena's 1st statement, Veena's car price is 53 lakh.
Bablu's car is either Blue or black. Since Veena owns a Blue car, Bablu's car is Black.
Babila owns Violet coloured car. Reena owns Red coloured car.
Since Veena's first statement is true, the second statement is false, and the fourth statement is false Veena
Veena can be an alternator or none.
If Veena is an alternator.
Babila is None among them, i.e. her statements can be any order.
The following cases are possible.
Since Babila's first statement is false fourth statement is true.
So second third statements can be either (FT),(FF),(TT)
when Second, third statements are F, T
when Second third statements are F,F
When second,third statements are TT
~Renault means, Reena doesnt own renault.
When Veena is None, and Babila is an alternator.
Babila cannot be an alternator because her fourth statement is False, which means her first statement should be true but which is false.
Hence contradictory.
Therefore Bablu is truthteller, Reena is a liar, Veena is an alternator and Babila does not belong to any category...
If Babila lies more number of times than she speaks the truth.
Then her second and third statements should be False. She lies 3 out of 4 times
So Bablu owns Volvo.
correct answer:-
2
Instruction for set :
Four friends Veena, Reena, Bablu and Babila, met after a very long time and told each other about the cars owned by them. They made four statements each regarding the color, cost and brand of the car owned by each of them. It is known that atleast one among them is truthteller who always speaks the truth, a liar who always lies and an alternator who alternates between truth and a lie starting with either truth or a lie. Note that a friend can be none of these 3 and can say lie or truth in any order.
Each of them owns exactly one of the car brands among Renault, Volvo, BMW or Bentley. The colors of the cars are black, blue, red, violet such that no two cars are of the same colour.
Reena:
1: Veena's car is 37 lakhs.
2: Colour of Bablu's car is neither Black nor blue.
3: Babila owns a red coloured car.
4: Bablu is a liar.
Bablu:
1: Only one among us has the same first letter of the colour of the car, the car brand and the name of the person who owns that car.
2: I own the most expensive car.
3: Blue coloured car is owned by Veena, which is not the cheapest.
4: Reena is a liar.
Veena:
1: When the price of any car is divided by 1 lakh, the digits are prime numbers when considered individually or together.
2: Bablu is an alternator.
3: Babila is neither truthteller nor alternator.
4: The price of Babila's car is 73 lakh.
Babila:
1: I own a red coloured car whose price is 23 lakh.
2: Sum of the price of my car and Veena's car is not 76 lakh.
3: The person whose first letter in their name, the car bran and the colour of their car is same is Bablu.
4: Veena is an alternator.
It is known that exactly one among them had the same starting letter in their name, car brand and the car colour.
The prices of the four cars are 23 lakhs, 37 lakhs, 53 lakhs and 73 lakhs in some order.
Question 8
Blue coloured car is owned by
Show Answer
Solution
Case 1:Let us consider Reena as Truthteller
Bibila's car is Red coloured.
Bablu's car is neither Black nor Blue: Red /Violet
Since Red is Babila's car, Bablu's car is violet coloured
Reena and Veena will own Black/Blue coloured car in any order, which will negate the condition that for one among them the colour of the car, brand and name starts with the same letter.
Case 2:Let us consider Veena as Truthteller
When the prices are divided by 100000, possible values 2,3,5,7, and since the prices are a 7-digited prime number, Only possible values are 23,37,53,73,97.
Bablu is an alternator.
Babila is neither truthteller nor alternator. So Babila can be either Liar/None.
Reena can be liar/Alternator/truthteller/none
Bablu's car price is not 7300000.
Bablu's first statement is true So if he is alternator the sequence of statements (T, F, T, F)
Bablu's car price can be 23/37/53.
Veena owns a blue coloured car which can be priced 37/53/73.
From Bablu's 4th statement, Reena cannot be a liar.
Since there has to be atleast one liar among them, Babila is the liar.
Let's consider Babila's statements.
$$2^{nd}$$ statement says Veena +Babila cars prices sums to 76 which is not possible.
Hence our initial consideration that Veena is truthteller is false.
Case 3:Lets consider Babila as truthteller.
Babila owns a red coloured car of price 23000000
Veena is an alternator who owns a car priced 53000000
If Veena is an alternator and her $$1^{st}$$ statement is true so the sequence should be (T, F, T, F)
$$3^{rd}$$ statement says Babila is neither truthteller nor alternator which contradicts our assumption.
Case 4: Bablu is truthteller.
Bablu's car price is 7300000
Veena owns a Blue coloured car whose price may be 37/53 lakhs.
Reena is a liar.
From Reena's 1st statement, Veena's car price is 53 lakh.
Bablu's car is either Blue or black. Since Veena owns a Blue car, Bablu's car is Black.
Babila owns Violet coloured car. Reena owns Red coloured car.
Since Veena's first statement is true, the second statement is false, and the fourth statement is false Veena
Veena can be an alternator or none.
If Veena is an alternator.
Babila is None among them, i.e. her statements can be any order.
The following cases are possible.
Since Babila's first statement is false fourth statement is true.
So second third statements can be either (FT),(FF),(TT)
when Second, third statements are F, T
when Second third statements are F,F
When second,third statements are TT
~Renault means, Reena doesnt own renault.
When Veena is None, and Babila is an alternator.
Babila cannot be an alternator because her fourth statement is False, which means her first statement should be true but which is false.
Hence contradictory.
Blue coloured car is owned by Veena.
C is the correct answer.
correct answer:-
3
Instruction for set :
Four friends Veena, Reena, Bablu and Babila, met after a very long time and told each other about the cars owned by them. They made four statements each regarding the color, cost and brand of the car owned by each of them. It is known that atleast one among them is truthteller who always speaks the truth, a liar who always lies and an alternator who alternates between truth and a lie starting with either truth or a lie. Note that a friend can be none of these 3 and can say lie or truth in any order.
Each of them owns exactly one of the car brands among Renault, Volvo, BMW or Bentley. The colors of the cars are black, blue, red, violet such that no two cars are of the same colour.
Reena:
1: Veena's car is 37 lakhs.
2: Colour of Bablu's car is neither Black nor blue.
3: Babila owns a red coloured car.
4: Bablu is a liar.
Bablu:
1: Only one among us has the same first letter of the colour of the car, the car brand and the name of the person who owns that car.
2: I own the most expensive car.
3: Blue coloured car is owned by Veena, which is not the cheapest.
4: Reena is a liar.
Veena:
1: When the price of any car is divided by 1 lakh, the digits are prime numbers when considered individually or together.
2: Bablu is an alternator.
3: Babila is neither truthteller nor alternator.
4: The price of Babila's car is 73 lakh.
Babila:
1: I own a red coloured car whose price is 23 lakh.
2: Sum of the price of my car and Veena's car is not 76 lakh.
3: The person whose first letter in their name, the car bran and the colour of their car is same is Bablu.
4: Veena is an alternator.
It is known that exactly one among them had the same starting letter in their name, car brand and the car colour.
The prices of the four cars are 23 lakhs, 37 lakhs, 53 lakhs and 73 lakhs in some order.
Question 9
If the number of true statements given by Babila is not equal to any of the other three people. Which of the following car brand cannot be owned by Bablu ?
Show Answer
Solution
Case 1:Let us consider Reena as Truthteller
Bibila's car is Red coloured.
Bablu's car is neither Black nor Blue: Red /Violet
Since Red is Babila's car, Bablu's car is violet coloured
Reena and Veena will own Black/Blue coloured car in any order, which will negate the condition that for one among them the colour of the car, brand and name starts with the same letter.
Case 2:Let us consider Veena as Truthteller
When the prices are divided by 100000, possible values 2,3,5,7, and since the prices are a 7-digited prime number, Only possible values are 23,37,53,73,97.
Bablu is an alternator.
Babila is neither truthteller nor alternator. So Babila can be either Liar/None.
Reena can be liar/Alternator/truthteller/none
Bablu's car price is not 7300000.
Bablu's first statement is true So if he is alternator the sequence of statements (T, F, T, F)
Bablu's car price can be 23/37/53.
Veena owns a blue coloured car which can be priced 37/53/73.
From Bablu's 4th statement, Reena cannot be a liar.
Since there has to be atleast one liar among them, Babila is the liar.
Let's consider Babila's statements.
2^{nd}2
n
d
statement says Veena +Babila cars prices sums to 76 which is not possible.
Hence our initial consideration that Veena is truthteller is false.
Case 3:Lets consider Babila as truthteller.
Babila owns a red coloured car of price 23000000
Veena is an alternator who owns a car priced 53000000
If Veena is an alternator and her 1^{st}1
s
t
statement is true so the sequence should be (T, F, T, F)
3^{rd}3
r
d
statement says Babila is neither truthteller nor alternator which contradicts our assumption.
Case 4: Bablu is truthteller.
Bablu's car price is 7300000
Veena owns a Blue coloured car whose price may be 37/53 lakhs.
Reena is a liar.
From Reena's 1st statement, Veena's car price is 53 lakh.
Bablu's car is either Blue or black. Since Veena owns a Blue car, Bablu's car is Black.
Babila owns Violet coloured car. Reena owns Red coloured car.
Since Veena's first statement is true, the second statement is false, and the fourth statement is false Veena
Veena can be an alternator or none.
If Veena is an alternator.
Babila is None among them, i.e. her statements can be any order.
The following cases are possible.
Since Babila's first statement is false fourth statement is true.
So second third statements can be either (FT),(FF),(TT)
when Second, third statements are F, T
when Second third statements are F,F
When second,third statements are TT
~Renault means, Reena doesnt own renault.
When Veena is None, and Babila is an alternator.
Babila cannot be an alternator because her fourth statement is False, which means her first statement should be true but which is false.
Hence contradictory.
If the number of true statements of Babila is not equal to any other person. Then Babila can either speak 1 True statement or 3 True statements.
Hence only Case 2 and Case 3 are feasible cases.In these cases Bablu can either own BMW or Bentley or Volvo.
Hence Renault cannot be owned by Bablu
correct answer:-
2
Instruction for set :
Four friends Veena, Reena, Bablu and Babila, met after a very long time and told each other about the cars owned by them. They made four statements each regarding the color, cost and brand of the car owned by each of them. It is known that atleast one among them is truthteller who always speaks the truth, a liar who always lies and an alternator who alternates between truth and a lie starting with either truth or a lie. Note that a friend can be none of these 3 and can say lie or truth in any order.
Each of them owns exactly one of the car brands among Renault, Volvo, BMW or Bentley. The colors of the cars are black, blue, red, violet such that no two cars are of the same colour.
Reena:
1: Veena's car is 37 lakhs.
2: Colour of Bablu's car is neither Black nor blue.
3: Babila owns a red coloured car.
4: Bablu is a liar.
Bablu:
1: Only one among us has the same first letter of the colour of the car, the car brand and the name of the person who owns that car.
2: I own the most expensive car.
3: Blue coloured car is owned by Veena, which is not the cheapest.
4: Reena is a liar.
Veena:
1: When the price of any car is divided by 1 lakh, the digits are prime numbers when considered individually or together.
2: Bablu is an alternator.
3: Babila is neither truthteller nor alternator.
4: The price of Babila's car is 73 lakh.
Babila:
1: I own a red coloured car whose price is 23 lakh.
2: Sum of the price of my car and Veena's car is not 76 lakh.
3: The person whose first letter in their name, the car bran and the colour of their car is same is Bablu.
4: Veena is an alternator.
It is known that exactly one among them had the same starting letter in their name, car brand and the car colour.
The prices of the four cars are 23 lakhs, 37 lakhs, 53 lakhs and 73 lakhs in some order.
Question 10
If all the attributes of at least one person Car brand, Car Cost, Car colour, and the kind of person (Truth teller, Liar, Alternator or none) can be exactly found. Who owns Renault ?
Show Answer
Solution
Case 1:Let us consider Reena as Truthteller
Bibila's car is Red coloured.
Bablu's car is neither Black nor Blue: Red /Violet
Since Red is Babila's car, Bablu's car is violet coloured
Reena and Veena will own Black/Blue coloured car in any order, which will negate the condition that for one among them the colour of the car, brand and name starts with the same letter.
Case 2:Let us consider Veena as Truthteller
When the prices are divided by 100000, possible values 2,3,5,7, and since the prices are a 7-digited prime number, Only possible values are 23,37,53,73,97.
Bablu is an alternator.
Babila is neither truthteller nor alternator. So Babila can be either Liar/None.
Reena can be liar/Alternator/truthteller/none
Bablu's car price is not 7300000.
Bablu's first statement is true So if he is alternator the sequence of statements (T, F, T, F)
Bablu's car price can be 23/37/53.
Veena owns a blue coloured car which can be priced 37/53/73.
From Bablu's 4th statement, Reena cannot be a liar.
Since there has to be atleast one liar among them, Babila is the liar.
Let's consider Babila's statements.
2^{nd}2
n
d
statement says Veena +Babila cars prices sums to 76 which is not possible.
Hence our initial consideration that Veena is truthteller is false.
Case 3:Lets consider Babila as truthteller.
Babila owns a red coloured car of price 23000000
Veena is an alternator who owns a car priced 53000000
If Veena is an alternator and her 1^{st}1
s
t
statement is true so the sequence should be (T, F, T, F)
3^{rd}3
r
d
statement says Babila is neither truthteller nor alternator which contradicts our assumption.
Case 4: Bablu is truthteller.
Bablu's car price is 7300000
Veena owns a Blue coloured car whose price may be 37/53 lakhs.
Reena is a liar.
From Reena's 1st statement, Veena's car price is 53 lakh.
Bablu's car is either Blue or black. Since Veena owns a Blue car, Bablu's car is Black.
Babila owns Violet coloured car. Reena owns Red coloured car.
Since Veena's first statement is true, the second statement is false, and the fourth statement is false Veena
Veena can be an alternator or none.
If Veena is an alternator.
Babila is None among them, i.e. her statements can be any order.
The following cases are possible.
Since Babila's first statement is false fourth statement is true.
So second third statements can be either (FT),(FF),(TT)
when Second, third statements are F, T
when Second third statements are F,F
When second,third statements are TT
~Renault means, Reena doesnt own renault.
When Veena is None, and Babila is an alternator.
Babila cannot be an alternator because her fourth statement is False, which means her first statement should be true but which is false.
Hence contradictory.
All the attributes for at least one person can be found if the second and the third statements of Babila are false which is the second case.
In this case Reena owns the Renault car.
correct answer:-
1
Instruction for set :
Read the below information carefully and answer the following questions.
There are 100 students in a class. Each of the students has to opt for one or more of the three specializations among Finance, Operations and Marketing. The number of students who opted for Marketing is more than the number of students who opted for Finance which is more than the number of students who opted for Operations which is more than the number of students who opted for exactly two of the three specializations which is more than the number of students who opted for all three specializations. At least one student opted for all three specializations.
Question 11
What is the maximum number of students who opted for Operations as a specialization?
Show Answer
Solution
It is known that the total number of students is 100. We also know that the number of students who opted for Marketing is more than the number of students who opted for Finance which is more than the number of students who opted for Operations.
To maximize the number of students who opted for Operations we have to maximize the number of students who study two specializations and three specializations.
This can be done by assigning 49 students to those who have opted for all three specializations and 51 students to those who have opted exactly two specializations. The 51 students have to be divided among Marketing, Finance and Operations as equally as possible which is as shown in the Venn diagram below.
Thus, the maximum number of students who opted for Operations as a specialization = 16+17+49 = 82
correct answer:-
82
Instruction for set :
Read the below information carefully and answer the following questions.
There are 100 students in a class. Each of the students has to opt for one or more of the three specializations among Finance, Operations and Marketing. The number of students who opted for Marketing is more than the number of students who opted for Finance which is more than the number of students who opted for Operations which is more than the number of students who opted for exactly two of the three specializations which is more than the number of students who opted for all three specializations. At least one student opted for all three specializations.
Question 12
What is the minimum number of students who opted for Marketing?
Show Answer
Solution
It is known that the total number of students is 100. We also know that the number of students who opted for Marketing is more than the number of students who opted for Finance which is more than the number of students who opted for Operations.
To minimize the number of students who opted for Marketing, which is the maximum among all, we have to assign minimum values to those who study all three and exactly two specializations and distribute the remaining in all three as equally as possible as shown in the Venn diagram below.
Thus, the minimum number of students who opted for Marketing = 33+2+1 = 36
correct answer:-
36
Instruction for set :
Read the below information carefully and answer the following questions.
There are 100 students in a class. Each of the students has to opt for one or more of the three specializations among Finance, Operations and Marketing. The number of students who opted for Marketing is more than the number of students who opted for Finance which is more than the number of students who opted for Operations which is more than the number of students who opted for exactly two of the three specializations which is more than the number of students who opted for all three specializations. At least one student opted for all three specializations.
Question 13
What is the maximum number of students who opted for only Finance?
Show Answer
Solution
It is known that the total number of students is 100. We also know that the number of students who opted for Marketing is more than the number of students who opted for Finance which is more than the number of students who opted for Operations.
The number of students who study study only finance cannot be 50. This is because in that case the number of people in only finance is 50 then there will be at least 51 people in finance (At least one person opted for all 3). Thus, marketing cannot be greater than finance in that case. Now let us consider the number of students in finance to be 49. In this case we can arrange the other people as shown in the venn diagram. None of the given condition is violated in the given diagram. Hence, at max 49 people can opt for only finance.
Thus, the maximum number of students who opted for only Finance is 49
correct answer:-
49
Instruction for set :
Read the below information carefully and answer the following questions.
There are 100 students in a class. Each of the students has to opt for one or more of the three specializations among Finance, Operations and Marketing. The number of students who opted for Marketing is more than the number of students who opted for Finance which is more than the number of students who opted for Operations which is more than the number of students who opted for exactly two of the three specializations which is more than the number of students who opted for all three specializations. At least one student opted for all three specializations.
Question 14
What is the maximum number of students who opted for Finance and Operations but not Marketing?
Show Answer
Solution
It is known that the total number of students is 100. We also know that the number of students who opted for Marketing is more than the number of students who opted for Finance which is more than the number of students who opted for Operations.
We have to maximize the number of students who chose both Finance and Operations as their specialization. We know that the number of students who chose Marketing will be greater than the number of students who opted for Finance and Operations as their specialization. This can be done as shown in the following Venn diagram.
Thus, the maximum number of students who opted for Finance and Operations but not Marketing = 48
correct answer:-
48
Instruction for set :
Faculty members in a management school can belong to one of four departments - Finance and Accounting (F&A;), Marketing and Strategy (M&S;), Operations and Quants (O&Q;) and Behaviour and Human Resources (B&H;). The numbers of faculty members in F&A;, M&S;, O&Q; and B&H; departments are 9, 7, 5 and 3 respectively.
Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q.;
Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below.
1. There cannot be more than two candidates from a single department.
2. A candidate cannot vote for himself/herself.
3. Faculty members cannot vote for a candidate from their own department.
After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi.
Question 15
Which two candidates can belong to the same department?
Faculty members in a management school can belong to one of four departments - Finance and Accounting (F&A;), Marketing and Strategy (M&S;), Operations and Quants (O&Q;) and Behaviour and Human Resources (B&H;). The numbers of faculty members in F&A;, M&S;, O&Q; and B&H; departments are 9, 7, 5 and 3 respectively.
Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q.;
Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below.
1. There cannot be more than two candidates from a single department.
2. A candidate cannot vote for himself/herself.
3. Faculty members cannot vote for a candidate from their own department.
After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi.
Question 16
Which of the following can be the number of votes that Prof. Qureshi received from a single department?
Faculty members in a management school can belong to one of four departments - Finance and Accounting (F&A;), Marketing and Strategy (M&S;), Operations and Quants (O&Q;) and Behaviour and Human Resources (B&H;). The numbers of faculty members in F&A;, M&S;, O&Q; and B&H; departments are 9, 7, 5 and 3 respectively.
Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q.;
Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below.
1. There cannot be more than two candidates from a single department.
2. A candidate cannot vote for himself/herself.
3. Faculty members cannot vote for a candidate from their own department.
After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi.
Question 17
If Prof. Samuel belongs to B&H;, which of the following statements is/are true?
Statement A: Prof. Pakrasi belongs to M&S.;
Statement B: Prof. Ramaswamy belongs to O&Q;
Faculty members in a management school can belong to one of four departments - Finance and Accounting (F&A;), Marketing and Strategy (M&S;), Operations and Quants (O&Q;) and Behaviour and Human Resources (B&H;). The numbers of faculty members in F&A;, M&S;, O&Q; and B&H; departments are 9, 7, 5 and 3 respectively.
Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q.;
Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below.
1. There cannot be more than two candidates from a single department.
2. A candidate cannot vote for himself/herself.
3. Faculty members cannot vote for a candidate from their own department.
After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi.
Question 18
What best can be concluded about the candidate from O&Q;?
Faculty members in a management school can belong to one of four departments - Finance and Accounting (F&A;), Marketing and Strategy (M&S;), Operations and Quants (O&Q;) and Behaviour and Human Resources (B&H;). The numbers of faculty members in F&A;, M&S;, O&Q; and B&H; departments are 9, 7, 5 and 3 respectively.
Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q.;
Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below.
1. There cannot be more than two candidates from a single department.
2. A candidate cannot vote for himself/herself.
3. Faculty members cannot vote for a candidate from their own department.
After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi.
Question 19
Which of the following statements is/are true?
Statement A: Non-candidates from M&S; voted for Prof. Qureshi.
Statement B: Non-candidates from F&A; voted for Prof. Qureshi.
Sassy Eateries is a well-known brunch place in BiIlekahalli. Due to COVID-19 restrictions, they had to limit the number of tables in their restaurant to be 4 with a maximum of 4 people allowed on a table. Menu card for the restaurant had the following information
On a particular day, 6 groups visited between morning shift (9 am to 12 noon). The following things are known about the groups
1. Group I had 3 people. They reached the restaurant at 9:15 and ordered 3 different food items with an overall bill of Rs. 600
2. Group II consisting of 4 people reached the restaurant at 09:30 am and ordered 2 sodas, 1 noodle, and 1 Pizza
3. Group III consisting of 2 people reached the restaurant at 10:00 and ordered a burger and a Pizza
4. Group IV consisting of 3 people ordered a Burger, a Dosa, and a Soda. They reached the restaurant at 10:10 am
5. Group V consisting of 2 people ordered a noodle and a dosa. They reached the restaurant at 10:25 am
6. Group VI consisting of 2 people reached the restaurant at 10:30 am and they were served food at 11:15 am. They had to pay a bill of Rs. 200.
7. Number of food items ordered by a group is equal to the number of members in that group
The following things are known about the restaurant and the management
I) There are 2 cooks who are employed by the management named A and B. A is the only chef who knows how to cook Pizza. The rest of the food items can be made by both the chefs
II) 4 tables are numbered Table 1,2,3 and 4. The lowest-numbered available table has to be occupied first
II) A Chef starts working on new order only after the there are no pending food items on current order. The group which placed an order earlier is given higher priority
II) Chefs work in such a way that the time required to serve the order is minimum.
II) All the food items belonging to the same table are served together. It takes 25 minutes to finish eating after which the group leaves. After that, the waiter takes 10 minutes to sanitize the table and it is ready for occupying
V) There is the negligible time elapsed in entering the restaurant and placing the order.
VI) If all tables are occupied then the group has to wait outside. As soon as any table is available they'll be allowed inside and can place order at that time
Question 20
If one more group reaches the restaurant immediately after Group VI has arrived, when is the earliest the new group can be seated in the restaurant?
Show Answer
Solution
Let us start with group I. Since it is given that there were 3 members, thus 3 food items were ordered totaling the bill of Rs 600. Thus we know pizza, a burger, and a dosa was ordered. SInce chef A can make pizza he will be making Pizza from 09:15 to 09:35(20 minutes). Burger and Pizza both take 15 minutes each. Chef B will start making any one of these from 09:15 to 09:30. And after this, e'll make the last food of the order from 09:30 to 09:45. Thus the food will be served at 09:45. Group will finish eating by 10:10. After sanitising the table will be again available at 10:20. The following can be represented as :
Thus group 2 coming at 09:30 ordered 2 sodas, 1 noodle, and a pizza. Since table 1 is occupied they will sit on table 2. Chef A will start working on their order at 09:35 whereas chef B will start working on the order from 09:45. To ensure the ordered is delivered in least time A will make 2 sodas and pizza.The remaining food item(noodle) will be made by B from 09:45 to 10:05. Thus the order will be served at 10:05. Group will finish eating by 10:30. Table 2 will be available by 10:40. It can be represented as
Group 3 will come at 10:00 and occupy table 3. The chef will start working on their order at 10:05. A will make Pizza and B will make a burger. Both orders will be served at 10:25. They will finish eating in 25 minutes. After which 10 minutes is taken for sanitization. The table will be available at 11:00
Group 4 comes at 10:10. They order 1 burger,1 dosa, and 1 soda. To minimize time soda will be made by chef B. Burger and Dosa both take 15 minutes each and can be made by either of them. One will make dosa and the r will make a burger. Order will be finished and served at 10:40.
Now group 5 came at 10:25. This time table 1 was available and hence will be occupied by them. Both chefs will get free at 10:40 and start cooking for group 5. One chef has to cook noodles which will take 20 minutes and another one will cook dosa which takes 15 minutes. Let us assume that A cooks noodle and B cooks Dosa( this assumption will not affect the solution as only 1 group is left to serve after group 5 and no further orders of Pizza are made)
Group 6 came at 10:30. But table 2 got free at 10:40 at the earliest. Hence they entered the restaurant at 10:40. There we 2 people hence 2 items were ordered worth 200. A possible combination is (burger and soda) or (Dosa and soda) or ( Sandwich and Noodles).
The 2 combinations (burger and soda) or (Dosa and soda) has a cooking time of 15 minutes+5minutes. In this case B will cook for 15 minutes and A will cook for 5 minutes to ensure that the order is made available at the least possible time. In this case, it will be possible at 11:10 am
Combination of sandwich and noodle has a cooking time of 10 minute+20 minutes. B has to cook for 20 minutes and finish by 11:15 whereas A will cook for 10 minutes and finish by 11:10. Thus food will be served at 11:15
In question it was given that the food was served to them at 11:15 hence they ordered a sandwich and a noodle.
We can see that after 10:30 when group 6 occupied table 2, the next table to get free was table 3 at 11:00
Sassy Eateries is a well-known brunch place in BiIlekahalli. Due to COVID-19 restrictions, they had to limit the number of tables in their restaurant to be 4 with a maximum of 4 people allowed on a table. Menu card for the restaurant had the following information
On a particular day, 6 groups visited between morning shift (9 am to 12 noon). The following things are known about the groups
1. Group I had 3 people. They reached the restaurant at 9:15 and ordered 3 different food items with an overall bill of Rs. 600
2. Group II consisting of 4 people reached the restaurant at 09:30 am and ordered 2 sodas, 1 noodle, and 1 Pizza
3. Group III consisting of 2 people reached the restaurant at 10:00 and ordered a burger and a Pizza
4. Group IV consisting of 3 people ordered a Burger, a Dosa, and a Soda. They reached the restaurant at 10:10 am
5. Group V consisting of 2 people ordered a noodle and a dosa. They reached the restaurant at 10:25 am
6. Group VI consisting of 2 people reached the restaurant at 10:30 am and they were served food at 11:15 am. They had to pay a bill of Rs. 200.
7. Number of food items ordered by a group is equal to the number of members in that group
The following things are known about the restaurant and the management
I) There are 2 cooks who are employed by the management named A and B. A is the only chef who knows how to cook Pizza. The rest of the food items can be made by both the chefs
II) 4 tables are numbered Table 1,2,3 and 4. The lowest-numbered available table has to be occupied first
II) A Chef starts working on new order only after the there are no pending food items on current order. The group which placed an order earlier is given higher priority
II) Chefs work in such a way that the time required to serve the order is minimum.
II) All the food items belonging to the same table are served together. It takes 25 minutes to finish eating after which the group leaves. After that, the waiter takes 10 minutes to sanitize the table and it is ready for occupying
V) There is the negligible time elapsed in entering the restaurant and placing the order.
VI) If all tables are occupied then the group has to wait outside. As soon as any table is available they'll be allowed inside and can place order at that time
Question 21
At what time was group VI allowed to enter the restaurant?
Show Answer
Solution
Let us start with group I. Since it is given that there were 3 members, thus 3 food items were ordered totaling the bill of Rs 600. Thus we know pizza, a burger, and a dosa was ordered. SInce chef A can make pizza he will be making Pizza from 09:15 to 09:35(20 minutes). Burger and Pizza both take 15 minutes each. Chef B will start making any one of these from 09:15 to 09:30. And after this, e'll make the last food of the order from 09:30 to 09:45. Thus the food will be served at 09:45. Group will finish eating by 10:10. After sanitising the table will be again available at 10:20. The following can be represented as :
Thus group 2 coming at 09:30 ordered 2 sodas, 1 noodle, and a pizza. Since table 1 is occupied they will sit on table 2. Chef A will start working on their order at 09:35 whereas chef B will start working on the order from 09:45. To ensure the ordered is delivered in least time A will make 2 sodas and pizza.The remaining food item(noodle) will be made by B from 09:45 to 10:05. Thus the order will be served at 10:05. Group will finish eating by 10:30. Table 2 will be available by 10:40. It can be represented as
Group 3 will come at 10:00 and occupy table 3. The chef will start working on their order at 10:05. A will make Pizza and B will make a burger. Both orders will be served at 10:25. They will finish eating in 25 minutes. After which 10 minutes is taken for sanitization. The table will be available at 11:00
Group 4 comes at 10:10. They order 1 burger,1 dosa, and 1 soda. To minimize time soda will be made by chef B. Burger and Dosa both take 15 minutes each and can be made by either of them. One will make dosa and the r will make a burger. Order will be finished and served at 10:40.
Now group 5 came at 10:25. This time table 1 was available and hence will be occupied by them. Both chefs will get free at 10:40 and start cooking for group 5. One chef has to cook noodles which will take 20 minutes and another one will cook dosa which takes 15 minutes. Let us assume that A cooks noodle and B cooks Dosa( this assumption will not affect the solution as only 1 group is left to serve after group 5 and no further orders of Pizza are made)
Group 6 came at 10:30. But table 2 got free at 10:40 at the earliest. Hence they entered the restaurant at 10:40. There we 2 people hence 2 items were ordered worth 200. A possible combination is (burger and soda) or (Dosa and soda) or ( Sandwich and Noodles).
The 2 combinations (burger and soda) or (Dosa and soda) has a cooking time of 15 minutes+5minutes. In this case B will cook for 15 minutes and A will cook for 5 minutes to ensure that the order is made available at the least possible time. In this case, it will be possible at 11:10 am
Combination of sandwich and noodle has a cooking time of 10 minute+20 minutes. B has to cook for 20 minutes and finish by 11:15 whereas A will cook for 10 minutes and finish by 11:10. Thus food will be served at 11:15
In question it was given that the food was served to them at 11:15 hence they ordered a sandwich and a noodle.
Group 6 was allowed to enter at 10:40
correct answer:-
4
Instruction for set :
Sassy Eateries is a well-known brunch place in BiIlekahalli. Due to COVID-19 restrictions, they had to limit the number of tables in their restaurant to be 4 with a maximum of 4 people allowed on a table. Menu card for the restaurant had the following information
On a particular day, 6 groups visited between morning shift (9 am to 12 noon). The following things are known about the groups
1. Group I had 3 people. They reached the restaurant at 9:15 and ordered 3 different food items with an overall bill of Rs. 600
2. Group II consisting of 4 people reached the restaurant at 09:30 am and ordered 2 sodas, 1 noodle, and 1 Pizza
3. Group III consisting of 2 people reached the restaurant at 10:00 and ordered a burger and a Pizza
4. Group IV consisting of 3 people ordered a Burger, a Dosa, and a Soda. They reached the restaurant at 10:10 am
5. Group V consisting of 2 people ordered a noodle and a dosa. They reached the restaurant at 10:25 am
6. Group VI consisting of 2 people reached the restaurant at 10:30 am and they were served food at 11:15 am. They had to pay a bill of Rs. 200.
7. Number of food items ordered by a group is equal to the number of members in that group
The following things are known about the restaurant and the management
I) There are 2 cooks who are employed by the management named A and B. A is the only chef who knows how to cook Pizza. The rest of the food items can be made by both the chefs
II) 4 tables are numbered Table 1,2,3 and 4. The lowest-numbered available table has to be occupied first
II) A Chef starts working on new order only after the there are no pending food items on current order. The group which placed an order earlier is given higher priority
II) Chefs work in such a way that the time required to serve the order is minimum.
II) All the food items belonging to the same table are served together. It takes 25 minutes to finish eating after which the group leaves. After that, the waiter takes 10 minutes to sanitize the table and it is ready for occupying
V) There is the negligible time elapsed in entering the restaurant and placing the order.
VI) If all tables are occupied then the group has to wait outside. As soon as any table is available they'll be allowed inside and can place order at that time
Question 22
Order for Group III was served at what time?
Show Answer
Solution
Let us start with group I. Since it is given that there were 3 members, thus 3 food items were ordered totaling the bill of Rs 600. Thus we know pizza, a burger, and a dosa was ordered. SInce chef A can make pizza he will be making Pizza from 09:15 to 09:35(20 minutes). Burger and Pizza both take 15 minutes each. Chef B will start making any one of these from 09:15 to 09:30. And after this, e'll make the last food of the order from 09:30 to 09:45. Thus the food will be served at 09:45. Group will finish eating by 10:10. After sanitising the table will be again available at 10:20. The following can be represented as :
Thus group 2 coming at 09:30 ordered 2 sodas, 1 noodle, and a pizza. Since table 1 is occupied they will sit on table 2. Chef A will start working on their order at 09:35 whereas chef B will start working on the order from 09:45. To ensure the ordered is delivered in least time A will make 2 sodas and pizza.The remaining food item(noodle) will be made by B from 09:45 to 10:05. Thus the order will be served at 10:05. Group will finish eating by 10:30. Table 2 will be available by 10:40. It can be represented as
Group 3 will come at 10:00 and occupy table 3. The chef will start working on their order at 10:05. A will make Pizza and B will make a burger. Both orders will be served at 10:25. They will finish eating in 25 minutes. After which 10 minutes is taken for sanitization. The table will be available at 11:00
Order for Group III was served at 10:25
correct answer:-
2
Instruction for set :
Sassy Eateries is a well-known brunch place in BiIlekahalli. Due to COVID-19 restrictions, they had to limit the number of tables in their restaurant to be 4 with a maximum of 4 people allowed on a table. Menu card for the restaurant had the following information
On a particular day, 6 groups visited between morning shift (9 am to 12 noon). The following things are known about the groups
1. Group I had 3 people. They reached the restaurant at 9:15 and ordered 3 different food items with an overall bill of Rs. 600
2. Group II consisting of 4 people reached the restaurant at 09:30 am and ordered 2 sodas, 1 noodle, and 1 Pizza
3. Group III consisting of 2 people reached the restaurant at 10:00 and ordered a burger and a Pizza
4. Group IV consisting of 3 people ordered a Burger, a Dosa, and a Soda. They reached the restaurant at 10:10 am
5. Group V consisting of 2 people ordered a noodle and a dosa. They reached the restaurant at 10:25 am
6. Group VI consisting of 2 people reached the restaurant at 10:30 am and they were served food at 11:15 am. They had to pay a bill of Rs. 200.
7. Number of food items ordered by a group is equal to the number of members in that group
The following things are known about the restaurant and the management
I) There are 2 cooks who are employed by the management named A and B. A is the only chef who knows how to cook Pizza. The rest of the food items can be made by both the chefs
II) 4 tables are numbered Table 1,2,3 and 4. The lowest-numbered available table has to be occupied first
II) A Chef starts working on new order only after the there are no pending food items on current order. The group which placed an order earlier is given higher priority
II) Chefs work in such a way that the time required to serve the order is minimum.
II) All the food items belonging to the same table are served together. It takes 25 minutes to finish eating after which the group leaves. After that, the waiter takes 10 minutes to sanitize the table and it is ready for occupying
V) There is the negligible time elapsed in entering the restaurant and placing the order.
VI) If all tables are occupied then the group has to wait outside. As soon as any table is available they'll be allowed inside and can place order at that time
Question 23
What is the number of food items which were cooked by chef B for group II?
Show Answer
Solution
Let us start with group I. Since it is given that there were 3 members, thus 3 food items were ordered totaling the bill of Rs 600. Thus we know pizza, a burger, and a dosa was ordered. SInce chef A can make pizza he will be making Pizza from 09:15 to 09:35(20 minutes). Burger and Pizza both take 15 minutes each. Chef B will start making any one of these from 09:15 to 09:30. And after this, e'll make the last food of the order from 09:30 to 09:45. Thus the food will be served at 09:45. Group will finish eating by 10:10. After sanitising the table will be again available at 10:20. The following can be represented as :
Thus group 2 coming at 09:30 ordered 2 sodas, 1 noodle, and a pizza. Since table 1 is occupied they will sit on table 2. Chef A will start working on their order at 09:35 whereas chef B will start working on the order from 09:45. To ensure the ordered is delivered in least time A will make 2 sodas and pizza.The remaining food item(noodle) will be made by B from 09:45 to 10:05. Thus the order will be served at 10:05. Group will finish eating by 10:30. Table 2 will be available by 10:40. It can be represented as
Chef B cooked 1 item for Group 2
correct answer:-
1
Instruction for set :
Sassy Eateries is a well-known brunch place in BiIlekahalli. Due to COVID-19 restrictions, they had to limit the number of tables in their restaurant to be 4 with a maximum of 4 people allowed on a table. Menu card for the restaurant had the following information
On a particular day, 6 groups visited between morning shift (9 am to 12 noon). The following things are known about the groups
1. Group I had 3 people. They reached the restaurant at 9:15 and ordered 3 different food items with an overall bill of Rs. 600
2. Group II consisting of 4 people reached the restaurant at 09:30 am and ordered 2 sodas, 1 noodle, and 1 Pizza
3. Group III consisting of 2 people reached the restaurant at 10:00 and ordered a burger and a Pizza
4. Group IV consisting of 3 people ordered a Burger, a Dosa, and a Soda. They reached the restaurant at 10:10 am
5. Group V consisting of 2 people ordered a noodle and a dosa. They reached the restaurant at 10:25 am
6. Group VI consisting of 2 people reached the restaurant at 10:30 am and they were served food at 11:15 am. They had to pay a bill of Rs. 200.
7. Number of food items ordered by a group is equal to the number of members in that group
The following things are known about the restaurant and the management
I) There are 2 cooks who are employed by the management named A and B. A is the only chef who knows how to cook Pizza. The rest of the food items can be made by both the chefs
II) 4 tables are numbered Table 1,2,3 and 4. The lowest-numbered available table has to be occupied first
II) A Chef starts working on new order only after the there are no pending food items on current order. The group which placed an order earlier is given higher priority
II) Chefs work in such a way that the time required to serve the order is minimum.
II) All the food items belonging to the same table are served together. It takes 25 minutes to finish eating after which the group leaves. After that, the waiter takes 10 minutes to sanitize the table and it is ready for occupying
V) There is the negligible time elapsed in entering the restaurant and placing the order.
VI) If all tables are occupied then the group has to wait outside. As soon as any table is available they'll be allowed inside and can place order at that time
Question 24
At what time will Table II be available for use again?
Show Answer
Solution
Let us start with group I. Since it is given that there were 3 members, thus 3 food items were ordered totaling the bill of Rs 600. Thus we know pizza, a burger, and a dosa was ordered. SInce chef A can make pizza he will be making Pizza from 09:15 to 09:35(20 minutes). Burger and Pizza both take 15 minutes each. Chef B will start making any one of these from 09:15 to 09:30. And after this, e'll make the last food of the order from 09:30 to 09:45. Thus the food will be served at 09:45. Group will finish eating by 10:10. After sanitising the table will be again available at 10:20. The following can be represented as :
Thus group 2 coming at 09:30 ordered 2 sodas, 1 noodle, and a pizza. Since table 1 is occupied they will sit on table 2. Chef A will start working on their order at 09:35 whereas chef B will start working on the order from 09:45. To ensure the ordered is delivered in least time A will make 2 sodas and pizza.The remaining food item(noodle) will be made by B from 09:45 to 10:05. Thus the order will be served at 10:05. Group will finish eating by 10:30. Table 2 will be available by 10:40. It can be represented as
Group 3 will come at 10:00 and occupy table 3. The chef will start working on their order at 10:05. A will make Pizza and B will make a burger. Both orders will be served at 10:25. They will finish eating in 25 minutes. After which 10 minutes is taken for sanitization. The table will be available at 11:00
Group 4 comes at 10:10. They order 1 burger,1 dosa, and 1 soda. To minimize time soda will be made by chef B. Burger and Dosa both take 15 minutes each and can be made by either of them. One will make dosa and the r will make a burger. Order will be finished and served at 10:40.
Now group 5 came at 10:25. This time table 1 was available and hence will be occupied by them. Both chefs will get free at 10:40 and start cooking for group 5. One chef has to cook noodles which will take 20 minutes and another one will cook dosa which takes 15 minutes. Let us assume that A cooks noodle and B cooks Dosa( this assumption will not affect the solution as only 1 group is left to serve after group 5 and no further orders of Pizza are made)
Group 6 came at 10:30. But table 2 got free at 10:40 at the earliest. Hence they entered the restaurant at 10:40. There we 2 people hence 2 items were ordered worth 200. A possible combination is (burger and soda) or (Dosa and soda) or ( Sandwich and Noodles).
The 2 combinations (burger and soda) or (Dosa and soda) has a cooking time of 15 minutes+5minutes. In this case B will cook for 15 minutes and A will cook for 5 minutes to ensure that the order is made available at the least possible time. In this case, it will be possible at 11:10 am
Combination of sandwich and noodle has a cooking time of 10 minute+20 minutes. B has to cook for 20 minutes and finish by 11:15 whereas A will cook for 10 minutes and finish by 11:10. Thus food will be served at 11:15
In question it was given that the food was served to them at 11:15 hence they ordered a sandwich and a noodle.
We can see that table 2 got free at 11:50
correct answer:-
4
Instruction for set :
Sassy Eateries is a well-known brunch place in BiIlekahalli. Due to COVID-19 restrictions, they had to limit the number of tables in their restaurant to be 4 with a maximum of 4 people allowed on a table. Menu card for the restaurant had the following information
On a particular day, 6 groups visited between morning shift (9 am to 12 noon). The following things are known about the groups
1. Group I had 3 people. They reached the restaurant at 9:15 and ordered 3 different food items with an overall bill of Rs. 600
2. Group II consisting of 4 people reached the restaurant at 09:30 am and ordered 2 sodas, 1 noodle, and 1 Pizza
3. Group III consisting of 2 people reached the restaurant at 10:00 and ordered a burger and a Pizza
4. Group IV consisting of 3 people ordered a Burger, a Dosa, and a Soda. They reached the restaurant at 10:10 am
5. Group V consisting of 2 people ordered a noodle and a dosa. They reached the restaurant at 10:25 am
6. Group VI consisting of 2 people reached the restaurant at 10:30 am and they were served food at 11:15 am. They had to pay a bill of Rs. 200.
7. Number of food items ordered by a group is equal to the number of members in that group
The following things are known about the restaurant and the management
I) There are 2 cooks who are employed by the management named A and B. A is the only chef who knows how to cook Pizza. The rest of the food items can be made by both the chefs
II) 4 tables are numbered Table 1,2,3 and 4. The lowest-numbered available table has to be occupied first
II) A Chef starts working on new order only after the there are no pending food items on current order. The group which placed an order earlier is given higher priority
II) Chefs work in such a way that the time required to serve the order is minimum.
II) All the food items belonging to the same table are served together. It takes 25 minutes to finish eating after which the group leaves. After that, the waiter takes 10 minutes to sanitize the table and it is ready for occupying
V) There is the negligible time elapsed in entering the restaurant and placing the order.
VI) If all tables are occupied then the group has to wait outside. As soon as any table is available they'll be allowed inside and can place order at that time
Question 25
For how many minutes was the table I occupied from 9 am to 12 noon?
Show Answer
Solution
Let us start with group I. Since it is given that there were 3 members, thus 3 food items were ordered totaling the bill of Rs 600. Thus we know pizza, a burger, and a dosa was ordered. SInce chef A can make pizza he will be making Pizza from 09:15 to 09:35(20 minutes). Burger and Pizza both take 15 minutes each. Chef B will start making any one of these from 09:15 to 09:30. And after this, e'll make the last food of the order from 09:30 to 09:45. Thus the food will be served at 09:45. Group will finish eating by 10:10. After sanitising the table will be again available at 10:20. The following can be represented as :
Thus group 2 coming at 09:30 ordered 2 sodas, 1 noodle, and a pizza. Since table 1 is occupied they will sit on table 2. Chef A will start working on their order at 09:35 whereas chef B will start working on the order from 09:45. To ensure the ordered is delivered in least time A will make 2 sodas and pizza.The remaining food item(noodle) will be made by B from 09:45 to 10:05. Thus the order will be served at 10:05. Group will finish eating by 10:30. Table 2 will be available by 10:40. It can be represented as
Group 3 will come at 10:00 and occupy table 3. The chef will start working on their order at 10:05. A will make Pizza and B will make a burger. Both orders will be served at 10:25. They will finish eating in 25 minutes. After which 10 minutes is taken for sanitization. The table will be available at 11:00
Group 4 comes at 10:10. They order 1 burger,1 dosa, and 1 soda. To minimize time soda will be made by chef B. Burger and Dosa both take 15 minutes each and can be made by either of them. One will make dosa and the r will make a burger. Order will be finished and served at 10:40.
Now group 5 came at 10:25. This time table 1 was available and hence will be occupied by them. Both chefs will get free at 10:40 and start cooking for group 5. One chef has to cook noodles which will take 20 minutes and another one will cook dosa which takes 15 minutes. Let us assume that A cooks noodle and B cooks Dosa( this assumption will not affect the solution as only 1 group is left to serve after group 5 and no further orders of Pizza are made)
Group 6 came at 10:30. But table 2 got free at 10:40 at the earliest. Hence they entered the restaurant at 10:40. There we 2 people hence 2 items were ordered worth 200. A possible combination is (burger and soda) or (Dosa and soda) or ( Sandwich and Noodles).
The 2 combinations (burger and soda) or (Dosa and soda) has a cooking time of 15 minutes+5minutes. In this case B will cook for 15 minutes and A will cook for 5 minutes to ensure that the order is made available at the least possible time. In this case, it will be possible at 11:10 am
Combination of sandwich and noodle has a cooking time of 10 minute+20 minutes. B has to cook for 20 minutes and finish by 11:15 whereas A will cook for 10 minutes and finish by 11:10. Thus food will be served at 11:15
In question it was given that the food was served to them at 11:15 hence they ordered a sandwich and a noodle.
We can see that after 10:30 when group 6 occupied table 2, the next table to get free was table 3 at 11:00
Table 1 was occupied from 09:15 to 10:20 and 10:25 to 11:35. The total time it was occupied was 65+70 = 135 minutes
correct answer:-
135
Instruction for set :
Eight delegates namely - Yameen, Irfan, Sirisena, Ashraf, Malcolm, Jacinda, Prayut and Widodo participated in a conference held in New York City. Each of the delegates belongs to a different nation among Australia, Pakistan, Afghanistan, Maldives, Sri Lanka, New Zealand, Indonesia and Thailand not necessarily in the same order. The per capita income (PCI) of the aforementioned nations is in an arithmetic progression. The delegates are seated around a round table and the number of delegates who are facing away from the centre is the same as the number of delegates facing towards the centre. Further additional information is given that -
1. The minimum PCI and maximum PCI are USD 7500 and USD 18000 respectively.
2. Ashraf, who is facing towards the centre and doesn't belong to the nation with the least PCI, is not an immediate neighbour of Jacinda and Sirisena.
3. Jacinda is not seated opposite to Sirisena.
4. The delegates from Afghanistan and Australia are facing towards each other, and the delegate from Pakistan is sitting to the immediate left of the delegate from Afghanistan.
5. Sirisena, who is facing outside, is sitting third to the right of the delegate from New Zealand.
6. Yameen's country PCI is equal to the sum of the PCI of his immediate neighbours.
7. Malcolm, who is facing outside, is an immediate neighbour of Irfan and Prayut.
8. Jacinda, who belongs to the nation with maximum PCI, is facing towards the centre. He is sitting second to the left of Malcolm, who is from Indonesia.
9. Irfan and Prayut belong to the nations whose PCI are USD 10500 and USD 12000, not necessarily in the same order.
10. New Zealand's PCI is greater than USD 9000. Neither Irfan nor Prayut is from New Zealand. Jacinda is not from New Zealand.
Question 26
Sirisena is definitely seated _____ ?
Show Answer
Solution
Let us draw a circular arrangement diagram with 8 spot numbered from 1 to 8.
It is given that the minimum PCI and maximum PCI are USD 7500 and USD 18000 respectively. Also, the PCI are in an arithmetic progression.
Hence, we can say that a = 7500, a+7d = 18000 => d = 1500
Therefore, the PCI of the eight nations are USD 7500, USD 9000, USD 10500, USD 12000, USD 13500, USD 15000 ,USD 16500 and USD 18000 in ascending order.
In statement 4, it is given that Sirisena, who is facing outside, is sitting third to the right of the delegate from New Zealand.
Let us assume that Sirisena is seated on 1st spot then we can say that the delegate from New Zealand is seated at either 4th or 6th spot.
Case 1:
When the delegate from New Zealand is seated on 4th spot.
It is given in statement 10 that Neither Irfan nor Prayut are from New Zealand. Also we know that Malcolm is sitting in between Irfan and Prayut Hence Malcolm should have 1 space vacant on both sides. Hence Malcolm can sit either at 6th or 7th spot. If Malcolm sits on 6th spot then Jacinda has to sit on 4th position. While it is given that Jacinda is not from New Zealand. Hence, we can say that Malcolm can't sit on 6th spot.
If Malcolm sits on 7th position then Jacinda will have to sit opposite to Sirisena whereas it is given that Sirisena and Jacinda are not seated opposite to each other. Hence, we can say that Malcolm can't sit on 7th spot.
Hence, we can say that the delegate from New Zealand is not seated on 4th spot.
Case 2:
When the delegate from New Zealand is seated on 6th spot.
Irfan and Prayut belong to the nations whose PCI are USD 10500 and USD 12000. Neither Irfan nor Prayut is from New Zealand. Hence, we can say that New Zealands's PCI can't be either USD 10500 or USD 12000.
In statement (6), it is given that Malcolm, who is facing outside, is an immediate neighbour of Irfan and Prayut.
Hence, we can say that Malcolm can be seated on any of 3rd, 4th and 6th spot.
If Malcolm is seated on 3rd spot then Jacinda should occupy 1st spot which is not vacant. Hence, we can say that Malcolm can't occupy 3rd spot.
If Malcolm is seated on 6th spot then Jacinda will occupy 4th spot. But in this case Ashraf has to sit on any one of 8th, 2nd and 3rd seat. In this case Ashraf has to be a neighbor of either Jacinda and Sirisena which contradicts to the information given in statement 2. Hence, we can say that Malcolm can't occupy 6th spot as well.
Therefore, we can say that Malcolm occupies 4th spot. Consequently, Jacinda sits on 2nd spot. Also, Irfan and Prayut can occupy 3rd and 4th spot in any order.
The delegates from Afghanistan and Australia are facing towards each other, and the delegate from Pakistan is sitting to the immediate left of the delegate from Afghanistan.
We can say that the delegates from Afghanistan and Australia are facing towards centre. That's only possible when they are seated at 3rd and 7th spot. Also, the delegate from Pakistan is sitting to the immediate left of the delegate from Afghanistan. This is possible only when the delegate from Afghanistan occupies 7th spot. Consequently, the delegates from Pakistan and Australia will occupy 8th and 3rd spot respectively.
Yameen's country PCI is equal to the sum of the PCI of his immediate neighbours. This is only possible when his neigbour's PCI are USD 7500 and 9000 in any order. Therefore, Yameen can occupy only 8th spot.
It is given that Ashraf is facing towards the centre and is not an immediate neighbour of Jacinda and Sirisena. Therefore, we can say that Ashraf is from Afghanistan and occupies 7th spot. Consequently, Widodo will occupy 6th spot.
Also, it is given that Ashraf doesn't belong to the nation with the least PCI. Hence, we can say that Sirisena belongs to the nation with the PCI USD 7500. Consequently, we can say that Afghanistan's PCI is 9000 USD. The PCI of New Zealand and Indonesia are USD 13500 and USD 15000 in any order.
From the arrangement, we can see that Sirisena is seated 3rd to the right of Widodo. Hence, option B is the correct answer.
correct answer:-
2
Instruction for set :
Eight delegates namely - Yameen, Irfan, Sirisena, Ashraf, Malcolm, Jacinda, Prayut and Widodo participated in a conference held in New York City. Each of the delegates belongs to a different nation among Australia, Pakistan, Afghanistan, Maldives, Sri Lanka, New Zealand, Indonesia and Thailand not necessarily in the same order. The per capita income (PCI) of the aforementioned nations is in an arithmetic progression. The delegates are seated around a round table and the number of delegates who are facing away from the centre is the same as the number of delegates facing towards the centre. Further additional information is given that -
1. The minimum PCI and maximum PCI are USD 7500 and USD 18000 respectively.
2. Ashraf, who is facing towards the centre and doesn't belong to the nation with the least PCI, is not an immediate neighbour of Jacinda and Sirisena.
3. Jacinda is not seated opposite to Sirisena.
4. The delegates from Afghanistan and Australia are facing towards each other, and the delegate from Pakistan is sitting to the immediate left of the delegate from Afghanistan.
5. Sirisena, who is facing outside, is sitting third to the right of the delegate from New Zealand.
6. Yameen's country PCI is equal to the sum of the PCI of his immediate neighbours.
7. Malcolm, who is facing outside, is an immediate neighbour of Irfan and Prayut.
8. Jacinda, who belongs to the nation with maximum PCI, is facing towards the centre. He is sitting second to the left of Malcolm, who is from Indonesia.
9. Irfan and Prayut belong to the nations whose PCI are USD 10500 and USD 12000, not necessarily in the same order.
10. New Zealand's PCI is greater than USD 9000. Neither Irfan nor Prayut is from New Zealand. Jacinda is not from New Zealand.
Question 27
Who is from Pakistan?
Show Answer
Solution
Let us draw a circular arrangement diagram with 8 spot numbered from 1 to 8.
It is given that the minimum PCI and maximum PCI are USD 7500 and USD 18000 respectively. Also, the PCI are in an arithmetic progression.
Hence, we can say that a = 7500, a+7d = 18000 => d = 1500
Therefore, the PCI of the eight nations are USD 7500, USD 9000, USD 10500, USD 12000, USD 13500, USD 15000 ,USD 16500 and USD 18000 in ascending order.
In statement 4, it is given that Sirisena, who is facing outside, is sitting third to the right of the delegate from New Zealand.
Let us assume that Sirisena is seated on 1st spot then we can say that the delegate from New Zealand is seated at either 4th or 6th spot.
Case 1:
When the delegate from New Zealand is seated on 4th spot.
It is given in statement 10 that Neither Irfan nor Prayut are from New Zealand. Also we know that Malcolm is sitting in between Irfan and Prayut Hence Malcolm should have 1 space vacant on both sides. Hence Malcolm can sit either at 6th or 7th spot. If Malcolm sits on 6th spot then Jacinda has to sit on 4th position. While it is given that Jacinda is not from New Zealand. Hence, we can say that Malcolm can't sit on 6th spot.
If Malcolm sits on 7th position then Jacinda will have to sit opposite to Sirisena whereas it is given that Sirisena and Jacinda are not seated opposite to each other. Hence, we can say that Malcolm can't sit on 7th spot.
Hence, we can say that the delegate from New Zealand is not seated on 4th spot.
Case 2:
When the delegate from New Zealand is seated on 6th spot.
Irfan and Prayut belong to the nations whose PCI are USD 10500 and USD 12000. Neither Irfan nor Prayut is from New Zealand. Hence, we can say that New Zealands's PCI can't be either USD 10500 or USD 12000.
In statement (6), it is given that Malcolm, who is facing outside, is an immediate neighbour of Irfan and Prayut.
Hence, we can say that Malcolm can be seated on any of 3rd, 4th and 6th spot.
If Malcolm is seated on 3rd spot then Jacinda should occupy 1st spot which is not vacant. Hence, we can say that Malcolm can't occupy 3rd spot.
If Malcolm is seated on 6th spot then Jacinda will occupy 4th spot. But in this case Ashraf has to sit on any one of 8th, 2nd and 3rd seat. In this case Ashraf has to be a neighbor of either Jacinda and Sirisena which contradicts to the information given in statement 2. Hence, we can say that Malcolm can't occupy 6th spot as well.
Therefore, we can say that Malcolm occupies 4th spot. Consequently, Jacinda sits on 2nd spot. Also, Irfan and Prayut can occupy 3rd and 4th spot in any order.
The delegates from Afghanistan and Australia are facing towards each other, and the delegate from Pakistan is sitting to the immediate left of the delegate from Afghanistan.
We can say that the delegates from Afghanistan and Australia are facing towards centre. That's only possible when they are seated at 3rd and 7th spot. Also, the delegate from Pakistan is sitting to the immediate left of the delegate from Afghanistan. This is possible only when the delegate from Afghanistan occupies 7th spot. Consequently, the delegates from Pakistan and Australia will occupy 8th and 3rd spot respectively.
Yameen's country PCI is equal to the sum of the PCI of his immediate neighbours. This is only possible when his neigbour's PCI are USD 7500 and 9000 in any order. Therefore, Yameen can occupy only 8th spot.
It is given that Ashraf is facing towards the centre and is not an immediate neighbour of Jacinda and Sirisena. Therefore, we can say that Ashraf is from Afghanistan and occupies 7th spot. Consequently, Widodo will occupy 6th spot.
Also, it is given that Ashraf doesn't belong to the nation with the least PCI. Hence, we can say that Sirisena belongs to the nation with the PCI USD 7500. Consequently, we can say that Afghanistan's PCI is 9000 USD. The PCI of New Zealand and Indonesia are USD 13500 and USD 15000 in any order.
From the arrangement, we can see that Yameen is from Pakistan. Hence, option C is the correct answer.
correct answer:-
3
Instruction for set :
Eight delegates namely - Yameen, Irfan, Sirisena, Ashraf, Malcolm, Jacinda, Prayut and Widodo participated in a conference held in New York City. Each of the delegates belongs to a different nation among Australia, Pakistan, Afghanistan, Maldives, Sri Lanka, New Zealand, Indonesia and Thailand not necessarily in the same order. The per capita income (PCI) of the aforementioned nations is in an arithmetic progression. The delegates are seated around a round table and the number of delegates who are facing away from the centre is the same as the number of delegates facing towards the centre. Further additional information is given that -
1. The minimum PCI and maximum PCI are USD 7500 and USD 18000 respectively.
2. Ashraf, who is facing towards the centre and doesn't belong to the nation with the least PCI, is not an immediate neighbour of Jacinda and Sirisena.
3. Jacinda is not seated opposite to Sirisena.
4. The delegates from Afghanistan and Australia are facing towards each other, and the delegate from Pakistan is sitting to the immediate left of the delegate from Afghanistan.
5. Sirisena, who is facing outside, is sitting third to the right of the delegate from New Zealand.
6. Yameen's country PCI is equal to the sum of the PCI of his immediate neighbours.
7. Malcolm, who is facing outside, is an immediate neighbour of Irfan and Prayut.
8. Jacinda, who belongs to the nation with maximum PCI, is facing towards the centre. He is sitting second to the left of Malcolm, who is from Indonesia.
9. Irfan and Prayut belong to the nations whose PCI are USD 10500 and USD 12000, not necessarily in the same order.
10. New Zealand's PCI is greater than USD 9000. Neither Irfan nor Prayut is from New Zealand. Jacinda is not from New Zealand.
Question 28
Who is from the nation with the least PCI?
Show Answer
Solution
Let us draw a circular arrangement diagram with 8 spot numbered from 1 to 8.
It is given that the minimum PCI and maximum PCI are USD 7500 and USD 18000 respectively. Also, the PCI are in an arithmetic progression.
Hence, we can say that a = 7500, a+7d = 18000 => d = 1500
Therefore, the PCI of the eight nations are USD 7500, USD 9000, USD 10500, USD 12000, USD 13500, USD 15000 ,USD 16500 and USD 18000 in ascending order.
In statement 4, it is given that Sirisena, who is facing outside, is sitting third to the right of the delegate from New Zealand.
Let us assume that Sirisena is seated on 1st spot then we can say that the delegate from New Zealand is seated at either 4th or 6th spot.
Case 1:
When the delegate from New Zealand is seated on 4th spot.
It is given in statement 10 that Neither Irfan nor Prayut are from New Zealand. Also we know that Malcolm is sitting in between Irfan and Prayut Hence Malcolm should have 1 space vacant on both sides. Hence Malcolm can sit either at 6th or 7th spot. If Malcolm sits on 6th spot then Jacinda has to sit on 4th position. While it is given that Jacinda is not from New Zealand. Hence, we can say that Malcolm can't sit on 6th spot.
If Malcolm sits on 7th position then Jacinda will have to sit opposite to Sirisena whereas it is given that Sirisena and Jacinda are not seated opposite to each other. Hence, we can say that Malcolm can't sit on 7th spot.
Hence, we can say that the delegate from New Zealand is not seated on 4th spot.
Case 2:
When the delegate from New Zealand is seated on 6th spot.
Irfan and Prayut belong to the nations whose PCI are USD 10500 and USD 12000. Neither Irfan nor Prayut is from New Zealand. Hence, we can say that New Zealands's PCI can't be either USD 10500 or USD 12000.
In statement (6), it is given that Malcolm, who is facing outside, is an immediate neighbour of Irfan and Prayut.
Hence, we can say that Malcolm can be seated on any of 3rd, 4th and 6th spot.
If Malcolm is seated on 3rd spot then Jacinda should occupy 1st spot which is not vacant. Hence, we can say that Malcolm can't occupy 3rd spot.
If Malcolm is seated on 6th spot then Jacinda will occupy 4th spot. But in this case Ashraf has to sit on any one of 8th, 2nd and 3rd seat. In this case Ashraf has to be a neighbor of either Jacinda and Sirisena which contradicts to the information given in statement 2. Hence, we can say that Malcolm can't occupy 6th spot as well.
Therefore, we can say that Malcolm occupies 4th spot. Consequently, Jacinda sits on 2nd spot. Also, Irfan and Prayut can occupy 3rd and 4th spot in any order.
The delegates from Afghanistan and Australia are facing towards each other, and the delegate from Pakistan is sitting to the immediate left of the delegate from Afghanistan.
We can say that the delegates from Afghanistan and Australia are facing towards centre. That's only possible when they are seated at 3rd and 7th spot. Also, the delegate from Pakistan is sitting to the immediate left of the delegate from Afghanistan. This is possible only when the delegate from Afghanistan occupies 7th spot. Consequently, the delegates from Pakistan and Australia will occupy 8th and 3rd spot respectively.
Yameen's country PCI is equal to the sum of the PCI of his immediate neighbours. This is only possible when his neigbour's PCI are USD 7500 and 9000 in any order. Therefore, Yameen can occupy only 8th spot.
It is given that Ashraf is facing towards the centre and is not an immediate neighbour of Jacinda and Sirisena. Therefore, we can say that Ashraf is from Afghanistan and occupies 7th spot. Consequently, Widodo will occupy 6th spot.
Also, it is given that Ashraf doesn't belong to the nation with the least PCI. Hence, we can say that Sirisena belongs to the nation with the PCI USD 7500. Consequently, we can say that Afghanistan's PCI is 9000 USD. The PCI of New Zealand and Indonesia are USD 13500 and USD 15000 in any order.
From the arrangement, we can see that Sirisena belongs to the nation with the least PCI. Hence, option A is the correct answer.
correct answer:-
1
Instruction for set :
Eight delegates namely - Yameen, Irfan, Sirisena, Ashraf, Malcolm, Jacinda, Prayut and Widodo participated in a conference held in New York City. Each of the delegates belongs to a different nation among Australia, Pakistan, Afghanistan, Maldives, Sri Lanka, New Zealand, Indonesia and Thailand not necessarily in the same order. The per capita income (PCI) of the aforementioned nations is in an arithmetic progression. The delegates are seated around a round table and the number of delegates who are facing away from the centre is the same as the number of delegates facing towards the centre. Further additional information is given that -
1. The minimum PCI and maximum PCI are USD 7500 and USD 18000 respectively.
2. Ashraf, who is facing towards the centre and doesn't belong to the nation with the least PCI, is not an immediate neighbour of Jacinda and Sirisena.
3. Jacinda is not seated opposite to Sirisena.
4. The delegates from Afghanistan and Australia are facing towards each other, and the delegate from Pakistan is sitting to the immediate left of the delegate from Afghanistan.
5. Sirisena, who is facing outside, is sitting third to the right of the delegate from New Zealand.
6. Yameen's country PCI is equal to the sum of the PCI of his immediate neighbours.
7. Malcolm, who is facing outside, is an immediate neighbour of Irfan and Prayut.
8. Jacinda, who belongs to the nation with maximum PCI, is facing towards the centre. He is sitting second to the left of Malcolm, who is from Indonesia.
9. Irfan and Prayut belong to the nations whose PCI are USD 10500 and USD 12000, not necessarily in the same order.
10. New Zealand's PCI is greater than USD 9000. Neither Irfan nor Prayut is from New Zealand. Jacinda is not from New Zealand.
Question 29
Which among the following nations does Widodo belong?
Show Answer
Solution
Let us draw a circular arrangement diagram with 8 spot numbered from 1 to 8.
It is given that the minimum PCI and maximum PCI are USD 7500 and USD 18000 respectively. Also, the PCI are in an arithmetic progression.
Hence, we can say that a = 7500, a+7d = 18000 => d = 1500
Therefore, the PCI of the eight nations are USD 7500, USD 9000, USD 10500, USD 12000, USD 13500, USD 15000 ,USD 16500 and USD 18000 in ascending order.
In statement 4, it is given that Sirisena, who is facing outside, is sitting third to the right of the delegate from New Zealand.
Let us assume that Sirisena is seated on 1st spot then we can say that the delegate from New Zealand is seated at either 4th or 6th spot.
Case 1:
When the delegate from New Zealand is seated on 4th spot.
It is given in statement 10 that Neither Irfan nor Prayut are from New Zealand. Also we know that Malcolm is sitting in between Irfan and Prayut Hence Malcolm should have 1 space vacant on both sides. Hence Malcolm can sit either at 6th or 7th spot. If Malcolm sits on 6th spot then Jacinda has to sit on 4th position. While it is given that Jacinda is not from New Zealand. Hence, we can say that Malcolm can't sit on 6th spot.
If Malcolm sits on 7th position then Jacinda will have to sit opposite to Sirisena whereas it is given that Sirisena and Jacinda are not seated opposite to each other. Hence, we can say that Malcolm can't sit on 7th spot.
Hence, we can say that the delegate from New Zealand is not seated on 4th spot.
Case 2:
When the delegate from New Zealand is seated on 6th spot.
Irfan and Prayut belong to the nations whose PCI are USD 10500 and USD 12000. Neither Irfan nor Prayut is from New Zealand. Hence, we can say that New Zealands's PCI can't be either USD 10500 or USD 12000.
In statement (6), it is given that Malcolm, who is facing outside, is an immediate neighbour of Irfan and Prayut.
Hence, we can say that Malcolm can be seated on any of 3rd, 4th and 6th spot.
If Malcolm is seated on 3rd spot then Jacinda should occupy 1st spot which is not vacant. Hence, we can say that Malcolm can't occupy 3rd spot.
If Malcolm is seated on 6th spot then Jacinda will occupy 4th spot. But in this case Ashraf has to sit on any one of 8th, 2nd and 3rd seat. In this case Ashraf has to be a neighbor of either Jacinda and Sirisena which contradicts to the information given in statement 2. Hence, we can say that Malcolm can't occupy 6th spot as well.
Therefore, we can say that Malcolm occupies 4th spot. Consequently, Jacinda sits on 2nd spot. Also, Irfan and Prayut can occupy 3rd and 4th spot in any order.
The delegates from Afghanistan and Australia are facing towards each other, and the delegate from Pakistan is sitting to the immediate left of the delegate from Afghanistan.
We can say that the delegates from Afghanistan and Australia are facing towards centre. That's only possible when they are seated at 3rd and 7th spot. Also, the delegate from Pakistan is sitting to the immediate left of the delegate from Afghanistan. This is possible only when the delegate from Afghanistan occupies 7th spot. Consequently, the delegates from Pakistan and Australia will occupy 8th and 3rd spot respectively.
Yameen's country PCI is equal to the sum of the PCI of his immediate neighbours. This is only possible when his neigbour's PCI are USD 7500 and 9000 in any order. Therefore, Yameen can occupy only 8th spot.
It is given that Ashraf is facing towards the centre and is not an immediate neighbour of Jacinda and Sirisena. Therefore, we can say that Ashraf is from Afghanistan and occupies 7th spot. Consequently, Widodo will occupy 6th spot.
Also, it is given that Ashraf doesn't belong to the nation with the least PCI. Hence, we can say that Sirisena belongs to the nation with the PCI USD 7500. Consequently, we can say that Afghanistan's PCI is 9000 USD. The PCI of New Zealand and Indonesia are USD 13500 and USD 15000 in any order.
From the arrangement, we can see that Widodo belongs to New Zealand. Hence, option D is the correct answer.
correct answer:-
4
Instruction for set :
Read the following and answer the questions.
Arjun, Ben, Charan and David play a game. They have a bag which contains an apple, an orange, a banana, a guava and a mango. The game consists of four rounds. In each round, each person randomly picks a fruit from the bag and places it back. Whenever a person picks a fruit he gets some money. He gets Re.1, Rs. 2, Rs. 3, Rs. 4 and Rs.5 when he picks an apple, an orange, a banana, a guava and a mango respectively.
Further it is known that:
1. In each of rounds I, III and IV no two players picked the same fruit.
2. The maximum money earned by any of Arjun, Ben and Charan is 12 in all rounds put together.
3. One of the five fruits contributed to Rs. 20 in all the rounds together.
4. The total money with Arjun and Ben was equal at the end of the game.
5. The maximum money was earned in round III.
6. Each fruit was picked by at least one person and each fruit was picked a different number of times.
7. The orange was picked more number of times than the mango.
8. The sum of the money earned by Arjun in round I and David in round IV is Rs.5
9. Arjun picked mango in round III
10. None of Arjun, Ben and Charan picked the same fruit in any two rounds.
Question 30
How much did Ben earn in all the four rounds put together?
Show Answer
Solution
There are four people and there were 4 rounds, hence the fruits were picked 16 times.
It is given that each fruit was picked a different number of times. The only possibility is 1, 2, 3, 4, 6 times.
It is given that one of the fruit contributed to 20 rupees. The only possibility is Mango being picked 4 times.
Since Mango is picked 4 times, orange is picked 6 times.
The maximum money earned by any of Arjun, Ben and Charan is 12. Hence, they cannot pick all of Mango, Guava and Banana.
Arjun, Ben and Charan have to choose one of apple or orange.
Since the mango is picked 4 times and orange is picked six times, the apple must be picked 3 times.
Since Arjun, Ben and Charan never picked the same fruit in any of the rounds, D must have picked orange 3 times.
David must have picked mango in the other round.
Arjun, Ben and Charan should have picked mango once each.
Since sum of the money earned by Arjun in round I and David in round IV is Rs.5
The only possibility is Arjun picking a banana in round I and David picking an orange in round IV.
Now, Arjun can score only 11 points.
Arjun and Ben scored the same points. Hence, banana must have been picked by Ben as well.
Thus, Guava was picked only once, by Charan.
Since, the maximum money was earned in III, Guava should have been picked in 4.
Arjun must have picked orange in round II as David already picked orange in round IV.
Arjun must have picked apple in round IV.
Ben can only pick banana in round IV.
Charan should have picked a mango in round IV. Apple in round I and orange in round II.
Ben can pick apple only in round III.
For Ben and David there are two possibilities of Mango/orange for one person and orange/mango for the other person in rounds I and II respectively.
Amount earned:
correct answer:-
2
Instruction for set :
Read the following and answer the questions.
Arjun, Ben, Charan and David play a game. They have a bag which contains an apple, an orange, a banana, a guava and a mango. The game consists of four rounds. In each round, each person randomly picks a fruit from the bag and places it back. Whenever a person picks a fruit he gets some money. He gets Re.1, Rs. 2, Rs. 3, Rs. 4 and Rs.5 when he picks an apple, an orange, a banana, a guava and a mango respectively.
Further it is known that:
1. In each of rounds I, III and IV no two players picked the same fruit.
2. The maximum money earned by any of Arjun, Ben and Charan is 12 in all rounds put together.
3. One of the five fruits contributed to Rs. 20 in all the rounds together.
4. The total money with Arjun and Ben was equal at the end of the game.
5. The maximum money was earned in round III.
6. Each fruit was picked by at least one person and each fruit was picked a different number of times.
7. The orange was picked more number of times than the mango.
8. The sum of the money earned by Arjun in round I and David in round IV is Rs.5
9. Arjun picked mango in round III
10. None of Arjun, Ben and Charan picked the same fruit in any two rounds.
Question 31
Which fruit did David pick in the first round?
Show Answer
Solution
There are four people and there were 4 rounds, hence the fruits were picked 16 times.
It is given that each fruit was picked a different number of times. The only possibility is 1, 2, 3, 4, 6 times.
It is given that one of the fruit contributed to 20 rupees. The only possibility is Mango being picked 4 times.
Since Mango is picked 4 times, orange is picked 6 times.
The maximum money earned by any of Arjun, Ben and Charan is 12. Hence, they cannot pick all of Mango, Guava and Banana.
Arjun, Ben and Charan have to choose one of apple or orange.
Since the mango is picked 4 times and orange is picked six times, the apple must be picked 3 times.
Since Arjun, Ben and Charan never picked the same fruit in any of the rounds, D must have picked orange 3 times.
David must have picked mango in the other round.
Arjun, Ben and Charan should have picked mango once each.
Since sum of the money earned by Arjun in round I and David in round IV is Rs.5
The only possibility is Arjun picking a banana in round I and David picking an orange in round IV.
Now, Arjun can score only 11 points.
Arjun and Ben scored the same points. Hence, banana must have been picked by Ben as well.
Thus, Guava was picked only once, by Charan.
Since, the maximum money was earned in III, Guava should have been picked in 4.
Arjun must have picked orange in round II as David already picked orange in round IV.
Arjun must have picked apple in round IV.
Ben can only pick banana in round IV.
Charan should have picked a mango in round IV. Apple in round I and orange in round II.
Ben can pick apple only in round III.
For Ben and David there are two possibilities of Mango/orange for one person and orange/mango for the other person in rounds I and II respectively.
Amount earned:
correct answer:-
4
Instruction for set :
Read the following and answer the questions.
Arjun, Ben, Charan and David play a game. They have a bag which contains an apple, an orange, a banana, a guava and a mango. The game consists of four rounds. In each round, each person randomly picks a fruit from the bag and places it back. Whenever a person picks a fruit he gets some money. He gets Re.1, Rs. 2, Rs. 3, Rs. 4 and Rs.5 when he picks an apple, an orange, a banana, a guava and a mango respectively.
Further it is known that:
1. In each of rounds I, III and IV no two players picked the same fruit.
2. The maximum money earned by any of Arjun, Ben and Charan is 12 in all rounds put together.
3. One of the five fruits contributed to Rs. 20 in all the rounds together.
4. The total money with Arjun and Ben was equal at the end of the game.
5. The maximum money was earned in round III.
6. Each fruit was picked by at least one person and each fruit was picked a different number of times.
7. The orange was picked more number of times than the mango.
8. The sum of the money earned by Arjun in round I and David in round IV is Rs.5
9. Arjun picked mango in round III
10. None of Arjun, Ben and Charan picked the same fruit in any two rounds.
Question 32
How many times was banana picked?
Show Answer
Solution
There are four people and there were 4 rounds, hence the fruits were picked 16 times.
It is given that each fruit was picked a different number of times. The only possibility is 1, 2, 3, 4, 6 times.
It is given that one of the fruit contributed to 20 rupees. The only possibility is Mango being picked 4 times.
Since Mango is picked 4 times, orange is picked 6 times.
The maximum money earned by any of Arjun, Ben and Charan is 12. Hence, they cannot pick all of Mango, Guava and Banana.
Arjun, Ben and Charan have to choose one of apple or orange.
Since the mango is picked 4 times and orange is picked six times, the apple must be picked 3 times.
Since Arjun, Ben and Charan never picked the same fruit in any of the rounds, D must have picked orange 3 times.
David must have picked mango in the other round.
Arjun, Ben and Charan should have picked mango once each.
Since sum of the money earned by Arjun in round I and David in round IV is Rs.5
The only possibility is Arjun picking a banana in round I and David picking an orange in round IV.
Now, Arjun can score only 11 points.
Arjun and Ben scored the same points. Hence, banana must have been picked by Ben as well.
Thus, Guava was picked only once, by Charan.
Since, the maximum money was earned in III, Guava should have been picked in 4.
Arjun must have picked orange in round II as David already picked orange in round IV.
Arjun must have picked apple in round IV.
Ben can only pick banana in round IV.
Charan should have picked a mango in round IV. Apple in round I and orange in round II.
Ben can pick apple only in round III.
For Ben and David there are two possibilities of Mango/orange for one person and orange/mango for the other person in rounds I and II respectively.
Amount earned:
correct answer:-
2
Instruction for set :
Read the following and answer the questions.
Arjun, Ben, Charan and David play a game. They have a bag which contains an apple, an orange, a banana, a guava and a mango. The game consists of four rounds. In each round, each person randomly picks a fruit from the bag and places it back. Whenever a person picks a fruit he gets some money. He gets Re.1, Rs. 2, Rs. 3, Rs. 4 and Rs.5 when he picks an apple, an orange, a banana, a guava and a mango respectively.
Further it is known that:
1. In each of rounds I, III and IV no two players picked the same fruit.
2. The maximum money earned by any of Arjun, Ben and Charan is 12 in all rounds put together.
3. One of the five fruits contributed to Rs. 20 in all the rounds together.
4. The total money with Arjun and Ben was equal at the end of the game.
5. The maximum money was earned in round III.
6. Each fruit was picked by at least one person and each fruit was picked a different number of times.
7. The orange was picked more number of times than the mango.
8. The sum of the money earned by Arjun in round I and David in round IV is Rs.5
9. Arjun picked mango in round III
10. None of Arjun, Ben and Charan picked the same fruit in any two rounds.
Question 33
Which fruit did Charan pick in round II?
Show Answer
Solution
There are four people and there were 4 rounds, hence the fruits were picked 16 times.
It is given that each fruit was picked a different number of times. The only possibility is 1, 2, 3, 4, 6 times.
It is given that one of the fruit contributed to 20 rupees. The only possibility is Mango being picked 4 times.
Since Mango is picked 4 times, orange is picked 6 times.
The maximum money earned by any of Arjun, Ben and Charan is 12. Hence, they cannot pick all of Mango, Guava and Banana.
Arjun, Ben and Charan have to choose one of apple or orange.
Since the mango is picked 4 times and orange is picked six times, the apple must be picked 3 times.
Since Arjun, Ben and Charan never picked the same fruit in any of the rounds, D must have picked orange 3 times.
David must have picked mango in the other round.
Arjun, Ben and Charan should have picked mango once each.
Since sum of the money earned by Arjun in round I and David in round IV is Rs.5
The only possibility is Arjun picking a banana in round I and David picking an orange in round IV.
Now, Arjun can score only 11 points.
Arjun and Ben scored the same points. Hence, banana must have been picked by Ben as well.
Thus, Guava was picked only once, by Charan.
Since, the maximum money was earned in III, Guava should have been picked in 4.
Arjun must have picked orange in round II as David already picked orange in round IV.
Arjun must have picked apple in round IV.
Ben can only pick banana in round IV.
Charan should have picked a mango in round IV. Apple in round I and orange in round II.
Ben can pick apple only in round III.
For Ben and David there are two possibilities of Mango/orange for one person and orange/mango for the other person in rounds I and II respectively.
Amount earned:
correct answer:-
3
Instruction for set :
A marketing company carried out a survey in one of the colleges regarding the laptops they have used. Overall 500 students have surveyed for this. The laptop companies considered for this survey were ASER, TELL, LEMOBO and HB. Upon survey, it was found that 280 of the students have used HB. 320 students have used TELL. 145 have used ASER and 115 have used LEMOBO. It is possible that one student has used more than one company's laptop.
Question 34
If it is given that all of the students have used laptops of at least 1 company and the number of students who have used exactly 2 companies laptop is maximum. What can be the number of students who have used exactly 1 laptop?
Show Answer
Solution
Let s,d,t,f represent the number of students who have used laptops of exactly one, two, three, and four company respectively.
As per the statement : $$s+d+t+f = 500$$ ...(I)
The number of laptops used :
$$s+2d+3t+4f = 280+320+115+145 = 860$$....(II)
(II) -(I) gives us
$$d+2t+3f = 360$$ ...(III)
We can say that the value of $$d$$ will be maximum when d = 360 and t=f = 0
Putting it in equation (I) we get $$s+360+0+0 = 500$$ or $$s = 140$$
correct answer:-
3
Instruction for set :
A marketing company carried out a survey in one of the colleges regarding the laptops they have used. Overall 500 students have surveyed for this. The laptop companies considered for this survey were ASER, TELL, LEMOBO and HB. Upon survey, it was found that 280 of the students have used HB. 320 students have used TELL. 145 have used ASER and 115 have used LEMOBO. It is possible that one student has used more than one company's laptop.
Question 35
If it is known that every student has at least 1 laptop of the above-mentioned companies and number of students who have laptops of exactly 2 companies is same as the number of students who have laptops of exactly 3 companies. What is the number of students who have used laptop of only 1 company if it is given that number of students who have used laptops of exactly 2 companies is maximum possible.
Show Answer
Solution
Let s,d,t,f represent the number of students who have used laptops of exactly one, two, three, and four company respectively.
As per the statement : $$s+d+t+f = 500$$ ...(I)
Total number of laptops:
$$s+2d+3t+4f = 280+320+115+145 = 860$$....(II)
(II) -(I) gives us
$$d+2t+3f = 360$$ ...(III)
Since we are given that d =t
$$3t+3f =360$$ or $$t+f = 120$$.
Max possible value of t = 120 when f = 0
Since d=t= 120
$$s +120+120+0 = 500$$ from(I)
$$s = 260$$
correct answer:-
260
Instruction for set :
A marketing company carried out a survey in one of the colleges regarding the laptops they have used. Overall 500 students have surveyed for this. The laptop companies considered for this survey were ASER, TELL, LEMOBO and HB. Upon survey, it was found that 280 of the students have used HB. 320 students have used TELL. 145 have used ASER and 115 have used LEMOBO. It is possible that one student has used more than one company's laptop.
Question 36
If it is given that the number of students who have used exactly one laptop is the maximum possible. What can be the maximum number of students who have used only TELL's laptop?
Show Answer
Solution
Let s,d,t,f represent the number of students who have used laptops of exactly one, two, three, and four company respectively.
Let n denote the number of students who have used laptops of none of the mentioned companies.
As per the statement : $$s+d+t+f+n = 500$$ ...(I)
Total number of laptops:
$$s+2d+3t+4f = 280+320+115+145 = 860$$....(II)
(II) -(I) gives us
$$d+2t+3f-n = 360$$ or $$d+2t+3f = 360+n$$ ...(III)
From (I) we can see that for s to be maximum, rest all has to be minimum possible.
Thus n has to be 0.
(III) can be modified to be written as $$d+2t+3f = 360$$. d+t+f will be minimum if d=t=0 and f = 120. But maximum value of the f can be 115 as it is the maximum number of students who owns LEMOBO. Thus putting f = 115 we get
$$d+2t = 15$$. Thus d = 1 and t = 7 will give minimum value of d+t+f = 1+7+115 = 123
s = 500 -(d+t+f+n)
s = 500 - 123 = 377
This can be represented in Venn-Diagram as follows
We need to fill the blanks such that d = 1 and t = 7. There is only one way to fill the blanks such that t=7
Maximum number of students who have used only TELL = 320-(115+7) = 320-122 = 198
correct answer:-
2
Instruction for set :
A marketing company carried out a survey in one of the colleges regarding the laptops they have used. Overall 500 students have surveyed for this. The laptop companies considered for this survey were ASER, TELL, LEMOBO and HB. Upon survey, it was found that 280 of the students have used HB. 320 students have used TELL. 145 have used ASER and 115 have used LEMOBO. It is possible that one student has used more than one company's laptop.
Question 37
What is the maximum number of students who have has used exactly one company's laptop?
Show Answer
Solution
Let s,d,t,f represent the number of students who have used laptops of exactly one, two, three, and four company respectively.
Let n denote the number of students who have used laptops of none of the mentioned companies.
As per the statement : $$s+d+t+f+n = 500$$ ...(I)
Total number of laptops:
$$s+2d+3t+4f = 280+320+115+145 = 860$$....(II)
(II) -(I) gives us
$$d+2t+3f-n = 360$$ or $$d+2t+3f = 360+n$$ ...(III)
From (I) we can see that for s to be maximum, rest all has to be minimum possible.
Thus n has to be 0.
(III) can be modified to be written as $$d+2t+3f = 360$$. d+t+f will be minimum if d=t=0 and f = 120. But maximum value of the f can be 115 as it is the maximum number of students who owns LEMOBO. Thus putting f = 115 we get
$$d+2t = 15$$. Thus d = 1 and t = 7 will give minimum value of d+t+f = 1+7+115 = 123
s = 500 -(d+t+f+n)
s = 500 - 123 = 377
correct answer:-
377
Instruction for set :
2 friends Virat and Sourav are playing a game that involves a dice. In each round, Virat rolls the dice twice, and then Sourav rolls the dice twice. If the sum of the numbers that Virat gets exceeds the sum of numbers that Sourav gets, Virat wins the round, else Sourav wins the round. In case the sum is the same, Sourav is given the advantage and he wins the round. The game ends when any one of them wins three consecutive rounds, and he is declared the winner. Based on the information given, answer the questions that follow.
Question 38
In a particular game, Sourav and Virat decide that either of them can start the first round, but whoever starts the first round has to start all subsequent rounds. Following is the sequence of numbers that come up starting from the first roll of dice in round 1. It is known that the game ends after the 12th throw of the dice (with the last roll of 2) as shown in the pattern.
3 6 5 4 2 5 A 1 B C 1 2
By varying the values of A, B and C, what is the total number of ways Sourav and Virat can throw the dice in the above pattern?
Show Answer
Solution
Since the total number of rolls = 12, the number of rounds in the game = 12/4 = 3
This implies that in all 3 rounds, the same player wins, in order to complete the game in round 3.
Let us suppose Virat starts the first round.
Now, in the first round, Virat's sum = 3 + 6 = 9, and Sourav's sum = 5 + 4 = 9.
In case the sum is the same, Sourav wins. Hence in Round 2 and Round 3 also, Sourav wins.
For Sourav to win in Round 2, he must roll a minimum sum of 7 so that he can match the sum of Virat and win the round. Hence, A can only be 6.
For Sourav to win the third round as well, Virat cannot exceed the sum of Sourav.
Sourav's sum = 1 + 2 = 3.
Hence, Virat can roll (1,1), (1,2) or (2,1). Hence B and C can together take 3 different ordered pairs as values.
Hence, the required count = 1 x 3 = 3
Let us suppose Sourav starts the first round.
Now, in the first round, Sourav's sum = 3 + 6 = 9, and Virat's sum = 5 + 4 = 9.
In case the sum is the same, Sourav wins. Hence in Round 2 and Round 3 also, Sourav wins.
Sourav rolls a sum of 2 + 5 = 7 in the second round. So Virat has to roll a sum less than or equal to 7. So, A can take 1 to 6. Hence, 6 values.
In round 3, Virat rolls a sum of 3. Sourav has to throw a minimum of a total of 3. So he can roll anything except (1,1). Hence number of possibilities = 36 - 1 = 35.
Hence, the required count = 35 x 6 = 210.
Hence, total count = 210 + 3 = 213.
correct answer:-
1
Instruction for set :
2 friends Virat and Sourav are playing a game that involves a dice. In each round, Virat rolls the dice twice, and then Sourav rolls the dice twice. If the sum of the numbers that Virat gets exceeds the sum of numbers that Sourav gets, Virat wins the round, else Sourav wins the round. In case the sum is the same, Sourav is given the advantage and he wins the round. The game ends when any one of them wins three consecutive rounds, and he is declared the winner. Based on the information given, answer the questions that follow.
Question 39
It is known that the game ends after the 8th round. The numbers rolled in the 8th round are successively 4, 5, 1, 6. How many of the choices given below can represent the successive numbers rolled in the 5th round?
The question says that the game ends after the 8th round. So, firstly the winner of the 8th round is the winner of the game. Secondly, the winner of the 5th round should be different from the winner of the game, because, to win, a player must win for the third consecutive time in the eighth round, so he should win in the 6th, 7th and 8th round. Suppose he wins in the 5th round, now if we win in the 6th and 7th round as well, the game ends after the 7th round, and if he loses any of the 6th or 7th rounds, the game goes beyond 8 rounds. In the question, Virat win the final round since 4 + 5 > 1 + 6. Hence, Virat must lose round 5 by all possible means.
4 + 3 < 2 + 6, Hence Sourav wins
4 + 1 < 1 + 5, Hence Sourav wins
2 + 3 = 1 + 4, Hence Sourav wins
5 + 6 > 5 + 5, Hence Virat wins
2 + 3 > 1 + 2, Hence Virat wins
1 + 2 < 3 + 4, Hence Sourav wins
Hence, in 4 possible scenarios, Virat loses. Hence 4 is the correct answer.
correct answer:-
4
Instruction for set :
2 friends Virat and Sourav are playing a game that involves a dice. In each round, Virat rolls the dice twice, and then Sourav rolls the dice twice. If the sum of the numbers that Virat gets exceeds the sum of numbers that Sourav gets, Virat wins the round, else Sourav wins the round. In case the sum is the same, Sourav is given the advantage and he wins the round. The game ends when any one of them wins three consecutive rounds, and he is declared the winner. Based on the information given, answer the questions that follow.
Question 40
Sourav has a special tool at his disposal, that allows him to always roll a 6, but he does not use it always. He only uses it in the final roll of a round only if the same player wins in both of the consecutive rounds preceding that round. He won't use it under any other circumstance.
In a particular game, Sourav uses this tool thrice, once in the 3rd round, once in the 6th round and once in the 10th round to win the game. How many rounds did Virat win?
Show Answer
Solution
Sourav uses the tool in the third round, and he does not win after that round, which means he saved himself from losing the game by using this tool, hence Virat was the winner of Rund 1 and Round 2, and Sourav used the tool to win Round 3.
Sourav again uses this tool in the sixth round, and he does not win after the round, which means he saved himself from losing the game by using the tool, hence Virat was the winner of Round 4 and Round 5, and Sourav is the winner in Round 6.
Sourav again uses the tool in the tenth round, but this time to win, so Sourav must have won the 8th and 9th rounds already. Hence he cannot win round 7.
2 friends Virat and Sourav are playing a game that involves a dice. In each round, Virat rolls the dice twice, and then Sourav rolls the dice twice. If the sum of the numbers that Virat gets exceeds the sum of numbers that Sourav gets, Virat wins the round, else Sourav wins the round. In case the sum is the same, Sourav is given the advantage and he wins the round. The game ends when any one of them wins three consecutive rounds, and he is declared the winner. Based on the information given, answer the questions that follow.
Question 41
Sourav has a special tool at his disposal, that allows him to always roll a 6, but he does not use it always. He only uses it in the final roll of a round only if the same player wins in both of the consecutive rounds preceding that round. He won't use it under any other circumstance.
Sourav used this tool to win a particular round. It is known that Sourav had rolled 1 in his initial roll in this round. Also, it is known that Virat had rolled the same number in both his chances in this round. What is the probability that Sourav wins this round, had he not used the tool?
Show Answer
Solution
Sourav wins by throwing a sum of 1 + 6 = 7
Virat rolls the same numbers. Hence possible alternatives are (1,1),(2,2),(3,3).
Now, had Sourav not used his tool, let us assume all three cases:
Case 1: (1,1)
Sourav wins by rolling any of 1 to 6 in the second round. So probability = 1.
Case 1: (2,2)
Sourav wins by rolling any of 3 to 6 in the second round. So probability = 4/6=2/3.
Case 3: (3,3)
Sourav wins by rolling any of 5 or 6 in the second round. So probability = 2/6=1/3.
Hence, total probability = $$\frac{1}{3}\times\ 1+\frac{1}{3}\times\ \frac{2}{3}+\frac{1}{3}\times\ \frac{1}{3}$$ = 2/3
correct answer:-
3
Instruction for set :
Read the following information carefully and answer the questions which follow.
Amit, Ravi, Sunil and Vinod are four members of the interview panel which has to select the candidates for admission to the MBA program at NIM-Calcutta. Each panel member has to rate the candidate on the scale of 1-10 in three different parameters. The parameters for rating the candidates are Confidence, Knowledge and Profile. Mohit and Rohit are two candidates who have been interviewed by the panel. All the panel members rated both these candidates on these parameters. All the members give integer ratings only. In confidence, Mohit got a better rating from Amit than Sunil and Sunil gave a better rating than Ravi. Mohit received a better rating in profile from Sunil than Vinod.
Table 1 given below presents the triplets, each comprising of the minimum, average and maximum rating received by each candidate in each of the three parameters.
Table 2 gives the minimum and maximum rating given by each panel member to both the candidates.
Table 3 gives the average rating given by each panel member on every parameter.
Question 42
How much rating did Sunil give to Rohit on profile?
Show Answer
Solution
For Mohit, the minimum and average score in confidence is 5 and 8. His average score is 6.5. This means that the sum of the scores given by 5 panelists to Mohit on confidence will be 6.5*4 = 26. Hence, the possible scores for Mohit in confidence are (5, 5, 8, 8), (5, 6, 7, 8). Similarly using the other values of table, 1 we can list down the possibilities as shown below
From the second table, we can observer that the 4 marks which Mohit got in Knowledge, must have been given by Ravi. Similarly, Rohit must have got 2 in confidence from Vinod. Average rating by Ravi on knowledge is 4.5. Hence Rohit must have got 5 from him in knowledge. Similarly, Vinod must have given 7 to Mohit in confidence. Hence, Mohit must have got 5,6,7,8 in confidence. Average rating by Ravi in confidence is 4.5. Hence, the possible ratings he can give to Mohit and Rohit are (5,4), (6,3) or (7,2). Since Rohit cannot get 9 from Amit, so he must get 9 from Sunil in knowledge.
Mohit got a better rating in confidence from Amit. Hence, Amit must have given him 8 in confidence. Hence, Rohit must have got 6 in confidence. Sunil must have given 6 in confidence to Mohit and Ravi must have given 5. From this we can get the confidence ratings of Rohit as well. Ravi gave maximum of 6 and minimum of 4 to Mohit. Hence, he must have given him 6 in profile. This means that he would have given 3 in profile to Rohit. Vinod gave a maximum of 7 to Rohit. Hence, it must have come in knowledge since from our given possibilities, we can see that Rohit did not get 7 in profile. Amit must have given Rohit 4 in profile. Using the other clues and the table of possibilities that we can fill the remaining table as given below
correct answer:-
1
Instruction for set :
Read the following information carefully and answer the questions which follow.
Amit, Ravi, Sunil and Vinod are four members of the interview panel which has to select the candidates for admission to the MBA program at NIM-Calcutta. Each panel member has to rate the candidate on the scale of 1-10 in three different parameters. The parameters for rating the candidates are Confidence, Knowledge and Profile. Mohit and Rohit are two candidates who have been interviewed by the panel. All the panel members rated both these candidates on these parameters. All the members give integer ratings only. In confidence, Mohit got a better rating from Amit than Sunil and Sunil gave a better rating than Ravi. Mohit received a better rating in profile from Sunil than Vinod.
Table 1 given below presents the triplets, each comprising of the minimum, average and maximum rating received by each candidate in each of the three parameters.
Table 2 gives the minimum and maximum rating given by each panel member to both the candidates.
Table 3 gives the average rating given by each panel member on every parameter.
Question 43
What is the average rating given by Ravi to Rohit?
Show Answer
Solution
For Mohit, the minimum and average score in confidence is 5 and 8. His average score is 6.5. This means that the sum of the scores given by 5 panelists to Mohit on confidence will be 6.5*4 = 26. Hence, the possible scores for Mohit in confidence are (5, 5, 8, 8), (5, 6, 7, 8). Similarly using the other values of table, 1 we can list down the possibilities as shown below
From the second table, we can observer that the 4 marks which Mohit got in Knowledge, must have been given by Ravi. Similarly, Rohit must have got 2 in confidence from Vinod. Average rating by Ravi on knowledge is 4.5. Hence Rohit must have got 5 from him in knowledge. Similarly, Vinod must have given 7 to Mohit in confidence. Hence, Mohit must have got 5,6,7,8 in confidence. Average rating by Ravi in confidence is 4.5. Hence, the possible ratings he can give to Mohit and Rohit are (5,4), (6,3) or (7,2). Since Rohit cannot get 9 from Amit, so he must get 9 from Sunil in knowledge.
Mohit got a better rating in confidence from Amit. Hence, Amit must have given him 8 in confidence. Hence, Rohit must have got 6 in confidence. Sunil must have given 6 in confidence to Mohit and Ravi must have given 5. From this we can get the confidence ratings of Rohit as well. Ravi gave maximum of 6 and minimum of 4 to Mohit. Hence, he must have given him 6 in profile. This means that he would have given 3 in profile to Rohit. Vinod gave a maximum of 7 to Rohit. Hence, it must have come in knowledge since from our given possibilities, we can see that Rohit did not get 7 in profile. Amit must have given Rohit 4 in profile. Using the other clues and the table of possibilities that we can fill the remaining table as given below
correct answer:-
2
Instruction for set :
Read the following information carefully and answer the questions which follow.
Amit, Ravi, Sunil and Vinod are four members of the interview panel which has to select the candidates for admission to the MBA program at NIM-Calcutta. Each panel member has to rate the candidate on the scale of 1-10 in three different parameters. The parameters for rating the candidates are Confidence, Knowledge and Profile. Mohit and Rohit are two candidates who have been interviewed by the panel. All the panel members rated both these candidates on these parameters. All the members give integer ratings only. In confidence, Mohit got a better rating from Amit than Sunil and Sunil gave a better rating than Ravi. Mohit received a better rating in profile from Sunil than Vinod.
Table 1 given below presents the triplets, each comprising of the minimum, average and maximum rating received by each candidate in each of the three parameters.
Table 2 gives the minimum and maximum rating given by each panel member to both the candidates.
Table 3 gives the average rating given by each panel member on every parameter.
Question 44
What is the difference between the rating given by Amit to Mohit in knowledge and the rating given by Sunil to Rohit in confidence?
Show Answer
Solution
For Mohit, the minimum and average score in confidence is 5 and 8. His average score is 6.5. This means that the sum of the scores given by 5 panelists to Mohit on confidence will be 6.5*4 = 26. Hence, the possible scores for Mohit in confidence are (5, 5, 8, 8), (5, 6, 7, 8). Similarly using the other values of table, 1 we can list down the possibilities as shown below
From the second table, we can observer that the 4 marks which Mohit got in Knowledge, must have been given by Ravi. Similarly, Rohit must have got 2 in confidence from Vinod. Average rating by Ravi on knowledge is 4.5. Hence Rohit must have got 5 from him in knowledge. Similarly, Vinod must have given 7 to Mohit in confidence. Hence, Mohit must have got 5,6,7,8 in confidence. Average rating by Ravi in confidence is 4.5. Hence, the possible ratings he can give to Mohit and Rohit are (5,4), (6,3) or (7,2). Since Rohit cannot get 9 from Amit, so he must get 9 from Sunil in knowledge.
Mohit got a better rating in confidence from Amit. Hence, Amit must have given him 8 in confidence. Hence, Rohit must have got 6 in confidence. Sunil must have given 6 in confidence to Mohit and Ravi must have given 5. From this we can get the confidence ratings of Rohit as well. Ravi gave maximum of 6 and minimum of 4 to Mohit. Hence, he must have given him 6 in profile. This means that he would have given 3 in profile to Rohit. Vinod gave a maximum of 7 to Rohit. Hence, it must have come in knowledge since from our given possibilities, we can see that Rohit did not get 7 in profile. Amit must have given Rohit 4 in profile. Using the other clues and the table of possibilities that we can fill the remaining table as given below
correct answer:-
3
Instruction for set :
Read the following information carefully and answer the questions which follow.
Amit, Ravi, Sunil and Vinod are four members of the interview panel which has to select the candidates for admission to the MBA program at NIM-Calcutta. Each panel member has to rate the candidate on the scale of 1-10 in three different parameters. The parameters for rating the candidates are Confidence, Knowledge and Profile. Mohit and Rohit are two candidates who have been interviewed by the panel. All the panel members rated both these candidates on these parameters. All the members give integer ratings only. In confidence, Mohit got a better rating from Amit than Sunil and Sunil gave a better rating than Ravi. Mohit received a better rating in profile from Sunil than Vinod.
Table 1 given below presents the triplets, each comprising of the minimum, average and maximum rating received by each candidate in each of the three parameters.
Table 2 gives the minimum and maximum rating given by each panel member to both the candidates.
Table 3 gives the average rating given by each panel member on every parameter.
Question 45
If the panel selects only those members whose average rating across all three parameters is greater than 5, then which of the following statements is correct?
Show Answer
Solution
For Mohit, the minimum and average score in confidence is 5 and 8. His average score is 6.5. This means that the sum of the scores given by 5 panelists to Mohit on confidence will be 6.5*4 = 26. Hence, the possible scores for Mohit in confidence are (5, 5, 8, 8), (5, 6, 7, 8). Similarly using the other values of table, 1 we can list down the possibilities as shown below
From the second table, we can observer that the 4 marks which Mohit got in Knowledge, must have been given by Ravi. Similarly, Rohit must have got 2 in confidence from Vinod. Average rating by Ravi on knowledge is 4.5. Hence Rohit must have got 5 from him in knowledge. Similarly, Vinod must have given 7 to Mohit in confidence. Hence, Mohit must have got 5,6,7,8 in confidence. Average rating by Ravi in confidence is 4.5. Hence, the possible ratings he can give to Mohit and Rohit are (5,4), (6,3) or (7,2). Since Rohit cannot get 9 from Amit, so he must get 9 from Sunil in knowledge.
Mohit got a better rating in confidence from Amit. Hence, Amit must have given him 8 in confidence. Hence, Rohit must have got 6 in confidence. Sunil must have given 6 in confidence to Mohit and Ravi must have given 5. From this we can get the confidence ratings of Rohit as well. Ravi gave maximum of 6 and minimum of 4 to Mohit. Hence, he must have given him 6 in profile. This means that he would have given 3 in profile to Rohit. Vinod gave a maximum of 7 to Rohit. Hence, it must have come in knowledge since from our given possibilities, we can see that Rohit did not get 7 in profile. Amit must have given Rohit 4 in profile. Using the other clues and the table of possibilities that we can fill the remaining table as given below
correct answer:-
2
Instruction for set :
P, Q, R, S, T, U and V are seven friends studying MBA in Michigan Business School. In the last semester each student has to take up some electives depending on the area of their interest. Each of Q, R, S, T and V have 2 electives common with one friend, 3 electives common with two friends and 4 electives common with three friends. U has the same number of electives common with V, P and Q. The following additional information is also known regarding the number of electives taken by the friends:
(i) P has 2 electives common with two friends, 3 electives common with two other friends and 4 electives common with the remaining two friends.
(ii) S has 4 electives common with each of R, V and P
(iii) V has 3 electives common with Q and 4 electives with R
(iv) T has 2 electives common with P and 3 electives common with S
(v) The number of electives V has in common with P is one less than what he has in common with U
Question 46
How many electives did T have common with R?
Show Answer
Solution
From the data given in the question we know that the number of electives V has with the other friends is 2,3 or 4. Thus, using information from (v) we can conclude that V has either 2 elective with P and 3 elective with U or 3 elective with P and 4 elective with U. Also, using information from (ii), (iii) and (iv) we can make the following table:
From the question, T has 2 electives common with only 1 friend. So, T-V = 4. Thus, V-U will be having only 3 electives in common => V-P has only 2 elective in common.
It is given that U has same number of electives with V, P and Q. Since, V-U is 3, U-P and U-Q will also be 3. From, (i) P should have 2, 3 and 4 electives common with 2 friends each. Thus, P should have either 4 or 3 electives common with Q. As Q can only have 3 electives common with 2 other people, Q and P must have 4 electives in common and P and R must have 3 electives in common. The table is as follows:
If we observe column Q, he can take either 4 or 2 with S as he already has 3 electives common with 2 other people. Also, from row S we can observe that S can take either 2 or 3 electives with Q. Thus, Q-S must have 2 electives in common. Thus, S-U must have 3 electives in common has S should have 3 electives common with 2 people.
Similarly, using clues from (i) to (v), the rest of the table can be filled. The final table is as follows:
From the table we can see that U had 3 electives common with T
correct answer:-
2
Instruction for set :
P, Q, R, S, T, U and V are seven friends studying MBA in Michigan Business School. In the last semester each student has to take up some electives depending on the area of their interest. Each of Q, R, S, T and V have 2 electives common with one friend, 3 electives common with two friends and 4 electives common with three friends. U has the same number of electives common with V, P and Q. The following additional information is also known regarding the number of electives taken by the friends:
(i) P has 2 electives common with two friends, 3 electives common with two other friends and 4 electives common with the remaining two friends.
(ii) S has 4 electives common with each of R, V and P
(iii) V has 3 electives common with Q and 4 electives with R
(iv) T has 2 electives common with P and 3 electives common with S
(v) The number of electives V has in common with P is one less than what he has in common with U
Question 47
With how many friends did U have 3 electives common?
Show Answer
Solution
From the data given in the question we know that the number of electives V has with the other friends is 2,3 or 4. Thus, using information from (v) we can conclude that V has either 2 elective with P and 3 elective with U or 3 elective with P and 4 elective with U. Also, using information from (ii), (iii) and (iv) we can make the following table:
From the question, T has 2 electives common with only 1 friend. So, T-V = 4. Thus, V-U will be having only 3 electives in common => V-P has only 2 elective in common.
It is given that U has same number of electives with V, P and Q. Since, V-U is 3, U-P and U-Q will also be 3. From, (i) P should have 2, 3 and 4 electives common with 2 friends each. Thus, P should have either 4 or 3 electives common with Q. As Q can only have 3 electives common with 2 other people, Q and P must have 4 electives in common and P and R must have 3 electives in common. The table is as follows:
If we observe column Q, he can take either 4 or 2 with S as he already has 3 electives common with 2 other people. Also, from row S we can observe that S can take either 2 or 3 electives with Q. Thus, Q-S must have 2 electives in common. Thus, S-U must have 3 electives in common has S should have 3 electives common with 2 people.
Similarly, using clues from (i) to (v), the rest of the table can be filled. The final table is as follows:
From the table we can see that U had 3 electives common with 4 people. Thus, B is the right choice.
correct answer:-
2
Instruction for set :
P, Q, R, S, T, U and V are seven friends studying MBA in Michigan Business School. In the last semester each student has to take up some electives depending on the area of their interest. Each of Q, R, S, T and V have 2 electives common with one friend, 3 electives common with two friends and 4 electives common with three friends. U has the same number of electives common with V, P and Q. The following additional information is also known regarding the number of electives taken by the friends:
(i) P has 2 electives common with two friends, 3 electives common with two other friends and 4 electives common with the remaining two friends.
(ii) S has 4 electives common with each of R, V and P
(iii) V has 3 electives common with Q and 4 electives with R
(iv) T has 2 electives common with P and 3 electives common with S
(v) The number of electives V has in common with P is one less than what he has in common with U
Question 48
For how many friends can the exact number of electives R has common with can be uniquely determined?
Show Answer
Solution
From the data given in the question we know that the number of electives V has with the other friends is 2,3 or 4. Thus, using information from (v) we can conclude that V has either 2 elective with P and 3 elective with U or 3 elective with P and 4 elective with U. Also, using information from (ii), (iii) and (iv) we can make the following table:
From the question, T has 2 electives common with only 1 friend. So, T-V = 4. Thus, V-U will be having only 3 electives in common => V-P has only 2 elective in common.
It is given that U has same number of electives with V, P and Q. Since, V-U is 3, U-P and U-Q will also be 3. From, (i) P should have 2, 3 and 4 electives common with 2 friends each. Thus, P should have either 4 or 3 electives common with Q. As Q can only have 3 electives common with 2 other people, Q and P must have 4 electives in common and P and R must have 3 electives in common. The table is as follows:
If we observe column Q, he can take either 4 or 2 with S as he already has 3 electives common with 2 other people. Also, from row S we can observe that S can take either 2 or 3 electives with Q. Thus, Q-S must have 2 electives in common. Thus, S-U must have 3 electives in common has S should have 3 electives common with 2 people.
Similarly, using clues from (i) to (v), the rest of the table can be filled. The final table is as follows:
From the table we can see that for all 6 friends we can determine the number of electives, they have common with R.
correct answer:-
4
Instruction for set :
P, Q, R, S, T, U and V are seven friends studying MBA in Michigan Business School. In the last semester each student has to take up some electives depending on the area of their interest. Each of Q, R, S, T and V have 2 electives common with one friend, 3 electives common with two friends and 4 electives common with three friends. U has the same number of electives common with V, P and Q. The following additional information is also known regarding the number of electives taken by the friends:
(i) P has 2 electives common with two friends, 3 electives common with two other friends and 4 electives common with the remaining two friends.
(ii) S has 4 electives common with each of R, V and P
(iii) V has 3 electives common with Q and 4 electives with R
(iv) T has 2 electives common with P and 3 electives common with S
(v) The number of electives V has in common with P is one less than what he has in common with U
Question 49
Which of the following statements are not true as per the question?
Show Answer
Solution
From the data given in the question we know that the number of electives V has with the other friends is 2,3 or 4. Thus, using information from (v) we can conclude that V has either 2 elective with P and 3 elective with U or 3 elective with P and 4 elective with U. Also, using information from (ii), (iii) and (iv) we can make the following table:
From the question, T has 2 electives common with only 1 friend. So, T-V = 4. Thus, V-U will be having only 3 electives in common => V-P has only 2 elective in common.
It is given that U has same number of electives with V, P and Q. Since, V-U is 3, U-P and U-Q will also be 3. From, (i) P should have 2, 3 and 4 electives common with 2 friends each. Thus, P should have either 4 or 3 electives common with Q. As Q can only have 3 electives common with 2 other people, Q and P must have 4 electives in common and P and R must have 3 electives in common. The table is as follows:
If we observe column Q, he can take either 4 or 2 with S as he already has 3 electives common with 2 other people. Also, from row S we can observe that S can take either 2 or 3 electives with Q. Thus, Q-S must have 2 electives in common. Thus, S-U must have 3 electives in common has S should have 3 electives common with 2 people.
Similarly, using clues from (i) to (v), the rest of the table can be filled. The final table is as follows:
From the table we can see that R has 3 electives common with R. Thus, statement A is incorrect.
correct answer:-
1
Instruction for set :
A college had eight different clubs - Quiz club, Maths club, Physics club, English club, Chess club, MUN, Singing club and Dance club. Each of these clubs had an election to elect the secretary of the clubs. The total votes in a club is equal to the total number of members in the club. But some members needn't vote in the election and the actual number of votes cast is equal to the number of members who voted.
The voting percentage equals $$\frac{\text {Number of votes cast}}{\text{Total Votes}}$$
The below graph gives the number of votes cast on the x-axis and the number of votes secured by the winning student in each club as a percentage of the total votes(members) in that club. T
Question 50
How many clubs necessarily have more total number of votes than MUN, if it is given that the winning student in MUN secured the lowest number of votes among all the eight winning candidates?
Show Answer
Solution
Let the number of members of MUN be x and of Maths club be a.
Hence, 20% of a > 35% of x
=> a > x
Thus, the number of members of Maths club is greater than that of MUN club.
Similarly, the winning students of the quiz club, maths club, english club, physics club, singing club and the dance club have less percentage of votes than the winning student from MUN and still have more number of votes than him.
So, these 6 clubs must have more total number of votes.
correct answer:-
4
Instruction for set :
A college had eight different clubs - Quiz club, Maths club, Physics club, English club, Chess club, MUN, Singing club and Dance club. Each of these clubs had an election to elect the secretary of the clubs. The total votes in a club is equal to the total number of members in the club. But some members needn't vote in the election and the actual number of votes cast is equal to the number of members who voted.
The voting percentage equals $$\frac{\text {Number of votes cast}}{\text{Total Votes}}$$
The below graph gives the number of votes cast on the x-axis and the number of votes secured by the winning student in each club as a percentage of the total votes(members) in that club. T
Question 51
The winning student from which of the following clubs had the highest number of votes if it is given that no club had a voting percentage of less than 50% and the winning student from each club got maximum possible votes.
Show Answer
Solution
Here, we need to consider those clubs whose winning candidates have high percentage of votes.
Chess club - 275 votes => max votes = 275/0.5 = 550 votes => winning candidate secured 220 votes
MUN - 350 votes => max votes = 350/0.5 = 700 => winning candidate secured 245 votes
Singing club - 375 votes => max votes = 375/0.5 = 750 => winning candidate secured 206 votes
Dance club - 400 votes => max votes = 400/0.5 = 800 => winning candidate secured 200 votes
=> MUN candidate secured highest number of votes.
correct answer:-
2
Instruction for set :
A college had eight different clubs - Quiz club, Maths club, Physics club, English club, Chess club, MUN, Singing club and Dance club. Each of these clubs had an election to elect the secretary of the clubs. The total votes in a club is equal to the total number of members in the club. But some members needn't vote in the election and the actual number of votes cast is equal to the number of members who voted.
The voting percentage equals $$\frac{\text {Number of votes cast}}{\text{Total Votes}}$$
The below graph gives the number of votes cast on the x-axis and the number of votes secured by the winning student in each club as a percentage of the total votes(members) in that club. T
Question 52
The secretary of which of the following clubs secured the highest number of votes?
Show Answer
Solution
As the total number of votes in each of these clubs is not given and cannot be found, we cannot determine the club in which the winning student secured the highest number of votes.
Hence, the answer is cannot be determined.
correct answer:-
4
Instruction for set :
A college had eight different clubs - Quiz club, Maths club, Physics club, English club, Chess club, MUN, Singing club and Dance club. Each of these clubs had an election to elect the secretary of the clubs. The total votes in a club is equal to the total number of members in the club. But some members needn't vote in the election and the actual number of votes cast is equal to the number of members who voted.
The voting percentage equals $$\frac{\text {Number of votes cast}}{\text{Total Votes}}$$
The below graph gives the number of votes cast on the x-axis and the number of votes secured by the winning student in each club as a percentage of the total votes(members) in that club. T
Question 53
If every club had at least 80% of voting percentage, then the maximum ratio of the total number of votes of dance club to total number of votes of Maths club is equal to?
Show Answer
Solution
To get the maximum ratio, we need to maximize the numerator and minimize the denominator.
Let x% be the voting percentage of dance club and y% the voting percentage of the maths club. We know that 80% <= x% ,y% <=100%
Hence, reqd ratio = (400/x%) / (200/y%)
For numerator to be max, x should be 80% and for denominator to be min, y should be 100%.
There are three countries A,B, and C. The total population of these three countries is 1440. Population of B is 40% of the total population. The total number of females is 20% less than the total number of males. There are two kinds of people: who play sports and who do not play sports.
(I) The number of males in A, B and C are all perfect squares.
(II) The number of men who do not play sports in country A is equal to 45% of the total number of females who do not play sports.
(III) The number of men who do not play sports in country B is equal to 48% of the total number of females who do not play sports.
(IV) The difference between the number of males in C and the total number of females who do not play sports is equal to 256.
(V) The number of females in B is 50% of the total number of females and the number of females in A and C are equal.
Question 54
How many men of A play sports?
Show Answer
Solution
Prepare the raw table and fill the data which is obtained instantaneously.
There are two kinds of persons: who play sports and who do not play sports, so there will be 4 kinds of people overall.
SM : Men who play sports NSM : Men who do not play sports TM : Total Men SF : Females who play sports NSF : Females who do not play sports TF : Total Females
The number of total females is 20% less than total males.
F=0.8M
M+0.8M = 1440
M=800
=> F= 640
Looking at the fifth statement, the number of females in A,B and C are 160, 320 and 160 respectively. So, the first design of table will look like this.
Note that we know that the sum of the number of males in A and C is 544 (800-256) and the only two perfect squares whose sum equals 544 is 400 and 144.
From the fourth statement, we can infer that the difference between the number of males in C and the number of females who do not play sports is equal to 256.
|k - x| =256
k - x = 256 or x - k = 256
Taking the first case: k - x = 256, then,
If k = 144, x will be negative. We can eliminate this case since x cannot be negative.
If k =400, x = 144.
Taking the second case: x - k = 256, then,
If k = 144, then x = 400
If k =400, x = 656 (but this can't happen as the total number of women is only 640)
Hence, x = 400 and k = 144.
Now fill the remaining values in the table.
0.45x = 180
0.48x = 192
As we can see, the number of males who play sports from A is 220. Therefore, option B is the right answer.
correct answer:-
2
Instruction for set :
There are three countries A,B, and C. The total population of these three countries is 1440. Population of B is 40% of the total population. The total number of females is 20% less than the total number of males. There are two kinds of people: who play sports and who do not play sports.
(I) The number of males in A, B and C are all perfect squares.
(II) The number of men who do not play sports in country A is equal to 45% of the total number of females who do not play sports.
(III) The number of men who do not play sports in country B is equal to 48% of the total number of females who do not play sports.
(IV) The difference between the number of males in C and the total number of females who do not play sports is equal to 256.
(V) The number of females in B is 50% of the total number of females and the number of females in A and C are equal.
Question 55
The total population of country A is
Show Answer
Solution
Prepare the raw table and fill the data which is obtained instantaneously.
There are two kinds of persons: who play sports and who do not play sports, so there will be 4 kinds of people overall.
SM : Men who play sports NSM : Men who do not play sports TM : Total Men SF : Females who play sports NSF : Females who do not play sports TF : Total Females
The number of total females is 20% less than total males.
F=0.8M
M+0.8M = 1440
M=800
=> F= 640
Looking at the fifth statement, the number of females in A,B and C are 160, 320 and 160 respectively. So, the first design of table will look like this.
Note that we know that the sum of the number of males in A and C is 544 (800-256) and the only two perfect squares whose sum equals 544 is 400 and 144.
From the fourth statement, we can infer that the difference between the number of males in C and the number of females who do not play sports is equal to 256.
|k - x| =256
k - x = 256 or x - k = 256
Taking the first case: k - x = 256, then,
If k = 144, x will be negative. We can eliminate this case since x cannot be negative.
If k =400, x = 144.
Taking the second case: x - k = 256, then,
If k = 144, then x = 400
If k =400, x = 656 (but this can't happen as the total number of women is only 640)
Hence, x = 400 and k = 144.
Now fill the remaining values in the table.
0.45x = 180
0.48x = 192
As we can see, the number of males who play sports from A is 220. Therefore, option B is the right answer.
Total population of country A is 560. Therefore, option C is the right answer
correct answer:-
3
Instruction for set :
There are three countries A,B, and C. The total population of these three countries is 1440. Population of B is 40% of the total population. The total number of females is 20% less than the total number of males. There are two kinds of people: who play sports and who do not play sports.
(I) The number of males in A, B and C are all perfect squares.
(II) The number of men who do not play sports in country A is equal to 45% of the total number of females who do not play sports.
(III) The number of men who do not play sports in country B is equal to 48% of the total number of females who do not play sports.
(IV) The difference between the number of males in C and the total number of females who do not play sports is equal to 256.
(V) The number of females in B is 50% of the total number of females and the number of females in A and C are equal.
Question 56
It is known the number of females who do not play sports in A is 60% the number of females who play sports in the same country. It is also given that the number of females who play sports in B is 4 more than the number of females who play sports in C.
In this scenario, which of the following options best describes the number of people in C do not play sports?
Show Answer
Solution
By referring to the previous explanation:
SF is square of composite number and NSF is 60% of SF.
By looking at the limit of TF, the only number that satisfies SF is 100.
If SF = 25, then NSF = 15.
=>TF =40 (rejected)
4^2 = 16, 60% of 16 is not an integer. Similarly, others.
Now, SF of B - SF of C = 4
=> SF of B = 72, SF of C = 68
NSM can vary from 92 to 304 because 92 already are NSF and hence, NSM in the worst case can be 0. Similarly, 68 people definitely play a sport. Therefore, the maximum possible number of persons who do not play a sport is 304 - 68 = 236.
The best choice among four is more than 91 but less than 237.
Hence, Option C is the correct answer.
correct answer:-
3
Instruction for set :
There are three countries A,B, and C. The total population of these three countries is 1440. Population of B is 40% of the total population. The total number of females is 20% less than the total number of males. There are two kinds of people: who play sports and who do not play sports.
(I) The number of males in A, B and C are all perfect squares.
(II) The number of men who do not play sports in country A is equal to 45% of the total number of females who do not play sports.
(III) The number of men who do not play sports in country B is equal to 48% of the total number of females who do not play sports.
(IV) The difference between the number of males in C and the total number of females who do not play sports is equal to 256.
(V) The number of females in B is 50% of the total number of females and the number of females in A and C are equal.
Question 57
If the governments of A,B and C respectively spend Rs.30, Rs.35, Rs.40 on every female who play sports and Rs.35, Rs. 40, Rs.0 on every male who play sports, then what is the ratio of amount spent on females and males by the governments? (Use data from the previous question)
Ratio = $$\frac{8240}{10260}$$ = $$\frac{412}{513}$$.
Hence, Option A is the right answer.
correct answer:-
1
Instruction for set :
In an academy of 900 students, a poll was conducted as to which cricket clubs the students follow regularly. There was a list of 4 top clubs A, B, C and D. The following points are known regarding the results of the poll:
1. A total of 45 students do not follow any of the above-mentioned clubs.
2. Ratio of the students who follow only A to those who follow only B to those who follow only C is 2:1:3.
3. The number of students who follow only A is 20 times the number of students who follow all the 4 clubs.
4. Any student who follows Club D also necessarily follows Club C.
5. Ratio of the students who follow only A and B to those who follow only A and C to those who follow only C and D to those who follow only B and C is 3:4:5:6. Also, it is known that the number of students who follow only A, C and D, the number of students who follow only A, B and C, and the number of students who follow only B, C and D are in the form of $$N^2+8,$$ $$(N+1)^2+8$$ and $$(N+3)^2+8$$ respectively, where N is a natural number and the sum of the number of these students is 190.
6. The number of students who are fans of C but not D is 407.
Based on the information given above, answer the questions that follow.
Question 58
How many students follow a maximum of 2 clubs?
Show Answer
Solution
This is a 4-circle Venn Diagram.
Also, point (4) mentions that anyone who follows D must necessarily follow C.
So, D is a subset of C.
The entire Venn Diagram comes out as,
From point (2), let the number of students who follow only A be 2x, the number of students who follow only B be x and the number of students who follow only C be 3x.
Also, from point (3), the number of people who followed all of A, B, C and D = $$\frac{2x}{20}=\frac{x}{10}$$
Also from point (5), let the number of students who follow only A and B be 3y, the number of students who follow only A and C be 4y, the number of students who follow only C and D be 5y and the number of students who follow only B and C be 6y. Adding the same in the Venn Diagrams, we get:
We can either expand the expression and solve the quadratic equation, or we can use hit and trial since we know that N is a natural number.
Solving, we get N = 6,
Hence, the number of students who follow only A, C and D = 44
The number of students who follow only A, B and C = 57
The number of students who follow only B, C and D = 89
Applying them in the Venn Diagram, we get,
We know that the total number of students = 900, Hence,
$$2x+x+3x+0.1x+3y+4y+5y+6y+44+57+89+45=900$$
$$6.1x+18y=665$$ .......(i)
Also, the number of students who are fans of C but not D = 407
Therefore, $$4y+3x+6y+57=407$$
$$3x+10y=350$$ .......(ii)
Solving equation 1 and 2 we get, x = 50 and y = 20
Hence the Venn Diagram comes out as,
Number of students who follow a maximum of 2 clubs = Number of students who follow no club + Number of students who follow one club + Number of students who follow 2 clubs = 45 + 100 + 50 + 150 + 60 + 80 + 100 + 120 = 705
Alternate solution using 4-set Venn Diagram:
We can denote the 4-set Venn Diagram as follows:
Also, point (4) mentions that anyone who follows D must necessarily follow C.
From point (2), let the number of students who follow only A be 2x, the number of students who follow only B be x and the number of students who follow only C be 3x.
Also, from point (3), the number of people who followed all of A, B, C and D = $$\frac{2x}{20}=\frac{x}{10}$$
Also from point (5), let the number of students who follow only A and B be 3y, the number of students who follow only A and C be 4y, the number of students who follow only C and D be 5y and the number of students who follow only B and C be 6y. Adding the same in the Venn Diagrams, we get:
We can either expand the expression and solve the quadratic equation, or we can use hit and trial since we know that N is a natural number.
Solving, we get N = 6,
Hence, the number of students who follow only A, C and D = 44
The number of students who follow only A, B and C = 57
The number of students who follow only B, C and D = 89
Applying them in the Venn Diagram, we get,
We know that the total number of students = 900, Hence,
$$2x+x+3x+0.1x+3y+4y+5y+6y+44+57+89+45=900$$
$$6.1x+18y=665$$ .......(i)
Also, the number of students who are fans of C but not D = 407
Therefore, $$4y+3x+6y+57=407$$
$$3x+10y=350$$ .......(ii)
Solving equation 1 and 2 we get, x = 50 and y = 20
Hence the Venn Diagram comes out as,
Number of students who follow a maximum of 2 clubs = Number of students who follow no club + Number of students who follow one club + Number of students who follow 2 clubs = 45 + 100 + 50 + 150 + 60 + 80 + 100 + 120 = 705
correct answer:-
705
Instruction for set :
In an academy of 900 students, a poll was conducted as to which cricket clubs the students follow regularly. There was a list of 4 top clubs A, B, C and D. The following points are known regarding the results of the poll:
1. A total of 45 students do not follow any of the above-mentioned clubs.
2. Ratio of the students who follow only A to those who follow only B to those who follow only C is 2:1:3.
3. The number of students who follow only A is 20 times the number of students who follow all the 4 clubs.
4. Any student who follows Club D also necessarily follows Club C.
5. Ratio of the students who follow only A and B to those who follow only A and C to those who follow only C and D to those who follow only B and C is 3:4:5:6. Also, it is known that the number of students who follow only A, C and D, the number of students who follow only A, B and C, and the number of students who follow only B, C and D are in the form of $$N^2+8,$$ $$(N+1)^2+8$$ and $$(N+3)^2+8$$ respectively, where N is a natural number and the sum of the number of these students is 190.
6. The number of students who are fans of C but not D is 407.
Based on the information given above, answer the questions that follow.
Question 59
How many students follow only C and D?
Show Answer
Solution
This is a 4-circle Venn Diagram.
Also, point (4) mentions that anyone who follows D must necessarily follow C.
So, D is a subset of C.
The entire Venn Diagram comes out as,
From point (2), let the number of students who follow only A be 2x, the number of students who follow only B be x and the number of students who follow only C be 3x.
Also, from point (3), the number of people who followed all of A, B, C and D = $$\frac{2x}{20}=\frac{x}{10}$$
Also from point (5), let the number of students who follow only A and B be 3y, the number of students who follow only A and C be 4y, the number of students who follow only C and D be 5y and the number of students who follow only B and C be 6y. Adding the same in the Venn Diagrams, we get:
We can either expand the expression and solve the quadratic equation, or we can use hit and trial since we know that N is a natural number.
Solving, we get N = 6,
Hence, the number of students who follow only A, C and D = 44
The number of students who follow only A, B and C = 57
The number of students who follow only B, C and D = 89
Applying them in the Venn Diagram, we get,
We know that the total number of students = 900, Hence,
$$2x+x+3x+0.1x+3y+4y+5y+6y+44+57+89+45=900$$
$$6.1x+18y=665$$ .......(i)
Also, the number of students who are fans of C but not D = 407
Therefore, $$4y+3x+6y+57=407$$
$$3x+10y=350$$ .......(ii)
Solving equation 1 and 2 we get, x = 50 and y = 20
Hence the Venn Diagram comes out as,
The number of students who follow only C and D is 100.
Alternate solution using 4-set Venn Diagram:
We can denote the 4-set Venn Diagram as follows:
Also, point (4) mentions that anyone who follows D must necessarily follow C.
From point (2), let the number of students who follow only A be 2x, the number of students who follow only B be x and the number of students who follow only C be 3x.
Also, from point (3), the number of people who followed all of A, B, C and D = \frac{2x}{20}=\frac{x}{10}202
x
=10
x
Also from point (5), let the number of students who follow only A and B be 3y, the number of students who follow only A and C be 4y, the number of students who follow only C and D be 5y and the number of students who follow only B and C be 6y. Adding the same in the Venn Diagrams, we get:
From point (5)
N^2+8+\left(N+1\right)^2+8+\left(N+3\right)^2+8=190
N
2+8+(
N
+1)2+8+(
N
+3)2+8=190
N^2+\left(N+1\right)^2+\left(N+3\right)^2=166
N
2+(
N
+1)2+(
N
+3)2=166
We can either expand the expression and solve the quadratic equation, or we can use hit and trial since we know that N is a natural number.
Solving, we get N = 6,
Hence, the number of students who follow only A, C and D = 44
The number of students who follow only A, B and C = 57
The number of students who follow only B, C and D = 89
Applying them in the Venn Diagram, we get,
We know that the total number of students = 900, Hence,
2x+x+3x+0.1x+3y+4y+5y+6y+44+57+89+45=9002
x
+
x
+3
x
+0.1
x
+3
y
+4
y
+5
y
+6
y
+44+57+89+45=900
6.1x+18y=6656.1
x
+18
y
=665 .......(i)
Also, the number of students who are fans of C but not D = 407
Therefore, 4y+3x+6y+57=4074
y
+3
x
+6
y
+57=407
3x+10y=3503
x
+10
y
=350 .......(ii)
Solving equation 1 and 2 we get, x = 50 and y = 20
Hence the Venn Diagram comes out as,
The number of students who follow only C and D is 100.
correct answer:-
100
Instruction for set :
In an academy of 900 students, a poll was conducted as to which cricket clubs the students follow regularly. There was a list of 4 top clubs A, B, C and D. The following points are known regarding the results of the poll:
1. A total of 45 students do not follow any of the above-mentioned clubs.
2. Ratio of the students who follow only A to those who follow only B to those who follow only C is 2:1:3.
3. The number of students who follow only A is 20 times the number of students who follow all the 4 clubs.
4. Any student who follows Club D also necessarily follows Club C.
5. Ratio of the students who follow only A and B to those who follow only A and C to those who follow only C and D to those who follow only B and C is 3:4:5:6. Also, it is known that the number of students who follow only A, C and D, the number of students who follow only A, B and C, and the number of students who follow only B, C and D are in the form of $$N^2+8,$$ $$(N+1)^2+8$$ and $$(N+3)^2+8$$ respectively, where N is a natural number and the sum of the number of these students is 190.
6. The number of students who are fans of C but not D is 407.
Based on the information given above, answer the questions that follow.
Question 60
Find the number of students who follow a minimum of 2 clubs?
Show Answer
Solution
This is a 4-circle Venn Diagram.
Also, point (4) mentions that anyone who follows D must necessarily follow C.
So, D is a subset of C.
The entire Venn Diagram comes out as,
From point (2), let the number of students who follow only A be 2x, the number of students who follow only B be x and the number of students who follow only C be 3x.
Also, from point (3), the number of people who followed all of A, B, C and D = $$\frac{2x}{20}=\frac{x}{10}$$
Also from point (5), let the number of students who follow only A and B be 3y, the number of students who follow only A and C be 4y, the number of students who follow only C and D be 5y and the number of students who follow only B and C be 6y. Adding the same in the Venn Diagrams, we get:
We can either expand the expression and solve the quadratic equation, or we can use hit and trial since we know that N is a natural number.
Solving, we get N = 6,
Hence, the number of students who follow only A, C and D = 44
The number of students who follow only A, B and C = 57
The number of students who follow only B, C and D = 89
Applying them in the Venn Diagram, we get,
We know that the total number of students = 900, Hence,
$$2x+x+3x+0.1x+3y+4y+5y+6y+44+57+89+45=900$$
$$6.1x+18y=665$$ .......(i)
Also, the number of students who are fans of C but not D = 407
Therefore, $$4y+3x+6y+57=407$$
$$3x+10y=350$$ .......(ii)
Solving equation 1 and 2 we get, x = 50 and y = 20
Hence the Venn Diagram comes out as,
The number of people who follow a minimum of 2 clubs = Total number of students - Number of students who follow zero club - Number of students who follow one club = 900 - 45 - 100 - 50 - 150 = 555.
Alternate solution using 4-set Venn Diagram:
We can denote the 4-set Venn Diagram as follows:
Also, point (4) mentions that anyone who follows D must necessarily follow C.
From point (2), let the number of students who follow only A be 2x, the number of students who follow only B be x and the number of students who follow only C be 3x.
Also, from point (3), the number of people who followed all of A, B, C and D = \frac{2x}{20}=\frac{x}{10}202
x
=10
x
Also from point (5), let the number of students who follow only A and B be 3y, the number of students who follow only A and C be 4y, the number of students who follow only C and D be 5y and the number of students who follow only B and C be 6y. Adding the same in the Venn Diagrams, we get:
From point (5)
N^2+8+\left(N+1\right)^2+8+\left(N+3\right)^2+8=190
N
2+8+(
N
+1)2+8+(
N
+3)2+8=190
N^2+\left(N+1\right)^2+\left(N+3\right)^2=166
N
2+(
N
+1)2+(
N
+3)2=166
We can either expand the expression and solve the quadratic equation, or we can use hit and trial since we know that N is a natural number.
Solving, we get N = 6,
Hence, the number of students who follow only A, C and D = 44
The number of students who follow only A, B and C = 57
The number of students who follow only B, C and D = 89
Applying them in the Venn Diagram, we get,
We know that the total number of students = 900, Hence,
2x+x+3x+0.1x+3y+4y+5y+6y+44+57+89+45=9002
x
+
x
+3
x
+0.1
x
+3
y
+4
y
+5
y
+6
y
+44+57+89+45=900
6.1x+18y=6656.1
x
+18
y
=665 .......(i)
Also, the number of students who are fans of C but not D = 407
Therefore, 4y+3x+6y+57=4074
y
+3
x
+6
y
+57=407
3x+10y=3503
x
+10
y
=350 .......(ii)
Solving equation 1 and 2 we get, x = 50 and y = 20
Hence the Venn Diagram comes out as,
The number of people who follow a minimum of 2 clubs = Total number of students - Number of students who follow zero club - Number of students who follow one club = 900 - 45 - 100 - 50 - 150 = 555.
In an academy of 900 students, a poll was conducted as to which cricket clubs the students follow regularly. There was a list of 4 top clubs A, B, C and D. The following points are known regarding the results of the poll:
1. A total of 45 students do not follow any of the above-mentioned clubs.
2. Ratio of the students who follow only A to those who follow only B to those who follow only C is 2:1:3.
3. The number of students who follow only A is 20 times the number of students who follow all the 4 clubs.
4. Any student who follows Club D also necessarily follows Club C.
5. Ratio of the students who follow only A and B to those who follow only A and C to those who follow only C and D to those who follow only B and C is 3:4:5:6. Also, it is known that the number of students who follow only A, C and D, the number of students who follow only A, B and C, and the number of students who follow only B, C and D are in the form of $$N^2+8,$$ $$(N+1)^2+8$$ and $$(N+3)^2+8$$ respectively, where N is a natural number and the sum of the number of these students is 190.
6. The number of students who are fans of C but not D is 407.
Based on the information given above, answer the questions that follow.
Question 61
In the Business Premier League, Club B performed miserably and as a result, all those who were following Club B and some other club(s), stopped following Club B and continued to follow the other club(s), and those who followed only Club B started following all the 3 remaining clubs. How many students now follow a minimum of 2 clubs?
Show Answer
Solution
This is a 4-circle Venn Diagram.
Also, point (4) mentions that anyone who follows D must necessarily follow C.
So, D is a subset of C.
The entire Venn Diagram comes out as,
From point (2), let the number of students who follow only A be 2x, the number of students who follow only B be x and the number of students who follow only C be 3x.
Also, from point (3), the number of people who followed all of A, B, C and D = $$\frac{2x}{20}=\frac{x}{10}$$
Also from point (5), let the number of students who follow only A and B be 3y, the number of students who follow only A and C be 4y, the number of students who follow only C and D be 5y and the number of students who follow only B and C be 6y. Adding the same in the Venn Diagrams, we get:
We can either expand the expression and solve the quadratic equation, or we can use hit and trial since we know that N is a natural number.
Solving, we get N = 6,
Hence, the number of students who follow only A, C and D = 44
The number of students who follow only A, B and C = 57
The number of students who follow only B, C and D = 89
Applying them in the Venn Diagram, we get,
We know that the total number of students = 900, Hence,
$$2x+x+3x+0.1x+3y+4y+5y+6y+44+57+89+45=900$$
$$6.1x+18y=665$$ .......(i)
Also, the number of students who are fans of C but not D = 407
Therefore, $$4y+3x+6y+57=407$$
$$3x+10y=350$$ .......(ii)
Solving equation 1 and 2 we get, x = 50 and y = 20
Hence the Venn Diagram comes out as,
As per the question, no student follows Club B any longer and also, those 50 students who followed only B started following all 3 remaining clubs. Hence the new Venn Diagram is as follows:
Number of students who follow a minimum of 2 clubs = Number of students who follow 2 clubs + Number of students who follow 3 clubs = 80 + 57 + 44 + 50 + 5 + 100 + 89 = 425 students.
Alternate solution using 4-set Venn Diagram:
We can denote the 4-set Venn Diagram as follows:
Also, point (4) mentions that anyone who follows D must necessarily follow C.
From point (2), let the number of students who follow only A be 2x, the number of students who follow only B be x and the number of students who follow only C be 3x.
Also, from point (3), the number of people who followed all of A, B, C and D = \frac{2x}{20}=\frac{x}{10}202
x
=10
x
Also from point (5), let the number of students who follow only A and B be 3y, the number of students who follow only A and C be 4y, the number of students who follow only C and D be 5y and the number of students who follow only B and C be 6y. Adding the same in the Venn Diagrams, we get:
From point (5)
N^2+8+\left(N+1\right)^2+8+\left(N+3\right)^2+8=190
N
2+8+(
N
+1)2+8+(
N
+3)2+8=190
N^2+\left(N+1\right)^2+\left(N+3\right)^2=166
N
2+(
N
+1)2+(
N
+3)2=166
We can either expand the expression and solve the quadratic equation, or we can use hit and trial since we know that N is a natural number.
Solving, we get N = 6,
Hence, the number of students who follow only A, C and D = 44
The number of students who follow only A, B and C = 57
The number of students who follow only B, C and D = 89
Applying them in the Venn Diagram, we get,
We know that the total number of students = 900, Hence,
2x+x+3x+0.1x+3y+4y+5y+6y+44+57+89+45=9002
x
+
x
+3
x
+0.1
x
+3
y
+4
y
+5
y
+6
y
+44+57+89+45=900
6.1x+18y=6656.1
x
+18
y
=665 .......(i)
Also, the number of students who are fans of C but not D = 407
Therefore, 4y+3x+6y+57=4074
y
+3
x
+6
y
+57=407
3x+10y=3503
x
+10
y
=350 .......(ii)
Solving equation 1 and 2 we get, x = 50 and y = 20
Hence the Venn Diagram comes out as,
As per the question, no student follows Club B any longer and also, those 50 students who followed only B started following all 3 remaining clubs. Hence the new Venn Diagram is as follows:
Number of students who follow a minimum of 2 clubs = Number of students who follow 2 clubs + Number of students who follow 3 clubs = 137 + 99 + 189 = 425 students.
correct answer:-
1
Instruction for set :
Six friends - Aman, Bimal, Chetan, Dinesh, Eshan and Farah joined online coaching to prepare for CAT. Each of them graduated in a different stream among Computer Science, Chemistry, Biotechnology, Thermal Engg, Physics and Geography. Each of them owns a different car among Maserati, Lancer, Elantra, Polo, Audi and McLaren. Also, each of them lives in a different city among Goa, Bhopal, Unnao, Hugli, Delhi and Faridabad.
Further, some additional information is known to us
1) Neither Aman nor Eshan graduated in Biotechnology or Chemistry. Neither of the two owns Elantra or lives in Hugli.
2) Either Chetan or Farah lives in Unnao, and neither of the two graduated in Computer Science or Chemistry.
3) Neither Bimal nor Dinesh owns McLaren or Elantra, also neither of them graduated in Computer Science or Geography.
4) Neither Bimal nor Eshan graduated in Physics or Thermal Engg, and neither of them owns Audi or lives in Bhopal.
5) Either Chetan or Farah owns Maserati. Also, the owner of Maserati didn't graduate in Thermal Engg.
6) The one who owns Lancer graduated in Biotechnology and the one who owns McLaren graduated in Physics.
7) The one who lives in Delhi graduated in Chemistry and the one who lives in Goa graduated in Thermal Engg.
Question 62
Which among the followings is a correct match?
Show Answer
Solution
Let us start by noting down the conditions.
1) Neither Aman nor Eshan graduated in Biotechnology or Chemistry. Neither of the two owns Elantra or lives in Hugli.
2) Either Chetan or Farah lives in Unnao, and neither of the two graduated in Computer Science or Chemistry.
3) Neither Bimal nor Dinesh owns McLaren or Elantra, also neither of them graduated in Computer Science or Geography.
4) Neither Bimal nor Eshan graduated in Physics or Thermal Engg, and neither of them owns Audi or lives in Bhopal.
5) Either Chetan or Farah owns Maserati.
Either Chetan or Farah should be from Unnao. Also, one of them should own a Maserati and the other should own Elantra.
=> Neither Chetan nor Farah owns McLaren or Lancer and hence, neither of them should have graduated in Biotechnology or Physics. Since Aman has not graduated in Biotechnology, he cannot be the owner of Lancer. Eshan cannot be the owner of Lancer. Therefore, Bimal should have graduated in Biotechnology and should own Lancer.
Dinesh is the only person who could have graduated in Chemistry (since Bimal has graduated in Biotechnology). Also, Dinesh should be from Delhi (given in the set).
Eshan is not from Delhi, Hugli, Bhopal, or Unnao. Also, Eshan did not graduate in thermal engineering . Eshan is not from Goa (since the person from Goa graduated in thermal). Therefore, Eshan should be from Faridabad. Bimal should be from Hugli since he is not from Bhopal, Unnao, Faridabad, Delhi, and Goa (The person from Goa graduated in thermal engineering). Bimal, Chetan, and Farah do not own a McLaren. The person who owns McLaren graduated in Physics and Eshan has graduated in Computer Science. Therefore, Eshan cannot be the person who owns McLaren. Dinesh graduated in Chemistry and hence, we can eliminate Dinesh as well. Therefore, Aman should have graduated in Physics and should own a McLaren.
Aman is not from Goa (since the person from Goa graduated in Thermal Engineering). Therefore, Aman should be from Bhopal. We know that Chetan and Farah own Elantra and Maserati (in any order). Therefore, Dinesh and Eshan should own Polo and Audi (in any order). Since we know that Eshan does not own Audi, Eshan should own Polo and Dinesh should own Audi.
Only option C gives the correct combination and hence, it is the right answer.
correct answer:-
3
Instruction for set :
Six friends - Aman, Bimal, Chetan, Dinesh, Eshan and Farah joined online coaching to prepare for CAT. Each of them graduated in a different stream among Computer Science, Chemistry, Biotechnology, Thermal Engg, Physics and Geography. Each of them owns a different car among Maserati, Lancer, Elantra, Polo, Audi and McLaren. Also, each of them lives in a different city among Goa, Bhopal, Unnao, Hugli, Delhi and Faridabad.
Further, some additional information is known to us
1) Neither Aman nor Eshan graduated in Biotechnology or Chemistry. Neither of the two owns Elantra or lives in Hugli.
2) Either Chetan or Farah lives in Unnao, and neither of the two graduated in Computer Science or Chemistry.
3) Neither Bimal nor Dinesh owns McLaren or Elantra, also neither of them graduated in Computer Science or Geography.
4) Neither Bimal nor Eshan graduated in Physics or Thermal Engg, and neither of them owns Audi or lives in Bhopal.
5) Either Chetan or Farah owns Maserati. Also, the owner of Maserati didn't graduate in Thermal Engg.
6) The one who owns Lancer graduated in Biotechnology and the one who owns McLaren graduated in Physics.
7) The one who lives in Delhi graduated in Chemistry and the one who lives in Goa graduated in Thermal Engg.
Question 63
Who graduated in Chemistry?
Show Answer
Solution
Let us start by noting down the conditions.
1) Neither Aman nor Eshan graduated in Biotechnology or Chemistry. Neither of the two owns Elantra or lives in Hugli.
2) Either Chetan or Farah lives in Unnao, and neither of the two graduated in Computer Science or Chemistry.
3) Neither Bimal nor Dinesh owns McLaren or Elantra, also neither of them graduated in Computer Science or Geography.
4) Neither Bimal nor Eshan graduated in Physics or Thermal Engg, and neither of them owns Audi or lives in Bhopal.
5) Either Chetan or Farah owns Maserati.
Either Chetan or Farah should be from Unnao. Also, one of them should own a Maserati and the other should own Elantra.
=> Neither Chetan nor Farah owns McLaren or Lancer and hence, neither of them should have graduated in Biotechnology or Physics. Since Aman has not graduated in Biotechnology, he cannot be the owner of Lancer. Eshan cannot be the owner of Lancer. Therefore, Bimal should have graduated in Biotechnology and should own Lancer.
Dinesh is the only person who could have graduated in Chemistry (since Bimal has graduated in Biotechnology). Also, Dinesh should be from Delhi (given in the set).
Eshan is not from Delhi, Hugli, Bhopal, or Unnao. Also, Eshan did not graduate in thermal engineering . Eshan is not from Goa (since the person from Goa graduated in thermal). Therefore, Eshan should be from Faridabad. Bimal should be from Hugli since he is not from Bhopal, Unnao, Faridabad, Delhi, and Goa (The person from Goa graduated in thermal engineering). Bimal, Chetan, and Farah do not own a McLaren. The person who owns McLaren graduated in Physics and Eshan has graduated in Computer Science. Therefore, Eshan cannot be the person who owns McLaren. Dinesh graduated in Chemistry and hence, we can eliminate Dinesh as well. Therefore, Aman should have graduated in Physics and should own a McLaren.
Aman is not from Goa (since the person from Goa graduated in Thermal Engineering). Therefore, Aman should be from Bhopal. We know that Chetan and Farah own Elantra and Maserati (in any order). Therefore, Dinesh and Eshan should own Polo and Audi (in any order). Since we know that Eshan does not own Audi, Eshan should own Polo and Dinesh should own Audi.
The owner of Audi graduated in Chemistry. Therefore, option A is the right answer.
correct answer:-
1
Instruction for set :
Six friends - Aman, Bimal, Chetan, Dinesh, Eshan and Farah joined online coaching to prepare for CAT. Each of them graduated in a different stream among Computer Science, Chemistry, Biotechnology, Thermal Engg, Physics and Geography. Each of them owns a different car among Maserati, Lancer, Elantra, Polo, Audi and McLaren. Also, each of them lives in a different city among Goa, Bhopal, Unnao, Hugli, Delhi and Faridabad.
Further, some additional information is known to us
1) Neither Aman nor Eshan graduated in Biotechnology or Chemistry. Neither of the two owns Elantra or lives in Hugli.
2) Either Chetan or Farah lives in Unnao, and neither of the two graduated in Computer Science or Chemistry.
3) Neither Bimal nor Dinesh owns McLaren or Elantra, also neither of them graduated in Computer Science or Geography.
4) Neither Bimal nor Eshan graduated in Physics or Thermal Engg, and neither of them owns Audi or lives in Bhopal.
5) Either Chetan or Farah owns Maserati. Also, the owner of Maserati didn't graduate in Thermal Engg.
6) The one who owns Lancer graduated in Biotechnology and the one who owns McLaren graduated in Physics.
7) The one who lives in Delhi graduated in Chemistry and the one who lives in Goa graduated in Thermal Engg.
Question 64
Which of the following statements are definitely false?
(I). Computer science graduate owns Polo.
(II). Geography graduate owns Elantra.
(III). Biotechnology graduate owns Audi.
(IV). The one who owns Lancer lives in Faridabad.
Show Answer
Solution
Let us start by noting down the conditions.
1) Neither Aman nor Eshan graduated in Biotechnology or Chemistry. Neither of the two owns Elantra or lives in Hugli.
2) Either Chetan or Farah lives in Unnao, and neither of the two graduated in Computer Science or Chemistry.
3) Neither Bimal nor Dinesh owns McLaren or Elantra, also neither of them graduated in Computer Science or Geography.
4) Neither Bimal nor Eshan graduated in Physics or Thermal Engg, and neither of them owns Audi or lives in Bhopal.
5) Either Chetan or Farah owns Maserati.
Either Chetan or Farah should be from Unnao. Also, one of them should own a Maserati and the other should own Elantra.
=> Neither Chetan nor Farah owns McLaren or Lancer and hence, neither of them should have graduated in Biotechnology or Physics. Since Aman has not graduated in Biotechnology, he cannot be the owner of Lancer. Eshan cannot be the owner of Lancer. Therefore, Bimal should have graduated in Biotechnology and should own Lancer.
Dinesh is the only person who could have graduated in Chemistry (since Bimal has graduated in Biotechnology). Also, Dinesh should be from Delhi (given in the set).
Eshan is not from Delhi, Hugli, Bhopal, or Unnao. Also, Eshan did not graduate in thermal engineering . Eshan is not from Goa (since the person from Goa graduated in thermal). Therefore, Eshan should be from Faridabad. Bimal should be from Hugli since he is not from Bhopal, Unnao, Faridabad, Delhi, and Goa (The person from Goa graduated in thermal engineering). Bimal, Chetan, and Farah do not own a McLaren. The person who owns McLaren graduated in Physics and Eshan has graduated in Computer Science. Therefore, Eshan cannot be the person who owns McLaren. Dinesh graduated in Chemistry and hence, we can eliminate Dinesh as well. Therefore, Aman should have graduated in Physics and should own a McLaren.
Aman is not from Goa (since the person from Goa graduated in Thermal Engineering). Therefore, Aman should be from Bhopal. We know that Chetan and Farah own Elantra and Maserati (in any order). Therefore, Dinesh and Eshan should own Polo and Audi (in any order). Since we know that Eshan does not own Audi, Eshan should own Polo and Dinesh should own Audi.
The first statement is correct (Computer Science - Polo).
The second statement is false since it has been given that the person who owns Maserati did not graduate in thermal engineering. Therefore, the person who graduated in geography owns Maserati.
The third and fourth statements are false.
Statements II, III, and IV are false. Therefore, option D is the right answer.
correct answer:-
4
Instruction for set :
Six friends - Aman, Bimal, Chetan, Dinesh, Eshan and Farah joined online coaching to prepare for CAT. Each of them graduated in a different stream among Computer Science, Chemistry, Biotechnology, Thermal Engg, Physics and Geography. Each of them owns a different car among Maserati, Lancer, Elantra, Polo, Audi and McLaren. Also, each of them lives in a different city among Goa, Bhopal, Unnao, Hugli, Delhi and Faridabad.
Further, some additional information is known to us
1) Neither Aman nor Eshan graduated in Biotechnology or Chemistry. Neither of the two owns Elantra or lives in Hugli.
2) Either Chetan or Farah lives in Unnao, and neither of the two graduated in Computer Science or Chemistry.
3) Neither Bimal nor Dinesh owns McLaren or Elantra, also neither of them graduated in Computer Science or Geography.
4) Neither Bimal nor Eshan graduated in Physics or Thermal Engg, and neither of them owns Audi or lives in Bhopal.
5) Either Chetan or Farah owns Maserati. Also, the owner of Maserati didn't graduate in Thermal Engg.
6) The one who owns Lancer graduated in Biotechnology and the one who owns McLaren graduated in Physics.
7) The one who lives in Delhi graduated in Chemistry and the one who lives in Goa graduated in Thermal Engg.
Question 65
Which among the following statement is definitely true?
Show Answer
Solution
Let us start by noting down the conditions.
1) Neither Aman nor Eshan graduated in Biotechnology or Chemistry. Neither of the two owns Elantra or lives in Hugli.
2) Either Chetan or Farah lives in Unnao, and neither of the two graduated in Computer Science or Chemistry.
3) Neither Bimal nor Dinesh owns McLaren or Elantra, also neither of them graduated in Computer Science or Geography.
4) Neither Bimal nor Eshan graduated in Physics or Thermal Engg, and neither of them owns Audi or lives in Bhopal.
5) Either Chetan or Farah owns Maserati.
Either Chetan or Farah should be from Unnao. Also, one of them should own a Maserati and the other should own Elantra.
=> Neither Chetan nor Farah owns McLaren or Lancer and hence, neither of them should have graduated in Biotechnology or Physics. Since Aman has not graduated in Biotechnology, he cannot be the owner of Lancer. Eshan cannot be the owner of Lancer. Therefore, Bimal should have graduated in Biotechnology and should own Lancer.
Dinesh is the only person who could have graduated in Chemistry (since Bimal has graduated in Biotechnology). Also, Dinesh should be from Delhi (given in the set).
Eshan is not from Delhi, Hugli, Bhopal, or Unnao. Also, Eshan did not graduate in thermal engineering . Eshan is not from Goa (since the person from Goa graduated in thermal). Therefore, Eshan should be from Faridabad. Bimal should be from Hugli since he is not from Bhopal, Unnao, Faridabad, Delhi, and Goa (The person from Goa graduated in thermal engineering). Bimal, Chetan, and Farah do not own a McLaren. The person who owns McLaren graduated in Physics and Eshan has graduated in Computer Science. Therefore, Eshan cannot be the person who owns McLaren. Dinesh graduated in Chemistry and hence, we can eliminate Dinesh as well. Therefore, Aman should have graduated in Physics and should own a McLaren.
Aman is not from Goa (since the person from Goa graduated in Thermal Engineering). Therefore, Aman should be from Bhopal. We know that Chetan and Farah own Elantra and Maserati (in any order). Therefore, Dinesh and Eshan should own Polo and Audi (in any order). Since we know that Eshan does not own Audi, Eshan should own Polo and Dinesh should own Audi.
Only option B can be said to be definitely true. The other 3 statements are either false or only partially correct. Hence, option B is the right answer.
correct answer:-
2
Instruction for set :
A visa processing office (VPO) accepts visa applications in four categories - US, UK, Schengen, and Others. The applications are scheduled for processing in twenty 15- minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.
There are ten counters in the office, four dedicated to US applications, and two each for UK applications, Schengen applications and Others applications. Applicants are called in for processing sequentially on a first-come-first-served basis whenever a counter gets freed for their category. The processing time for an application is the same within each category. But it may vary across the categories. Each US and UK application requires 10 minutes of processing time. Depending on the number of applications in a category and time required to process an application for that category, it is possible that an applicant for a slot may be processed later.
On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15 am slot but entered the VPO at 9:20 am. When they entered the office, exactly six out of the ten counters were either processing applications, or had finished processing one and ready to start processing the next.
Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category.
The following additional information is known about that day.
1. All slots were full.
2. The number of US applications was the same in all the slots. The same was true for the other three categories.
3. 50% of the applications were US applications.
4. All applicants except Ira, Vijay and Nandini arrived on time.
5. Vijay was called to a counter at 9:25 am.
Question 66
How many UK applications were scheduled on that day?
A visa processing office (VPO) accepts visa applications in four categories - US, UK, Schengen, and Others. The applications are scheduled for processing in twenty 15- minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.
There are ten counters in the office, four dedicated to US applications, and two each for UK applications, Schengen applications and Others applications. Applicants are called in for processing sequentially on a first-come-first-served basis whenever a counter gets freed for their category. The processing time for an application is the same within each category. But it may vary across the categories. Each US and UK application requires 10 minutes of processing time. Depending on the number of applications in a category and time required to process an application for that category, it is possible that an applicant for a slot may be processed later.
On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15 am slot but entered the VPO at 9:20 am. When they entered the office, exactly six out of the ten counters were either processing applications, or had finished processing one and ready to start processing the next.
Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category.
The following additional information is known about that day.
1. All slots were full.
2. The number of US applications was the same in all the slots. The same was true for the other three categories.
3. 50% of the applications were US applications.
4. All applicants except Ira, Vijay and Nandini arrived on time.
5. Vijay was called to a counter at 9:25 am.
Question 67
What is the maximum possible value of the total time (in minutes, nearest to its integer value) required to process all applications in the Others category on that day?
A visa processing office (VPO) accepts visa applications in four categories - US, UK, Schengen, and Others. The applications are scheduled for processing in twenty 15- minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.
There are ten counters in the office, four dedicated to US applications, and two each for UK applications, Schengen applications and Others applications. Applicants are called in for processing sequentially on a first-come-first-served basis whenever a counter gets freed for their category. The processing time for an application is the same within each category. But it may vary across the categories. Each US and UK application requires 10 minutes of processing time. Depending on the number of applications in a category and time required to process an application for that category, it is possible that an applicant for a slot may be processed later.
On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15 am slot but entered the VPO at 9:20 am. When they entered the office, exactly six out of the ten counters were either processing applications, or had finished processing one and ready to start processing the next.
Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category.
The following additional information is known about that day.
1. All slots were full.
2. The number of US applications was the same in all the slots. The same was true for the other three categories.
3. 50% of the applications were US applications.
4. All applicants except Ira, Vijay and Nandini arrived on time.
5. Vijay was called to a counter at 9:25 am.
Question 68
Which of the following is the closest to the time when Nandini’s application process got over?
A visa processing office (VPO) accepts visa applications in four categories - US, UK, Schengen, and Others. The applications are scheduled for processing in twenty 15- minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.
There are ten counters in the office, four dedicated to US applications, and two each for UK applications, Schengen applications and Others applications. Applicants are called in for processing sequentially on a first-come-first-served basis whenever a counter gets freed for their category. The processing time for an application is the same within each category. But it may vary across the categories. Each US and UK application requires 10 minutes of processing time. Depending on the number of applications in a category and time required to process an application for that category, it is possible that an applicant for a slot may be processed later.
On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15 am slot but entered the VPO at 9:20 am. When they entered the office, exactly six out of the ten counters were either processing applications, or had finished processing one and ready to start processing the next.
Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category.
The following additional information is known about that day.
1. All slots were full.
2. The number of US applications was the same in all the slots. The same was true for the other three categories.
3. 50% of the applications were US applications.
4. All applicants except Ira, Vijay and Nandini arrived on time.
5. Vijay was called to a counter at 9:25 am.
A visa processing office (VPO) accepts visa applications in four categories - US, UK, Schengen, and Others. The applications are scheduled for processing in twenty 15- minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.
There are ten counters in the office, four dedicated to US applications, and two each for UK applications, Schengen applications and Others applications. Applicants are called in for processing sequentially on a first-come-first-served basis whenever a counter gets freed for their category. The processing time for an application is the same within each category. But it may vary across the categories. Each US and UK application requires 10 minutes of processing time. Depending on the number of applications in a category and time required to process an application for that category, it is possible that an applicant for a slot may be processed later.
On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15 am slot but entered the VPO at 9:20 am. When they entered the office, exactly six out of the ten counters were either processing applications, or had finished processing one and ready to start processing the next.
Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category.
The following additional information is known about that day.
1. All slots were full.
2. The number of US applications was the same in all the slots. The same was true for the other three categories.
3. 50% of the applications were US applications.
4. All applicants except Ira, Vijay and Nandini arrived on time.
5. Vijay was called to a counter at 9:25 am.
Question 70
When did the application processing for all US applicants get over on that day?
Read the following information carefully and answer the questions which follow.
Zcar, a car magazine ranked five cars - 7S, Veetle, A6, Q8 and Boyce on the basis of Power, Control, Suspension, Storage and Interiors. In each parameter the magazine ranked the cars from 1 to 5. A lower number indicates a better rank. No two cars got the same rank in any of the parameters.
1. Veetle was ranked worse than 7S in all the parameters except Storage.
2. Boyce was ranked fourth in control and Q8 was ranked second in two parameters.
3. Q8 was ranked better than 7S in Power.
4. Boyce was ranked fifth in Storage but was ranked better than Q8 and 7S in Power and Suspension.
5. Q8 ranked neither first nor last in Interiors.
6. 7S was ranked better in Control than at least three cars.
7. No car received the same rank in more than two parameters.
8. Veetle did not receive the same rank in any two parameters.
9. Every car was ranked third in at least one parameter and exactly two cars were not ranked first in any parameters.
10. Boyce was not ranked first in Power and Suspension.
Question 71
What is Q8’s rank in Power?
Show Answer
Solution
To solve this question, we will first draw a 5X5 table with the given parameters and fill the given details.
From 4, Boyce was ranked fifth in storage.
From 2, Boyce was ranked fourth in control.
From 8 and 1, Veetle did not receive same rank in any two parameters and Veetle was ranked worse than 7S in all parameters except Storage. Hence, Veetle must be ranked 1 in Storage.
From 6, 7S was ranked first or second in Control.
From 4, Boyce was ranked better than Q8 and 7S in Power and Suspension.
Also, from 3, Q8 was ranked better than 7S in Power.
Since 7S cannot be 5 in Power, the ranks of Boyce, Q8, 7S are 2, 3 and 4 respectively.
Since 7S is ranked fourth, Veetle should be ranked fifth in Power.
A6 has to be ranked first in Power.
7S can neither be fourth or fifth in suspension as Vettle is already fifth in Power. Which implies Boyce has to be second in Suspension.
Veetle has to be fourth in suspension and Q8 has to be fifth in Suspension.
A6 has to be first in Suspension.
Since every car has to be third in at least one parameter, Boyce has to be third in Interiors.
Since Veetle cannot be third in Interiors, it has to be third in Control. Veetle has to be second in Interiors.
7S has to be first in Interiors.
Since Q8 was second in two parameters, Q8 has to be second in both Control and Storage. Which implies it has to be fourth in Interiors.
A6 has to be fifth in Interiors.
7S has to be first in Control.
A6 has to be fifth in Control. Hence, A6 has to be third in Storage.
7S has to be fourth in Storage.
correct answer:-
1
Instruction for set :
Read the following information carefully and answer the questions which follow.
Zcar, a car magazine ranked five cars - 7S, Veetle, A6, Q8 and Boyce on the basis of Power, Control, Suspension, Storage and Interiors. In each parameter the magazine ranked the cars from 1 to 5. A lower number indicates a better rank. No two cars got the same rank in any of the parameters.
1. Veetle was ranked worse than 7S in all the parameters except Storage.
2. Boyce was ranked fourth in control and Q8 was ranked second in two parameters.
3. Q8 was ranked better than 7S in Power.
4. Boyce was ranked fifth in Storage but was ranked better than Q8 and 7S in Power and Suspension.
5. Q8 ranked neither first nor last in Interiors.
6. 7S was ranked better in Control than at least three cars.
7. No car received the same rank in more than two parameters.
8. Veetle did not receive the same rank in any two parameters.
9. Every car was ranked third in at least one parameter and exactly two cars were not ranked first in any parameters.
10. Boyce was not ranked first in Power and Suspension.
Question 72
Which car has the same rank in Power as Q8 has in storage?
Show Answer
Solution
To solve this question, we will first draw a 5X5 table with the given parameters and fill the given details.
From 4, Boyce was ranked fifth in storage.
From 2, Boyce was ranked fourth in control.
From 8 and 1, Veetle did not receive same rank in any two parameters and Veetle was ranked worse than 7S in all parameters except Storage. Hence, Veetle must be ranked 1 in Storage.
From 6, 7S was ranked first or second in Control.
From 4, Boyce was ranked better than Q8 and 7S in Power and Suspension.
Also, from 3, Q8 was ranked better than 7S in Power.
Since 7S cannot be 5 in Power, the ranks of Boyce, Q8, 7S are 2, 3 and 4 respectively.
Since 7S is ranked fourth, Veetle should be ranked fifth in Power.
A6 has to be ranked first in Power.
7S can neither be fourth or fifth in suspension as Vettle is already fifth in Power. Which implies Boyce has to be second in Suspension.
Veetle has to be fourth in suspension and Q8 has to be fifth in Suspension.
A6 has to be first in Suspension.
Since every car has to be third in at least one parameter, Boyce has to be third in Interiors.
Since Veetle cannot be third in Interiors, it has to be third in Control. Veetle has to be second in Interiors.
7S has to be first in Interiors.
Since Q8 was second in two parameters, Q8 has to be second in both Control and Storage. Which implies it has to be fourth in Interiors.
A6 has to be fifth in Interiors.
7S has to be first in Control.
A6 has to be fifth in Control. Hence, A6 has to be third in Storage.
7S has to be fourth in Storage.
correct answer:-
4
Instruction for set :
Read the following information carefully and answer the questions which follow.
Zcar, a car magazine ranked five cars - 7S, Veetle, A6, Q8 and Boyce on the basis of Power, Control, Suspension, Storage and Interiors. In each parameter the magazine ranked the cars from 1 to 5. A lower number indicates a better rank. No two cars got the same rank in any of the parameters.
1. Veetle was ranked worse than 7S in all the parameters except Storage.
2. Boyce was ranked fourth in control and Q8 was ranked second in two parameters.
3. Q8 was ranked better than 7S in Power.
4. Boyce was ranked fifth in Storage but was ranked better than Q8 and 7S in Power and Suspension.
5. Q8 ranked neither first nor last in Interiors.
6. 7S was ranked better in Control than at least three cars.
7. No car received the same rank in more than two parameters.
8. Veetle did not receive the same rank in any two parameters.
9. Every car was ranked third in at least one parameter and exactly two cars were not ranked first in any parameters.
10. Boyce was not ranked first in Power and Suspension.
Question 73
If the car with the least sum of ranks across the five parameters is declared the car of the year, which car will be the car of the year?
Show Answer
Solution
To solve this question, we will first draw a 5X5 table with the given parameters and fill the given details.
From 4, Boyce was ranked fifth in storage.
From 2, Boyce was ranked fourth in control.
From 8 and 1, Veetle did not receive same rank in any two parameters and Veetle was ranked worse than 7S in all parameters except Storage. Hence, Veetle must be ranked 1 in Storage.
From 6, 7S was ranked first or second in Control.
From 4, Boyce was ranked better than Q8 and 7S in Power and Suspension.
Also, from 3, Q8 was ranked better than 7S in Power.
Since 7S cannot be 5 in Power, the ranks of Boyce, Q8, 7S are 2, 3 and 4 respectively.
Since 7S is ranked fourth, Veetle should be ranked fifth in Power.
A6 has to be ranked first in Power.
7S can neither be fourth or fifth in suspension as Vettle is already fifth in Power. Which implies Boyce has to be second in Suspension.
Veetle has to be fourth in suspension and Q8 has to be fifth in Suspension.
A6 has to be first in Suspension.
Since every car has to be third in at least one parameter, Boyce has to be third in Interiors.
Since Veetle cannot be third in Interiors, it has to be third in Control. Veetle has to be second in Interiors.
7S has to be first in Interiors.
Since Q8 was second in two parameters, Q8 has to be second in both Control and Storage. Which implies it has to be fourth in Interiors.
A6 has to be fifth in Interiors.
7S has to be first in Control.
A6 has to be fifth in Control. Hence, A6 has to be third in Storage.
7S has to be fourth in Storage.
7S has the least sum - 13.
correct answer:-
2
Instruction for set :
Read the following information carefully and answer the questions which follow.
Zcar, a car magazine ranked five cars - 7S, Veetle, A6, Q8 and Boyce on the basis of Power, Control, Suspension, Storage and Interiors. In each parameter the magazine ranked the cars from 1 to 5. A lower number indicates a better rank. No two cars got the same rank in any of the parameters.
1. Veetle was ranked worse than 7S in all the parameters except Storage.
2. Boyce was ranked fourth in control and Q8 was ranked second in two parameters.
3. Q8 was ranked better than 7S in Power.
4. Boyce was ranked fifth in Storage but was ranked better than Q8 and 7S in Power and Suspension.
5. Q8 ranked neither first nor last in Interiors.
6. 7S was ranked better in Control than at least three cars.
7. No car received the same rank in more than two parameters.
8. Veetle did not receive the same rank in any two parameters.
9. Every car was ranked third in at least one parameter and exactly two cars were not ranked first in any parameters.
10. Boyce was not ranked first in Power and Suspension.
Question 74
How many cars are ranked better than Boyce in Interiors?
Show Answer
Solution
To solve this question, we will first draw a 5X5 table with the given parameters and fill the given details.
From 4, Boyce was ranked fifth in storage.
From 2, Boyce was ranked fourth in control.
From 8 and 1, Veetle did not receive same rank in any two parameters and Veetle was ranked worse than 7S in all parameters except Storage. Hence, Veetle must be ranked 1 in Storage.From 6, 7S was ranked first or second in Control.
From 4, Boyce was ranked better than Q8 and 7S in Power and Suspension.
Also, from 3, Q8 was ranked better than 7S in Power.
Since 7S cannot be 5 in Power, the ranks of Boyce, Q8, 7S are 2, 3 and 4 respectively.
Since 7S is ranked fourth, Veetle should be ranked fifth in Power.
A6 has to be ranked first in Power.
7S can neither be fourth or fifth in suspension as Vettle is already fifth in Power. Which implies Boyce has to be second in Suspension.
Veetle has to be fourth in suspension and Q8 has to be fifth in Suspension.
A6 has to be first in Suspension.
Since every car has to be third in at least one parameter, Boyce has to be third in Interiors.
Since Veetle cannot be third in Interiors, it has to be third in Control. Veetle has to be second in Interiors.
7S has to be first in Interiors.
Since Q8 was second in two parameters, Q8 has to be second in both Control and Storage. Which implies it has to be fourth in Interiors.
A6 has to be fifth in Interiors.
7S has to be first in Control.
A6 has to be fifth in Control. Hence, A6 has to be third in Storage.
7S has to be fourth in Storage.
correct answer:-
2
Instruction for set :
8 players are participating in the World Chess Championships - Anand, Magnus Carlsen, Aravind, John, Vladimir, Alexander, Aaron and Anna. The players are divided into two groups of 4 players each. In the first round, each player in a group plays exactly 2 games against every other player in the group. Two points are awarded for a win and no points are awarded for a loss. At the end of the first round, the top two scorers from each group qualify to the semi-finals. It is known that Aravind, Alexander, Anna and Magnus Carlsen reached the semi-finals.
The following information is also known about the first round:
a) In both the groups, no game was a tie and no two players in a group won the same number of points.
b) Aravind lost both his games against Magnus.
c) Aaron won the same number of games as that by Alexander.
d) Anand lost both his games against all the other players in his group, except against John, who in turn won at least one of his games with each of the other players in his group, except one.
Question 75
Who won the highest number of games in the first round?
Show Answer
Solution
Aravind and Magnus are in the same group. Aaron and Alexander are in different groups. Since Aravind, Magnus, Alexander and Anna qualified to the semi-finals and Aravind and Magnus are in the same group, Alexander and Anna are in a different group. Aaron is in the same group as Aravind and Magnus. So, Anand and John are in the other group. The groups are as follows:
Group 1: Aravind, Magnus, Aaron, Vladimir
Group 2: Anand, John, Alexander, Anna
If Anand won both his games against John, he would have 2 wins. John would then have at least 3 wins and Alexander and Anna should have 4 and 5 wins between them. This is not possible since there are only a total of 12 wins in a group. So, Anand won only 1 game and John won 2 games. Alexander and Aaron won the same number of games. Since Aaron did not qualify to the semi-finals, he could have won a maximum of only 3 games. So, Anna won 6 games. Since Aaron won 3 games and did not qualify to the semi-finals, Aravind won 4 games, Magnus won 5 games and Vladimir did not win any game.
The distribution is as follows:
Group 1: Aravind 4, Magnus 5, Aaron 3, Vladimir 0
Group 2: Anand 1, John 2, Alexander 3, Anna 6
So, Anna won the highest number of games.
correct answer:-
2
Instruction for set :
8 players are participating in the World Chess Championships - Anand, Magnus Carlsen, Aravind, John, Vladimir, Alexander, Aaron and Anna. The players are divided into two groups of 4 players each. In the first round, each player in a group plays exactly 2 games against every other player in the group. Two points are awarded for a win and no points are awarded for a loss. At the end of the first round, the top two scorers from each group qualify to the semi-finals. It is known that Aravind, Alexander, Anna and Magnus Carlsen reached the semi-finals.
The following information is also known about the first round:
a) In both the groups, no game was a tie and no two players in a group won the same number of points.
b) Aravind lost both his games against Magnus.
c) Aaron won the same number of games as that by Alexander.
d) Anand lost both his games against all the other players in his group, except against John, who in turn won at least one of his games with each of the other players in his group, except one.
Question 76
Which player won the least number of games in the first round?
Show Answer
Solution
Aravind and Magnus are in the same group. Aaron and Alexander are in different groups. Since Aravind, Magnus, Alexander and Anna qualified to the semi-finals and Aravind and Magnus are in the same group, Alexander and Anna are in a different group. Aaron is in the same group as Aravind and Magnus. So, Anand and John are in the other group. The groups are as follows:
Group 1: Aravind, Magnus, Aaron, Vladimir
Group 2: Anand, John, Alexander, Anna
If Anand won both his games against John, he would have 2 wins. John would then have at least 3 wins and Alexander and Anna should have 4 and 5 wins between them. This is not possible since there are only a total of 12 wins in a group. So, Anand won only 1 game and John won 2 games. Alexander and Aaron won the same number of games. Since Aaron did not qualify to the semi-finals, he could have won a maximum of only 3 games. So, Anna won 6 games. Since Aaron won 3 games and did not qualify to the semi-finals, Aravind won 4 games, Magnus won 5 games and Vladimir did not win any game.
The distribution is as follows:
Group 1: Aravind 4, Magnus 5, Aaron 3, Vladimir 0
Group 2: Anand 1, John 2, Alexander 3, Anna 6
Vladimir won the least number of games in the first round.
correct answer:-
2
Instruction for set :
8 players are participating in the World Chess Championships - Anand, Magnus Carlsen, Aravind, John, Vladimir, Alexander, Aaron and Anna. The players are divided into two groups of 4 players each. In the first round, each player in a group plays exactly 2 games against every other player in the group. Two points are awarded for a win and no points are awarded for a loss. At the end of the first round, the top two scorers from each group qualify to the semi-finals. It is known that Aravind, Alexander, Anna and Magnus Carlsen reached the semi-finals.
The following information is also known about the first round:
a) In both the groups, no game was a tie and no two players in a group won the same number of points.
b) Aravind lost both his games against Magnus.
c) Aaron won the same number of games as that by Alexander.
d) Anand lost both his games against all the other players in his group, except against John, who in turn won at least one of his games with each of the other players in his group, except one.
Question 77
How many games did John win in the first round?
Show Answer
Solution
Aravind and Magnus are in the same group. Aaron and Alexander are in different groups. Since Aravind, Magnus, Alexander and Anna qualified to the semi-finals and Aravind and Magnus are in the same group, Alexander and Anna are in a different group. Aaron is in the same group as Aravind and Magnus. So, Anand and John are in the other group. The groups are as follows:
Group 1: Aravind, Magnus, Aaron, Vladimir
Group 2: Anand, John, Alexander, Anna
If Anand won both his games against John, he would have 2 wins. John would then have at least 3 wins and Alexander and Anna should have 4 and 5 wins between them. This is not possible since there are only a total of 12 wins in a group. So, Anand won only 1 game and John won 2 games. Alexander and Aaron won the same number of games. Since Aaron did not qualify to the semi-finals, he could have won a maximum of only 3 games. So, Anna won 6 games. Since Aaron won 3 games and did not qualify to the semi-finals, Aravind won 4 games, Magnus won 5 games and Vladimir did not win any game.
The distribution is as follows:
Group 1: Aravind 4, Magnus 5, Aaron 3, Vladimir 0
Group 2: Anand 1, John 2, Alexander 3, Anna 6
John won 2 games.
correct answer:-
3
Instruction for set :
8 players are participating in the World Chess Championships - Anand, Magnus Carlsen, Aravind, John, Vladimir, Alexander, Aaron and Anna. The players are divided into two groups of 4 players each. In the first round, each player in a group plays exactly 2 games against every other player in the group. Two points are awarded for a win and no points are awarded for a loss. At the end of the first round, the top two scorers from each group qualify to the semi-finals. It is known that Aravind, Alexander, Anna and Magnus Carlsen reached the semi-finals.
The following information is also known about the first round:
a) In both the groups, no game was a tie and no two players in a group won the same number of points.
b) Aravind lost both his games against Magnus.
c) Aaron won the same number of games as that by Alexander.
d) Anand lost both his games against all the other players in his group, except against John, who in turn won at least one of his games with each of the other players in his group, except one.
Question 78
Who lost against Aaron at least once in the first round?
Show Answer
Solution
Aravind and Magnus are in the same group. Aaron and Alexander are in different groups. Since Aravind, Magnus, Alexander and Anna qualified to the semi-finals and Aravind and Magnus are in the same group, Alexander and Anna are in a different group. Aaron is in the same group as Aravind and Magnus. So, Anand and John are in the other group. The groups are as follows:
Group 1: Aravind, Magnus, Aaron, Vladimir
Group 2: Anand, John, Alexander, Anna
If Anand won both his games against John, he would have 2 wins. John would then have at least 3 wins and Alexander and Anna should have 4 and 5 wins between them. This is not possible since there are only a total of 12 wins in a group. So, Anand won only 1 game and John won 2 games. Alexander and Aaron won the same number of games. Since Aaron did not qualify to the semi-finals, he could have won a maximum of only 3 games. So, Anna won 6 games. Since Aaron won 3 games and did not qualify to the semi-finals, Aravind won 4 games, Magnus won 5 games and Vladimir did not win any game.
The distribution is as follows:
Group 1: Aravind 4, Magnus 5, Aaron 3, Vladimir 0
Group 2: Anand 1, John 2, Alexander 3, Anna 6
Only Vladimir and Magnus lost to Aaron in the first round.
correct answer:-
4
Instruction for set :
Manisha is a kindergarten class teacher who planned a schedule for the incoming batch of students. The classes were supposed to be held from Monday to Friday. Each day has four slots named A, B, C, and D in that order. Slot A starts from 8:00, Slot B from 09:00, slot C from 10:00, and slot D from 11:00. The classes are English, Counting, Dancing, Painting, Singing and Physical Education.
There are 3 types of categories in which classes are distributed. The details of the category are as follows::
a) Compulsory: Classes which happen 4 days a week
b) Optional: Classes which happen 2 times a week
c) Necessary: Classes which happen once a week.
Each of the 3 categories has at least 1 of the 6 subjects in them.
Furthermore, the following things are known:
1) No subject happened in the same slot or the same day twice. None of the subjects belonging to the Optional category happened on Friday.
2) Every day exactly 1 slot had to be free. Slot A had classes on all days.
3) Overall 3 classes each happened in the B and C slots throughout the week.
4) Painting was taught on Wednesday's C slot. Exactly one of the optional subjects was not taught on consecutive days.
5) Counting was taught on Monday. The Singing class did not happen on Tuesday.
6) There were 2 instances where the free period was in the same slot as the preceding day.
7) Physical Education only happened in the A slot. Slot D of Monday was a free slot
8) Week started with teaching English. Dance was not taught on Thursday.
9) On a particular day, Singing happened after a free slot
10) On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day.
Question 79
Which subject was not taught in A slot?
Show Answer
Solution
The slot is made for 5 days with 4 slots each. Thus the total number of fields to be filled = $$5\times4 = 20$$
We know each day there is 1 free slot. Let $$a,b$$ and $$c$$ be the number of Compulsory, Optional, and Necessary subjects be there.
Then a+b+c = 6 ....(I)
Then 5+4a+2b+c = 20 or 4a+2b+c = 15....(II) It is clear that c has to be odd.
when c= 1, then b=3 and a = 2
when c= 3, then b=0 and a= 3 which is rejected as we know there is one subject of each category.
Thus Number of Compulsory classes = 2, Number of Optional classes = 3, and Number of Necessary subject = 1.
Let us start by filling in the known information.
> Painting was taught on Wednesday C slot
>Slot D of Monday was a free slot
> Week starts with teaching English
> Physical Education happens only on A slot. Thus we know that it is the subject in the Necessary Category. We know that none of the optional category classes was conducted on Friday. Thus only the Compulsory and Necessary category subject happened on Friday. Thus Physical Education happened on Friday A slot
>On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day. Thus Dancing and English are the Compulsory category subjects
> Overall 3 classes each happened in the B and C slots throughout the week. Implies overall 2 free slots were there in B and C slot each.
>There were 2 instances that the free period was in the same slot as that of the preceding day.
From above we can say that Thursday and Friday had C as free slots and Tuesday and Wednesday had B as their free slot.
Since English is a Compulsory category. 4 classes have to happen. All in different slots. From the above table, the only possibility is when Thursday B and Tuesday C are English
We are also given that Dance does not happen on Thursday, which implies it needs to happen on all 4 other days. For Monday it is possible only when it happens in C slot.
>On a particular day, singing happened after a free slot. It is only possible when Singing is taught on Thursday D slot
Since Counting was taught on Monday, it has to be in B slot.
Singing class did not happen on Tuesday, it implies that one of the two singing classes has to happen on Wednesday. The only possibility is A slot. This will imply that the Wednesday D slot is Dance and thus Tuesday A slot is Dance
Exactly one of the optional subjects was not taught on consecutive days Thus counting has to be taught on Thursday. And Painting has to be taught on Tuesday
We can see that Painting was not taught in A slot
correct answer:-
3
Instruction for set :
Manisha is a kindergarten class teacher who planned a schedule for the incoming batch of students. The classes were supposed to be held from Monday to Friday. Each day has four slots named A, B, C, and D in that order. Slot A starts from 8:00, Slot B from 09:00, slot C from 10:00, and slot D from 11:00. The classes are English, Counting, Dancing, Painting, Singing and Physical Education.
There are 3 types of categories in which classes are distributed. The details of the category are as follows::
a) Compulsory: Classes which happen 4 days a week
b) Optional: Classes which happen 2 times a week
c) Necessary: Classes which happen once a week.
Each of the 3 categories has at least 1 of the 6 subjects in them.
Furthermore, the following things are known:
1) No subject happened in the same slot or the same day twice. None of the subjects belonging to the Optional category happened on Friday.
2) Every day exactly 1 slot had to be free. Slot A had classes on all days.
3) Overall 3 classes each happened in the B and C slots throughout the week.
4) Painting was taught on Wednesday's C slot. Exactly one of the optional subjects was not taught on consecutive days.
5) Counting was taught on Monday. The Singing class did not happen on Tuesday.
6) There were 2 instances where the free period was in the same slot as the preceding day.
7) Physical Education only happened in the A slot. Slot D of Monday was a free slot
8) Week started with teaching English. Dance was not taught on Thursday.
9) On a particular day, Singing happened after a free slot
10) On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day.
Question 80
Which subject was not taught on Wednesday?
Show Answer
Solution
The slot is made for 5 days with 4 slots each. Thus the total number of fields to be filled = $$5\times4 = 20$$
We know each day there is 1 free slot. Let $$a,b$$ and $$c$$ be the number of Compulsory, Optional, and Necessary subjects be there.
Then a+b+c = 6 ....(I)
Then 5+4a+2b+c = 20 or 4a+2b+c = 15....(II) It is clear that c has to be odd.
when c= 1, then b=3 and a = 2
when c= 3, then b=0 and a= 3 which is rejected as we know there is one subject of each category.
Thus Number of Compulsory classes = 2, Number of Optional classes = 3, and Number of Necessary subject = 1.
Let us start by filling in the known information.
> Painting was taught on Wednesday C slot
>Slot D of Monday was a free slot
> Week starts with teaching English
> Physical Education happens only on A slot. Thus we know that it is the subject in the Necessary Category. We know that none of the optional category classes was conducted on Friday. Thus only the Compulsory and Necessary category subject happened on Friday. Thus Physical Education happened on Friday A slot
>On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day. Thus Dancing and English are the Compulsory category subjects
> Overall 3 classes each happened in the B and C slots throughout the week. Implies overall 2 free slots were there in B and C slot each.
>There were 2 instances that the free period was in the same slot as that of the preceding day.
From above we can say that Thursday and Friday had C as free slots and Tuesday and Wednesday had B as their free slot.
Since English is a Compulsory category. 4 classes have to happen. All in different slots. From the above table, the only possibility is when Thursday B and Tuesday C are English
We are also given that Dance does not happen on Thursday, which implies it needs to happen on all 4 other days. For Monday it is possible only when it happens in C slot.
>On a particular day, singing happened after a free slot. It is only possible when Singing is taught on Thursday D slot
Since Counting was taught on Monday, it has to be in B slot.
Singing class did not happen on Tuesday, it implies that one of the two singing classes has to happen on Wednesday. The only possibility is A slot. This will imply that the Wednesday D slot is Dance and thus Tuesday A slot is Dance
Exactly one of the optional subjects was not taught on consecutive days Thus counting has to be taught on Thursday. And Painting has to be taught on Tuesday
We can see that English was not taught on Wednesday
Manisha is a kindergarten class teacher who planned a schedule for the incoming batch of students. The classes were supposed to be held from Monday to Friday. Each day has four slots named A, B, C, and D in that order. Slot A starts from 8:00, Slot B from 09:00, slot C from 10:00, and slot D from 11:00. The classes are English, Counting, Dancing, Painting, Singing and Physical Education.
There are 3 types of categories in which classes are distributed. The details of the category are as follows::
a) Compulsory: Classes which happen 4 days a week
b) Optional: Classes which happen 2 times a week
c) Necessary: Classes which happen once a week.
Each of the 3 categories has at least 1 of the 6 subjects in them.
Furthermore, the following things are known:
1) No subject happened in the same slot or the same day twice. None of the subjects belonging to the Optional category happened on Friday.
2) Every day exactly 1 slot had to be free. Slot A had classes on all days.
3) Overall 3 classes each happened in the B and C slots throughout the week.
4) Painting was taught on Wednesday's C slot. Exactly one of the optional subjects was not taught on consecutive days.
5) Counting was taught on Monday. The Singing class did not happen on Tuesday.
6) There were 2 instances where the free period was in the same slot as the preceding day.
7) Physical Education only happened in the A slot. Slot D of Monday was a free slot
8) Week started with teaching English. Dance was not taught on Thursday.
9) On a particular day, Singing happened after a free slot
10) On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day.
Question 81
Which of the following can not be a subject of the Optional Category?
Show Answer
Solution
The slot is made for 5 days with 4 slots each. Thus the total number of fields to be filled = $$5\times4 = 20$$
We know each day there is 1 free slot. Let $$a,b$$ and $$c$$ be the number of Compulsory, Optional, and Necessary subjects be there.
Then a+b+c = 6 ....(I)
Then 5+4a+2b+c = 20 or 4a+2b+c = 15....(II) It is clear that c has to be odd.
when c= 1, then b=3 and a = 2
when c= 3, then b=0 and a= 3 which is rejected as we know there is one subject of each category.
Thus Number of Compulsory classes = 2, Number of Optional classes = 3, and Number of Necessary subject = 1.
Let us start by filling in the known information.
> Painting was taught on Wednesday C slot
>Slot D of Monday was a free slot
> Week starts with teaching English
> Physical Education happens only on A slot. Thus we know that it is the subject in the Necessary Category. We know that none of the optional category classes was conducted on Friday. Thus only the Compulsory and Necessary category subject happened on Friday. Thus Physical Education happened on Friday A slot
>On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day. Thus Dance and English are the Compulsory category subjects
Thus Dance is not a subject of Optional Category
correct answer:-
3
Instruction for set :
Manisha is a kindergarten class teacher who planned a schedule for the incoming batch of students. The classes were supposed to be held from Monday to Friday. Each day has four slots named A, B, C, and D in that order. Slot A starts from 8:00, Slot B from 09:00, slot C from 10:00, and slot D from 11:00. The classes are English, Counting, Dancing, Painting, Singing and Physical Education.
There are 3 types of categories in which classes are distributed. The details of the category are as follows::
a) Compulsory: Classes which happen 4 days a week
b) Optional: Classes which happen 2 times a week
c) Necessary: Classes which happen once a week.
Each of the 3 categories has at least 1 of the 6 subjects in them.
Furthermore, the following things are known:
1) No subject happened in the same slot or the same day twice. None of the subjects belonging to the Optional category happened on Friday.
2) Every day exactly 1 slot had to be free. Slot A had classes on all days.
3) Overall 3 classes each happened in the B and C slots throughout the week.
4) Painting was taught on Wednesday's C slot. Exactly one of the optional subjects was not taught on consecutive days.
5) Counting was taught on Monday. The Singing class did not happen on Tuesday.
6) There were 2 instances where the free period was in the same slot as the preceding day.
7) Physical Education only happened in the A slot. Slot D of Monday was a free slot
8) Week started with teaching English. Dance was not taught on Thursday.
9) On a particular day, Singing happened after a free slot
10) On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day.
Question 82
In how many ways can the time-table be drawn?
Show Answer
Solution
The slot is made for 5 days with 4 slots each. Thus the total number of fields to be filled = $$5\times4 = 20$$
We know each day there is 1 free slot. Let $$a,b$$ and $$c$$ be the number of Compulsory, Optional, and Necessary subjects be there.
Then a+b+c = 6 ....(I)
Then 5+4a+2b+c = 20 or 4a+2b+c = 15....(II) It is clear that c has to be odd.
when c= 1, then b=3 and a = 2
when c= 3, then b=0 and a= 3 which is rejected as we know there is one subject of each category.
Thus Number of Compulsory classes = 2, Number of Optional classes = 3, and Number of Necessary subject = 1.
Let us start by filling in the known information.
> Painting was taught on Wednesday C slot
>Slot D of Monday was a free slot
> Week starts with teaching English
> Physical Education happens only on A slot. Thus we know that it is the subject in the Necessary Category. We know that none of the optional category classes was conducted on Friday. Thus only the Compulsory and Necessary category subject happened on Friday. Thus Physical Education happened on Friday A slot
>On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day. Thus Dancing and English are the Compulsory category subjects
> Overall 3 classes each happened in the B and C slots throughout the week. Implies overall 2 free slots were there in B and C slot each.
>There were 2 instances that the free period was in the same slot as that of the preceding day.
From above we can say that Thursday and Friday had C as free slots and Tuesday and Wednesday had B as their free slot.
Since English is a Compulsory category. 4 classes have to happen. All in different slots. From the above table, the only possibility is when Thursday B and Tuesday C are English
We are also given that Dance does not happen on Thursday, which implies it needs to happen on all 4 other days. For Monday it is possible only when it happens in C slot.
>On a particular day, singing happened after a free slot. It is only possible when Singing is taught on Thursday D slot
Since Counting was taught on Monday, it has to be in B slot.
Singing class did not happen on Tuesday, it implies that one of the two singing classes has to happen on Wednesday. The only possibility is A slot. This will imply that the Wednesday D slot is Dance and thus Tuesday A slot is Dance
Exactly one of the optional subjects was not taught on consecutive days Thus counting has to be taught on Thursday. And Painting has to be taught on Tuesday
There is only 1 possiblilty
correct answer:-
1
Instruction for set :
Manisha is a kindergarten class teacher who planned a schedule for the incoming batch of students. The classes were supposed to be held from Monday to Friday. Each day has four slots named A, B, C, and D in that order. Slot A starts from 8:00, Slot B from 09:00, slot C from 10:00, and slot D from 11:00. The classes are English, Counting, Dancing, Painting, Singing and Physical Education.
There are 3 types of categories in which classes are distributed. The details of the category are as follows::
a) Compulsory: Classes which happen 4 days a week
b) Optional: Classes which happen 2 times a week
c) Necessary: Classes which happen once a week.
Each of the 3 categories has at least 1 of the 6 subjects in them.
Furthermore, the following things are known:
1) No subject happened in the same slot or the same day twice. None of the subjects belonging to the Optional category happened on Friday.
2) Every day exactly 1 slot had to be free. Slot A had classes on all days.
3) Overall 3 classes each happened in the B and C slots throughout the week.
4) Painting was taught on Wednesday's C slot. Exactly one of the optional subjects was not taught on consecutive days.
5) Counting was taught on Monday. The Singing class did not happen on Tuesday.
6) There were 2 instances where the free period was in the same slot as the preceding day.
7) Physical Education only happened in the A slot. Slot D of Monday was a free slot
8) Week started with teaching English. Dance was not taught on Thursday.
9) On a particular day, Singing happened after a free slot
10) On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day.
Question 83
How many days both English and Dance classes were held?
Show Answer
Solution
The slot is made for 5 days with 4 slots each. Thus the total number of fields to be filled = $$5\times4 = 20$$
We know each day there is 1 free slot. Let $$a,b$$ and $$c$$ be the number of Compulsory, Optional, and Necessary subjects be there.
Then a+b+c = 6 ....(I)
Then 5+4a+2b+c = 20 or 4a+2b+c = 15....(II) It is clear that c has to be odd.
when c= 1, then b=3 and a = 2
when c= 3, then b=0 and a= 3 which is rejected as we know there is one subject of each category.
Thus Number of Compulsory classes = 2, Number of Optional classes = 3, and Number of Necessary subject = 1.
Let us start by filling in the known information.
> Painting was taught on Wednesday C slot
>Slot D of Monday was a free slot
> Week starts with teaching English
> Physical Education happens only on A slot. Thus we know that it is the subject in the Necessary Category. We know that none of the optional category classes was conducted on Friday. Thus only the Compulsory and Necessary category subject happened on Friday. Thus Physical Education happened on Friday A slot
>On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day. Thus Dancing and English are the Compulsory category subjects
> Overall 3 classes each happened in the B and C slots throughout the week. Implies overall 2 free slots were there in B and C slot each.
>There were 2 instances that the free period was in the same slot as that of the preceding day.
From above we can say that Thursday and Friday had C as free slots and Tuesday and Wednesday had B as their free slot.
Since English is a Compulsory category. 4 classes have to happen. All in different slots. From the above table, the only possibility is when Thursday B and Tuesday C are English
We are also given that Dance does not happen on Thursday, which implies it needs to happen on all 4 other days. For Monday it is possible only when it happens in C slot.
>On a particular day, singing happened after a free slot. It is only possible when Singing is taught on Thursday D slot
Since Counting was taught on Monday, it has to be in B slot.
Singing class did not happen on Tuesday, it implies that one of the two singing classes has to happen on Wednesday. The only possibility is A slot. This will imply that the Wednesday D slot is Dance and thus Tuesday A slot is Dance
Exactly one of the optional subjects was not taught on consecutive days Thus counting has to be taught on Thursday. And Painting has to be taught on Tuesday
English and Dance classes were held on Monday, Tuesday and Friday
correct answer:-
3
Instruction for set :
Manisha is a kindergarten class teacher who planned a schedule for the incoming batch of students. The classes were supposed to be held from Monday to Friday. Each day has four slots named A, B, C, and D in that order. Slot A starts from 8:00, Slot B from 09:00, slot C from 10:00, and slot D from 11:00. The classes are English, Counting, Dancing, Painting, Singing and Physical Education.
There are 3 types of categories in which classes are distributed. The details of the category are as follows::
a) Compulsory: Classes which happen 4 days a week
b) Optional: Classes which happen 2 times a week
c) Necessary: Classes which happen once a week.
Each of the 3 categories has at least 1 of the 6 subjects in them.
Furthermore, the following things are known:
1) No subject happened in the same slot or the same day twice. None of the subjects belonging to the Optional category happened on Friday.
2) Every day exactly 1 slot had to be free. Slot A had classes on all days.
3) Overall 3 classes each happened in the B and C slots throughout the week.
4) Painting was taught on Wednesday's C slot. Exactly one of the optional subjects was not taught on consecutive days.
5) Counting was taught on Monday. The Singing class did not happen on Tuesday.
6) There were 2 instances where the free period was in the same slot as the preceding day.
7) Physical Education only happened in the A slot. Slot D of Monday was a free slot
8) Week started with teaching English. Dance was not taught on Thursday.
9) On a particular day, Singing happened after a free slot
10) On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day.
Question 84
Which of the following subject was not conducted in D slot?
Show Answer
Solution
The slot is made for 5 days with 4 slots each. Thus the total number of fields to be filled = $$5\times4 = 20$$
We know each day there is 1 free slot. Let $$a,b$$ and $$c$$ be the number of Compulsory, Optional, and Necessary subjects be there.
Then a+b+c = 6 ....(I)
Then 5+4a+2b+c = 20 or 4a+2b+c = 15....(II) It is clear that c has to be odd.
when c= 1, then b=3 and a = 2
when c= 3, then b=0 and a= 3 which is rejected as we know there is one subject of each category.
Thus Number of Compulsory classes = 2, Number of Optional classes = 3, and Number of Necessary subject = 1.
Let us start by filling in the known information.
> Painting was taught on Wednesday C slot
>Slot D of Monday was a free slot
> Week starts with teaching English
> Physical Education happens only on A slot. Thus we know that it is the subject in the Necessary Category. We know that none of the optional category classes was conducted on Friday. Thus only the Compulsory and Necessary category subject happened on Friday. Thus Physical Education happened on Friday A slot
>On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day. Thus Dancing and English are the Compulsory category subjects
> Overall 3 classes each happened in the B and C slots throughout the week. Implies overall 2 free slots were there in B and C slot each.
>There were 2 instances that the free period was in the same slot as that of the preceding day.
From above we can say that Thursday and Friday had C as free slots and Tuesday and Wednesday had B as their free slot.
Since English is a Compulsory category. 4 classes have to happen. All in different slots. From the above table, the only possibility is when Thursday B and Tuesday C are English
We are also given that Dance does not happen on Thursday, which implies it needs to happen on all 4 other days. For Monday it is possible only when it happens in C slot.
>On a particular day, singing happened after a free slot. It is only possible when Singing is taught on Thursday D slot
Since Counting was taught on Monday, it has to be in B slot.
Singing class did not happen on Tuesday, it implies that one of the two singing classes has to happen on Wednesday. The only possibility is A slot. This will imply that the Wednesday D slot is Dance and thus Tuesday A slot is Dance
Exactly one of the optional subjects was not taught on consecutive days Thus counting has to be taught on Thursday. And Painting has to be taught on Tuesday
We can see that Counting was not taught in the D slot.
correct answer:-
4
Instruction for set :
5 friends Ajith, Badri, Chetan, Dileep, and Edward work in the same company. Each of them were provided a grade point from 1 to 5 on 3 parameters - Perseverance, Punctuality, and Professionalism. Since certain traits are more valuable to the company than others, punctuality was assigned a credit of 1, perseverance was assigned a credit of 2 and professionalism was assigned a credit of 3. A cumulative grade point average (CGPA) was computed for each of the 5 persons and they were ranked. It is known that the CGPA of all the 5 persons were integers and were different. The persons were ranked in the decreasing order of their CGPA.
Further, it is known that,
Edward had the best rank among the five.
Chetan had a better grade in perseverance than professionalism.
The grade obtained by Chetan in Punctuality and the grade obtained by Badri in perseverance are the same.
Chetan and Badri are the only persons who did not obtain the same grade in more than one parameter.
Dileep had the worst rank among the five.
Badri and Edward had the same grade in perseverance.
The grade received by Badri in professionalism and the grade received by Ajith in punctuality are the same.
Question 85
What grade did Ajith receive in perseverance?
Show Answer
Solution
Edward had the best rank among the five. Therefore, he should have obtained a CGPA of 5 by securing 5 points in all 3 parameters.
Dileep had the worst rank among the five. Therefore, Dileep should have obtained 1 point in all 3 parameters, securing a CGPA of 1.
Now, we have to distribute the points according to the given conditions such that the CGPA obtained by Ajith, Chetan, and Badri are 2, 3, and 4 in any order.
Badri and Edward had the same grade in perseverance.
Therefore, Badri should have gotten 5 points in perseverance.
It has been given that Chetan and Badri did not obtain the same grade in more than one parameter.
Also, we know that the CGPA obtained by Badri is an integer.
Let 'a' be the points obtained by Badri in Punctuality and 'c' be the points obtained by Badri in professionalism.
(a+2*5+3c)/6 is an integer.
(10+a+3c)/6 is an integer. Also, we know that neither 'a' nor 'c' is equal to 5.
10/6 can be written as 1+4/6. Therefore, the (a+3c)/6 part should be equal to 2/6 or 8/6 or 14/6... and so on.
Since the least value 'c' can take is 1, (a+3c) cannot be 2.
The combination a=2 and c=2 will yield 8 as the value of a+3c. However, 'a' cannot be equal to 'c' and hence, we can eliminate this case.
a=2, and c=4 will make the value of a+3c 14. This is a valid combination.
This is the only value that satisfies the condition (Other values will not yield values in the series 2/6, 8/6, 14/6, 20,6,..).
Therefore, B should have gotten a score of 2 in punctuality and 4 in professionalism. His CGPA should be 4.
The grade obtained by Chetan in Punctuality and the grade obtained by Badri in perseverance are the same.
Therefore, Chetan should have obtained 5 points in Punctuality.
Let the grades obtained by Chetan in perseverance and professionalism be 'a' and 'b'.
(5/6) + (2a+3b)/6 is an integer.
=> (2a+3b)/6 should be of the form 1/6 or 7/6 or 13/6 and so on.
Also, we know that Chetan did not obtain the same grade in more than one parameter.
=> 'a' cannot be equal to 'b' and the values of 'a' or 'b' cannot be equal to 5.
2a+3b cannot be equal to 1.
a=2 and b=1 will make the value of (2a+3b) equal to 7.
This is a valid combination. Also, this is in line with the condition that Chetan obtained a better grade in perseverance than professionalism. Also, the CGPA obtained in this case will be 2, which does not violate any of the inferences made so far.
Let us check for other combinations.
2a+3b will be equal to 13 when a=2, b=3 or a=5 and b=1.
a=2, b=3 violates the condition that Chetan obtained a better grade in perseverance than professionalism.
We have already seen that 'a' or 'b' cannot be equal to 5 and hence, we can eliminate the combination a=5,b=1.
2a+3b cannot take higher values since the CGPA obtained will be 4 if the value of the expression equals 19. We know that B obtained a CGPA of 4.
Therefore, the grades obtained by Chetan in Punctuality, Perseverance, and Professionalism are 5, 2, and 1.
Ajith should have obtained a CGPA of 3 (Since we know the CGPA of the other 4 persons).
Now, Ajith had the same grade in at least 2 subjects.
The grade received by Badri in professionalism and the grade obtained by Ajith in Punctuality are the same.
Therefore, Ajith should have obtained 4 points in punctuality.
Let us assume that Ajith scored the same in perseverance and professionalism.
=> (4+5a)/6 = 3
=> a = 14/5.
Therefore, Ajith could not have scored the same in perseverance and professionalism.
Let us assume that Ajith scored 'a' points in perseverance and 'b' points in professionalism.
(4+2a+3b)/6 = 3
2a + 3b = 14
If a = 4, b will be 2.
If b = 4, a will be 1.
As we can see, there are 2 possible cases.
The grade obtained by Ajith in Perseverance cannot be determined and hence, option D is the right answer.
correct answer:-
4
Instruction for set :
5 friends Ajith, Badri, Chetan, Dileep, and Edward work in the same company. Each of them were provided a grade point from 1 to 5 on 3 parameters - Perseverance, Punctuality, and Professionalism. Since certain traits are more valuable to the company than others, punctuality was assigned a credit of 1, perseverance was assigned a credit of 2 and professionalism was assigned a credit of 3. A cumulative grade point average (CGPA) was computed for each of the 5 persons and they were ranked. It is known that the CGPA of all the 5 persons were integers and were different. The persons were ranked in the decreasing order of their CGPA.
Further, it is known that,
Edward had the best rank among the five.
Chetan had a better grade in perseverance than professionalism.
The grade obtained by Chetan in Punctuality and the grade obtained by Badri in perseverance are the same.
Chetan and Badri are the only persons who did not obtain the same grade in more than one parameter.
Dileep had the worst rank among the five.
Badri and Edward had the same grade in perseverance.
The grade received by Badri in professionalism and the grade received by Ajith in punctuality are the same.
Question 86
Which grade was not received by any person in any of the parameters?
Show Answer
Solution
Edward had the best rank among the five. Therefore, he should have obtained a CGPA of 5 by securing 5 points in all 3 parameters.
Dileep had the worst rank among the five. Therefore, Dileep should have obtained 1 point in all 3 parameters, securing a CGPA of 1.
Now, we have to distribute the points according to the given conditions such that the CGPA obtained by Ajith, Chetan, and Badri are 2, 3, and 4 in any order.
Badri and Edward had the same grade in perseverance.
Therefore, Badri should have gotten 5 points in perseverance.
It has been given that Chetan and Badri did not obtain the same grade in more than one parameter.
Also, we know that the CGPA obtained by Badri is an integer.
Let 'a' be the points obtained by Badri in Punctuality and 'c' be the points obtained by Badri in professionalism.
(a+2*5+3c)/6 is an integer.
(10+a+3c)/6 is an integer. Also, we know that neither 'a' nor 'c' is equal to 5.
10/6 can be written as 1+4/6. Therefore, the (a+3c)/6 part should be equal to 2/6 or 8/6 or 14/6... and so on.
Since the least value 'c' can take is 1, (a+3c) cannot be 2.
The combination a=2 and c=2 will yield 8 as the value of a+3c. However, 'a' cannot be equal to 'c' and hence, we can eliminate this case.
a=2, and c=4 will make the value of a+3c 14. This is a valid combination.
This is the only value that satisfies the condition (Other values will not yield values in the series 2/6, 8/6, 14/6, 20,6,..).
Therefore, B should have gotten a score of 2 in punctuality and 4 in professionalism. His CGPA should be 4.
The grade obtained by Chetan in Punctuality and the grade obtained by Badri in perseverance are the same.
Therefore, Chetan should have obtained 5 points in Punctuality.
Let the grades obtained by Chetan in perseverance and professionalism be 'a' and 'b'.
(5/6) + (2a+3b)/6 is an integer.
=> (2a+3b)/6 should be of the form 1/6 or 7/6 or 13/6 and so on.
Also, we know that Chetan did not obtain the same grade in more than one parameter.
=> 'a' cannot be equal to 'b' and the values of 'a' or 'b' cannot be equal to 5.
2a+3b cannot be equal to 1.
a=2 and b=1 will make the value of (2a+3b) equal to 7.
This is a valid combination. Also, this is in line with the condition that Chetan obtained a better grade in perseverance than professionalism. Also, the CGPA obtained in this case will be 2, which does not violate any of the inferences made so far.
Let us check for other combinations.
2a+3b will be equal to 13 when a=2, b=3 or a=5 and b=1.
a=2, b=3 violates the condition that Chetan obtained a better grade in perseverance than professionalism.
We have already seen that 'a' or 'b' cannot be equal to 5 and hence, we can eliminate the combination a=5,b=1.
2a+3b cannot take higher values since the CGPA obtained will be 4 if the value of the expression equals 19. We know that B obtained a CGPA of 4.
Therefore, the grades obtained by Chetan in Punctuality, Perseverance, and Professionalism are 5, 2, and 1.
Ajith should have obtained a CGPA of 3 (Since we know the CGPA of the other 4 persons).
Now, Ajith had the same grade in at least 2 subjects.
The grade received by Badri in professionalism and the grade obtained by Ajith in Punctuality are the same.
Therefore, Ajith should have obtained 4 points in punctuality.
Let us assume that Ajith scored the same in perseverance and professionalism.
=> (4+5a)/6 = 3
=> a = 14/5.
Therefore, Ajith could not have scored the same in perseverance and professionalism.
Let us assume that Ajith scored 'a' points in perseverance and 'b' points in professionalism.
(4+2a+3b)/6 = 3
2a + 3b = 14
If a = 4, b will be 2.
If b = 4, a will be 1.
As we can see, there are 2 possible cases.
No person received a grade of 3 in any of the parameters and hence, option B is the right answer.
correct answer:-
2
Instruction for set :
5 friends Ajith, Badri, Chetan, Dileep, and Edward work in the same company. Each of them were provided a grade point from 1 to 5 on 3 parameters - Perseverance, Punctuality, and Professionalism. Since certain traits are more valuable to the company than others, punctuality was assigned a credit of 1, perseverance was assigned a credit of 2 and professionalism was assigned a credit of 3. A cumulative grade point average (CGPA) was computed for each of the 5 persons and they were ranked. It is known that the CGPA of all the 5 persons were integers and were different. The persons were ranked in the decreasing order of their CGPA.
Further, it is known that,
Edward had the best rank among the five.
Chetan had a better grade in perseverance than professionalism.
The grade obtained by Chetan in Punctuality and the grade obtained by Badri in perseverance are the same.
Chetan and Badri are the only persons who did not obtain the same grade in more than one parameter.
Dileep had the worst rank among the five.
Badri and Edward had the same grade in perseverance.
The grade received by Badri in professionalism and the grade received by Ajith in punctuality are the same.
Question 87
How many persons did not receive a grade less than 3 in Punctuality?
Show Answer
Solution
Edward had the best rank among the five. Therefore, he should have obtained a CGPA of 5 by securing 5 points in all 3 parameters.
Dileep had the worst rank among the five. Therefore, Dileep should have obtained 1 point in all 3 parameters, securing a CGPA of 1.
Now, we have to distribute the points according to the given conditions such that the CGPA obtained by Ajith, Chetan, and Badri are 2, 3, and 4 in any order.
Badri and Edward had the same grade in perseverance.
Therefore, Badri should have gotten 5 points in perseverance.
It has been given that Chetan and Badri did not obtain the same grade in more than one parameter.
Also, we know that the CGPA obtained by Badri is an integer.
Let 'a' be the points obtained by Badri in Punctuality and 'c' be the points obtained by Badri in professionalism.
(a+2*5+3c)/6 is an integer.
(10+a+3c)/6 is an integer. Also, we know that neither 'a' nor 'c' is equal to 5.
10/6 can be written as 1+4/6. Therefore, the (a+3c)/6 part should be equal to 2/6 or 8/6 or 14/6... and so on.
Since the least value 'c' can take is 1, (a+3c) cannot be 2.
The combination a=2 and c=2 will yield 8 as the value of a+3c. However, 'a' cannot be equal to 'c' and hence, we can eliminate this case.
a=2, and c=4 will make the value of a+3c 14. This is a valid combination.
This is the only value that satisfies the condition (Other values will not yield values in the series 2/6, 8/6, 14/6, 20,6,..).
Therefore, B should have gotten a score of 2 in punctuality and 4 in professionalism. His CGPA should be 4.
The grade obtained by Chetan in Punctuality and the grade obtained by Badri in perseverance are the same.
Therefore, Chetan should have obtained 5 points in Punctuality.
Let the grades obtained by Chetan in perseverance and professionalism be 'a' and 'b'.
(5/6) + (2a+3b)/6 is an integer.
=> (2a+3b)/6 should be of the form 1/6 or 7/6 or 13/6 and so on.
Also, we know that Chetan did not obtain the same grade in more than one parameter.
=> 'a' cannot be equal to 'b' and the values of 'a' or 'b' cannot be equal to 5.
2a+3b cannot be equal to 1.
a=2 and b=1 will make the value of (2a+3b) equal to 7.
This is a valid combination. Also, this is in line with the condition that Chetan obtained a better grade in perseverance than professionalism. Also, the CGPA obtained in this case will be 2, which does not violate any of the inferences made so far.
Let us check for other combinations.
2a+3b will be equal to 13 when a=2, b=3 or a=5 and b=1.
a=2, b=3 violates the condition that Chetan obtained a better grade in perseverance than professionalism.
We have already seen that 'a' or 'b' cannot be equal to 5 and hence, we can eliminate the combination a=5,b=1.
2a+3b cannot take higher values since the CGPA obtained will be 4 if the value of the expression equals 19. We know that B obtained a CGPA of 4.
Therefore, the grades obtained by Chetan in Punctuality, Perseverance, and Professionalism are 5, 2, and 1.
Ajith should have obtained a CGPA of 3 (Since we know the CGPA of the other 4 persons).
Now, Ajith had the same grade in at least 2 subjects.
The grade received by Badri in professionalism and the grade obtained by Ajith in Punctuality are the same.
Therefore, Ajith should have obtained 4 points in punctuality.
Let us assume that Ajith scored the same in perseverance and professionalism.
=> (4+5a)/6 = 3
=> a = 14/5.
Therefore, Ajith could not have scored the same in perseverance and professionalism.
Let us assume that Ajith scored 'a' points in perseverance and 'b' points in professionalism.
(4+2a+3b)/6 = 3
2a + 3b = 14
If a = 4, b will be 2.
If b = 4, a will be 1.
As we can see, there are 2 possible cases.
3 persons did not receive a grade less than 3 in punctuality and hence, option B is the right answer.
correct answer:-
2
Instruction for set :
5 friends Ajith, Badri, Chetan, Dileep, and Edward work in the same company. Each of them were provided a grade point from 1 to 5 on 3 parameters - Perseverance, Punctuality, and Professionalism. Since certain traits are more valuable to the company than others, punctuality was assigned a credit of 1, perseverance was assigned a credit of 2 and professionalism was assigned a credit of 3. A cumulative grade point average (CGPA) was computed for each of the 5 persons and they were ranked. It is known that the CGPA of all the 5 persons were integers and were different. The persons were ranked in the decreasing order of their CGPA.
Further, it is known that,
Edward had the best rank among the five.
Chetan had a better grade in perseverance than professionalism.
The grade obtained by Chetan in Punctuality and the grade obtained by Badri in perseverance are the same.
Chetan and Badri are the only persons who did not obtain the same grade in more than one parameter.
Dileep had the worst rank among the five.
Badri and Edward had the same grade in perseverance.
The grade received by Badri in professionalism and the grade received by Ajith in punctuality are the same.
Question 88
Who among the following was ranked fourth according to CGPA?
Show Answer
Solution
Edward had the best rank among the five. Therefore, he should have obtained a CGPA of 5 by securing 5 points in all 3 parameters.
Dileep had the worst rank among the five. Therefore, Dileep should have obtained 1 point in all 3 parameters, securing a CGPA of 1.
Now, we have to distribute the points according to the given conditions such that the CGPA obtained by Ajith, Chetan, and Badri are 2, 3, and 4 in any order.
Badri and Edward had the same grade in perseverance.
Therefore, Badri should have gotten 5 points in perseverance.
It has been given that Chetan and Badri did not obtain the same grade in more than one parameter.
Also, we know that the CGPA obtained by Badri is an integer.
Let 'a' be the points obtained by Badri in Punctuality and 'c' be the points obtained by Badri in professionalism.
(a+2*5+3c)/6 is an integer.
(10+a+3c)/6 is an integer. Also, we know that neither 'a' nor 'c' is equal to 5.
10/6 can be written as 1+4/6. Therefore, the (a+3c)/6 part should be equal to 2/6 or 8/6 or 14/6... and so on.
Since the least value 'c' can take is 1, (a+3c) cannot be 2.
The combination a=2 and c=2 will yield 8 as the value of a+3c. However, 'a' cannot be equal to 'c' and hence, we can eliminate this case.
a=2, and c=4 will make the value of a+3c 14. This is a valid combination.
This is the only value that satisfies the condition (Other values will not yield values in the series 2/6, 8/6, 14/6, 20,6,..).
Therefore, B should have gotten a score of 2 in punctuality and 4 in professionalism. His CGPA should be 4.
The grade obtained by Chetan in Punctuality and the grade obtained by Badri in perseverance are the same.
Therefore, Chetan should have obtained 5 points in Punctuality.
Let the grades obtained by Chetan in perseverance and professionalism be 'a' and 'b'.
(5/6) + (2a+3b)/6 is an integer.
=> (2a+3b)/6 should be of the form 1/6 or 7/6 or 13/6 and so on.
Also, we know that Chetan did not obtain the same grade in more than one parameter.
=> 'a' cannot be equal to 'b' and the values of 'a' or 'b' cannot be equal to 5.
2a+3b cannot be equal to 1.
a=2 and b=1 will make the value of (2a+3b) equal to 7.
This is a valid combination. Also, this is in line with the condition that Chetan obtained a better grade in perseverance than professionalism. Also, the CGPA obtained in this case will be 2, which does not violate any of the inferences made so far.
Let us check for other combinations.
2a+3b will be equal to 13 when a=2, b=3 or a=5 and b=1.
a=2, b=3 violates the condition that Chetan obtained a better grade in perseverance than professionalism.
We have already seen that 'a' or 'b' cannot be equal to 5 and hence, we can eliminate the combination a=5,b=1.
2a+3b cannot take higher values since the CGPA obtained will be 4 if the value of the expression equals 19. We know that B obtained a CGPA of 4.
Therefore, the grades obtained by Chetan in Punctuality, Perseverance, and Professionalism are 5, 2, and 1.
Ajith should have obtained a CGPA of 3 (Since we know the CGPA of the other 4 persons).
Now, Ajith had the same grade in at least 2 subjects.
The grade received by Badri in professionalism and the grade obtained by Ajith in Punctuality are the same.
Therefore, Ajith should have obtained 4 points in punctuality.
Let us assume that Ajith scored the same in perseverance and professionalism.
=> (4+5a)/6 = 3
=> a = 14/5.
Therefore, Ajith could not have scored the same in perseverance and professionalism.
Let us assume that Ajith scored 'a' points in perseverance and 'b' points in professionalism.
(4+2a+3b)/6 = 3
2a + 3b = 14
If a = 4, b will be 2.
If b = 4, a will be 1.
As we can see, there are 2 possible cases.
Chetan was ranked fourth and hence, option A is the right answer.
correct answer:-
1
Question 89
Point A is the reflection of the point (1,2) about the line 2x-4y=5 and point B is the reflection of the same point about the line x-y=3. What is the distance between A and B?
Show Answer
Solution
The slope of the given line 2x-4y=5 is 0.5 and thus, the slope of the line containing (1,2) and it’s reflection is -2.
Thus, the equation of this line will be:-
y-2 = -2(x-1)
=> y-2 = -2x + 2
I.e 2x+y = 4.
The point of intersection of 2x-4y=5 and 2x+y = 4 will be the mid-point of (1,2) and A.
The point of intersection of these 2 lines can be found out by subtracting 1 equation from the other.
The point of intersection comes out to be (2.1, -0.2)
This point is the mid-point of the line joining (1,2) and A(p,q)(assume).
Thus, we get $$\dfrac{p+1}{2} = 2.1 => p = 3.2$$ and $$\dfrac{q+2}{2} = -0.2 => q = -2.4$$
Thus, A = (3.2, -2.4)
The slope of the given line x-y=3 is 1 and thus, the slope of the line containing (1,2) and it’s reflection is -1.
Thus, the equation of this line will be:-
y-2 = -1(x-1)
=> y-2 = -x + 1
I.e x+y = 3.
The point of intersection of x-y=3 and x+y=3 will be the mid-point of (1,2) and B.
The point of intersection of these 2 lines can be found out by adding 1 equation to the other.
The point of intersection comes out to be (3, 0).
This point is the mid-point of the line joining (1,2) and B(l,m)(assume).
Thus, we get $$\dfrac{l+1}{2} = 3 => l = 5$$ and $$\dfrac{m+2}{2} = 0 => m = -2$$
Thus, B = (5,-2)
Thus, the distance between A and B = $$\sqrt{(5-3.2)^2 + (-2+2.4)^2} = \sqrt{1.8^2 + 0.4^2} = \sqrt{3.4}$$
Hence, option C is the correct answer.
correct answer:-
3
Instruction for set :
Five women of Sri Krishna society, Lakshmi, Saraswati, Durga, Gauri and Parvati went to buy diyas for the upcoming Diwali festival. There are five varieties of diyas available in the market with different prices per diya among Rs.25, Rs.30, Rs.35, Rs.45 and Rs.60, not necessarily in any order. Each of the five women bought a different number of diyas among 25, 40, 60, 70, and 90, not necessarily in that order.
It is also known that:
Each person buys only one variety of diya.(i.e. The person who purchases the Rs25 diya shall not purchase the Rs.30 diya)
Lakshmi did not buy the highest number of diyas.
The absolute difference between the total amount spent by Durga and Lakshmi is less than 200.
Each one of the ladies spent different amounts and bought diyas worth more than Rs. 1000.
Gauri spent the maximum amount which is more than twice the minimum amount spent.
Parvati did not buy the cheapest diya but she spent the minimum amount.
The cost per piece of diya bought by Gauri is 25% less than the cost per piece of diya bought by Saraswati.
The absolute difference between the number of diyas bought by Durga and Lakshmi and the absolute difference between the number of diyas bought by Gauri and Parvati are same.
Question 90
What is the sum of the amounts (in Rs.) spent by Durga and Lakshmi combined?
(Enter ‘0’ as the answer if the answer cannot be determined.)
Show Answer
Solution
The absolute difference between the number of diyas bought by Durga and Lakshmi and the absolute difference between the number of diyas bought by Gauri and Parvati are same. From this we can conclude that the pairs can be either (90, 60) and (70, 40) or (90, 70) and (60, 40). So, Saraswati must have bought 25 diyas.
The cost per piece of diya bought by Gauri is 25% less than the cost per piece of diya bought by Saraswati. This is only possible when Saraswati bought diyas worth Rs. 60 per piece and Gauri bought diyas worth Rs. 45 per piece. Therefore, the amount spent by Saraswati must be Rs.(25 * 60) = Rs.1500.
Gauri spent the maximum amount. So, the lady who would have bought 90 diyas even at a price of Rs.25 per diya would have spent Rs.(90 * 25) = Rs.2250. So, Gauri must have spent more than at least Rs.2250. As Gauri bought diyas worth Rs.45 per piece, she must have bought more than 50 diyas i.e. either 60 diyas or 70 diyas or 90 diyas.
It is given that Parvati spent the least amount and she did not buy the cheapest diya. Therefore, Parvati must have spent less than Rs.1500 and she must have bought diyas costing at least Rs.30 per piece. Thus, we can conclude that Parvati must have bought less than 50 diyas i.e. 40 diyas and the cost of diyas could be Rs.30 per piece or Rs.35 per piece. If Parvati bought 40 diyas, Gauri must have bought either 60 diyas or 70 diyas. Therefore, either Durga or Lakshmi must have bought 90 diyas. But, it is given that Lakshmi did not buy the highest number of diyas. So, Durga must have bought 90 diyas.
Gauri spent the maximum amount. So, Durga must have spent less than her. Gauri could have spent either Rs.2700 or Rs.3150. So, Durga could not have bought diya worth Rs.35 per piece.
All the possible total values for Durga is either Rs.(90 * 25) = Rs.2250 or Rs.(90 * 30) = Rs.2700.
The absolute difference between the total amount spent by Durga and Lakshmi is less than 200. So, the total for Lakshmi should lie either between Rs.2050 and Rs.2450 or between Rs.2500 and Rs.2900. This would be only possible when Lakshmi either bought 70 diyas worth Rs.30 per piece or 60 diyas worth Rs.35 per piece. In both the cases, Durga must have bought diyas worth Rs.25 per piece to maintain the absoulte difference less than 200.
If Parvati bought diyas worth Rs.35 per piece, the minimum amount would be Rs.1400. In that case, Lakshmi would have bought 70 diyas worth Rs.30 per piece. Thus, Gauri would have bought 60 diyas worth Rs.45 which would total as Rs.2700. However, in this case, the maximum amount would not be more than twice the minimum amount.
Therefore, Parvati must have bought diyas worth Rs.30 per piece. We get the final table as:
From the table we can see that the sum of the amounts spent by Durga and Lakshmi combined is Rs.(2100+2250) = Rs.4350
Hence, 4350 is the correct answer.
Five women of Sri Krishna society, Lakshmi, Saraswati, Durga, Gauri and Parvati went to buy diyas for the upcoming Diwali festival. There are five varieties of diyas available in the market with different prices per diya among Rs.25, Rs.30, Rs.35, Rs.45 and Rs.60, not necessarily in any order. Each of the five women bought a different number of diyas among 25, 40, 60, 70, and 90, not necessarily in that order.
It is also known that:
Each person buys only one variety of diya.(i.e. The person who purchases the Rs25 diya shall not purchase the Rs.30 diya)
Lakshmi did not buy the highest number of diyas.
The absolute difference between the total amount spent by Durga and Lakshmi is less than 200.
Each one of the ladies spent different amounts and bought diyas worth more than Rs. 1000.
Gauri spent the maximum amount which is more than twice the minimum amount spent.
Parvati did not buy the cheapest diya but she spent the minimum amount.
The cost per piece of diya bought by Gauri is 25% less than the cost per piece of diya bought by Saraswati.
The absolute difference between the number of diyas bought by Durga and Lakshmi and the absolute difference between the number of diyas bought by Gauri and Parvati are same.
Question 91
Who spent the second least amount?
Show Answer
Solution
The absolute difference between the number of diyas bought by Durga and Lakshmi and the absolute difference between the number of diyas bought by Gauri and Parvati are same. From this we can conclude that the pairs can be either (90, 60) and (70, 40) or (90, 70) and (60, 40). So, Saraswati must have bought 25 diyas.
The cost per piece of diya bought by Gauri is 25% less than the cost per piece of diya bought by Saraswati. This is only possible when Saraswati bought diyas worth Rs. 60 per piece and Gauri bought diyas worth Rs. 45 per piece. Therefore, the amount spent by Saraswati must be Rs.(25 * 60) = Rs.1500.
Gauri spent the maximum amount. So, the lady who would have bought 90 diyas even at a price of Rs.25 per diya would have spent Rs.(90 * 25) = Rs.2250. So, Gauri must have spent more than at least Rs.2250. As Gauri bought diyas worth Rs.45 per piece, she must have bought more than 50 diyas i.e. either 60 diyas or 70 diyas or 90 diyas.
It is given that Parvati spent the least amount and she did not buy the cheapest diya. Therefore, Parvati must have spent less than Rs.1500 and she must have bought diyas costing at least Rs.30 per piece. Thus, we can conclude that Parvati must have bought less than 50 diyas i.e. 40 diyas and the cost of diyas could be Rs.30 per piece or Rs.35 per piece. If Parvati bought 40 diyas, Gauri must have bought either 60 diyas or 70 diyas. Therefore, either Durga or Lakshmi must have bought 90 diyas. But, it is given that Lakshmi did not buy the highest number of diyas. So, Durga must have bought 90 diyas.
Gauri spent the maximum amount. So, Durga must have spent less than her. Gauri could have spent either Rs.2700 or Rs.3150. So, Durga could not have bought diya worth Rs.35 per piece.
All the possible total values for Durga is either Rs.(90 * 25) = Rs.2250 or Rs.(90 * 30) = Rs.2700.
The absolute difference between the total amount spent by Durga and Lakshmi is less than 200. So, the total for Lakshmi should lie either between Rs.2050 and Rs.2450 or between Rs.2500 and Rs.2900. This would be only possible when Lakshmi either bought 70 diyas worth Rs.30 per piece or 60 diyas worth Rs.35 per piece. In both the cases, Durga must have bought diyas worth Rs.25 per piece to maintain the absoulte difference less than 200.
If Parvati bought diyas worth Rs.35 per piece, the minimum amount would be Rs.1400. In that case, Lakshmi would have bought 70 diyas worth Rs.30 per piece. Thus, Gauri would have bought 60 diyas worth Rs.45 which would total as Rs.2700. However, in this case, the maximum amount would not be more than twice the minimum amount.
Therefore, Parvati must have bought diyas worth Rs.30 per piece. We get the final table as:
From the table we can see that Saraswati spent the second least amount.
Hence, option B is the correct answer.
correct answer:-
2
Instruction for set :
Five women of Sri Krishna society, Lakshmi, Saraswati, Durga, Gauri and Parvati went to buy diyas for the upcoming Diwali festival. There are five varieties of diyas available in the market with different prices per diya among Rs.25, Rs.30, Rs.35, Rs.45 and Rs.60, not necessarily in any order. Each of the five women bought a different number of diyas among 25, 40, 60, 70, and 90, not necessarily in that order.
It is also known that:
Each person buys only one variety of diya.(i.e. The person who purchases the Rs25 diya shall not purchase the Rs.30 diya)
Lakshmi did not buy the highest number of diyas.
The absolute difference between the total amount spent by Durga and Lakshmi is less than 200.
Each one of the ladies spent different amounts and bought diyas worth more than Rs. 1000.
Gauri spent the maximum amount which is more than twice the minimum amount spent.
Parvati did not buy the cheapest diya but she spent the minimum amount.
The cost per piece of diya bought by Gauri is 25% less than the cost per piece of diya bought by Saraswati.
The absolute difference between the number of diyas bought by Durga and Lakshmi and the absolute difference between the number of diyas bought by Gauri and Parvati are same.
Question 92
What is the absolute difference between the number of diyas bought by Saraswati and the number of diyas bought by Gauri?
(Enter ‘0’ as the answer if the answer cannot be determined.)
Show Answer
Solution
The absolute difference between the number of diyas bought by Durga and Lakshmi and the absolute difference between the number of diyas bought by Gauri and Parvati are same. From this we can conclude that the pairs can be either (90, 60) and (70, 40) or (90, 70) and (60, 40). So, Saraswati must have bought 25 diyas.
The cost per piece of diya bought by Gauri is 25% less than the cost per piece of diya bought by Saraswati. This is only possible when Saraswati bought diyas worth Rs. 60 per piece and Gauri bought diyas worth Rs. 45 per piece. Therefore, the amount spent by Saraswati must be Rs.(25 * 60) = Rs.1500.
Gauri spent the maximum amount. So, the lady who would have bought 90 diyas even at a price of Rs.25 per diya would have spent Rs.(90 * 25) = Rs.2250. So, Gauri must have spent more than at least Rs.2250. As Gauri bought diyas worth Rs.45 per piece, she must have bought more than 50 diyas i.e. either 60 diyas or 70 diyas or 90 diyas.
It is given that Parvati spent the least amount and she did not buy the cheapest diya. Therefore, Parvati must have spent less than Rs.1500 and she must have bought diyas costing at least Rs.30 per piece. Thus, we can conclude that Parvati must have bought less than 50 diyas i.e. 40 diyas and the cost of diyas could be Rs.30 per piece or Rs.35 per piece. If Parvati bought 40 diyas, Gauri must have bought either 60 diyas or 70 diyas. Therefore, either Durga or Lakshmi must have bought 90 diyas. But, it is given that Lakshmi did not buy the highest number of diyas. So, Durga must have bought 90 diyas.
Gauri spent the maximum amount. So, Durga must have spent less than her. Gauri could have spent either Rs.2700 or Rs.3150. So, Durga could not have bought diya worth Rs.35 per piece.
All the possible total values for Durga is either Rs.(90 * 25) = Rs.2250 or Rs.(90 * 30) = Rs.2700.
The absolute difference between the total amount spent by Durga and Lakshmi is less than 200. So, the total for Lakshmi should lie either between Rs.2050 and Rs.2450 or between Rs.2500 and Rs.2900. This would be only possible when Lakshmi either bought 70 diyas worth Rs.30 per piece or 60 diyas worth Rs.35 per piece. In both the cases, Durga must have bought diyas worth Rs.25 per piece to maintain the absoulte difference less than 200.
If Parvati bought diyas worth Rs.35 per piece, the minimum amount would be Rs.1400. In that case, Lakshmi would have bought 70 diyas worth Rs.30 per piece. Thus, Gauri would have bought 60 diyas worth Rs.45 which would total as Rs.2700. However, in this case, the maximum amount would not be more than twice the minimum amount.
Therefore, Parvati must have bought diyas worth Rs.30 per piece. We get the final table as:
From the table we can see that the absolute difference between the number of diyas bought by Saraswati and the number of diyas bought by Gauri is (70 - 25) = 45.
Hence, 45 is the correct answer.
correct answer:-
45
Instruction for set :
Anet is an electronic chip manufacturing company in India. The chip manufacturing is done in five production stages P, Q, R, S and T in the sequence P-Q-R-S-T. Each stage of production takes one working day and the product from one stage to another can be transferred only in the next day. The following table shows the number of chips that can processed in each day of the week in a certain production plant.
If a production process is delivered more chips that it can handle, then the unfinished chips are processed in the next day.
Production unit P works to its full capacity on all days of the week with no chips pending processing. (All unfinished products on Saturday is delivered to another production plant to be completed. ) Also on Monday, the number of chips fed to the different production stages Q, R, S and T are 100, 300, 500 and 600 respectively.
Question 93
What is the number of unfinished chips of S by the end of Friday ?
Show Answer
Solution
Since the work of P is independent of other stages and P
works to its full capacity on all days and all other units works on full
capacity on Monday, the starting point of production for each day is shown:
The capacity of Q on Tuesday is 300 but it is delivered only
200 units, thus 200 units will be processed by Q on Tuesday. The capacity of S
on Tuesday is 200 but it is delivered 300 units. So only 200 units are
processed by S on Tuesday, the remaining 100 units would be processed by S on
Wednesday. In this manner, the number of processed and unprocessed chips can be
calculated for each day. The table for
the processed chips is as shown:
The unfinished chips are shown in brackets.
From the table, we can see that S has 200 unfinished chips on Friday.
correct answer:-
3
Instruction for set :
Anet is an electronic chip manufacturing company in India. The chip manufacturing is done in five production stages P, Q, R, S and T in the sequence P-Q-R-S-T. Each stage of production takes one working day and the product from one stage to another can be transferred only in the next day. The following table shows the number of chips that can processed in each day of the week in a certain production plant.
If a production process is delivered more chips that it can handle, then the unfinished chips are processed in the next day.
Production unit P works to its full capacity on all days of the week with no chips pending processing. (All unfinished products on Saturday is delivered to another production plant to be completed. ) Also on Monday, the number of chips fed to the different production stages Q, R, S and T are 100, 300, 500 and 600 respectively.
Question 94
How many chips are manufactured by the production unit in a week ?
Show Answer
Solution
Since the work of P is independent of other stages and P
works to its full capacity on all days and all other units works on full
capacity on Monday, the starting point of production for each day is shown:
The capacity of Q on Tuesday is 300 but it is delivered only
200 units, thus 200 units will be processed by Q on Tuesday. The capacity of S
on Tuesday is 200 but it is delivered 300 units. So only 200 units are
processed by S on Tuesday, the remaining 100 units would be processed by S on
Wednesday. In this manner, the number of processed and unprocessed chips can be
calculated for each day. The table for
the processed chips is as shown:
The unfinished chips are shown in brackets.
The number of chips the plant manufactured is equal to the number of chips processed by T. Thus, from the table we can see that the plant manufactures 1800 chips in a week.
correct answer:-
1
Instruction for set :
Anet is an electronic chip manufacturing company in India. The chip manufacturing is done in five production stages P, Q, R, S and T in the sequence P-Q-R-S-T. Each stage of production takes one working day and the product from one stage to another can be transferred only in the next day. The following table shows the number of chips that can processed in each day of the week in a certain production plant.
If a production process is delivered more chips that it can handle, then the unfinished chips are processed in the next day.
Production unit P works to its full capacity on all days of the week with no chips pending processing. (All unfinished products on Saturday is delivered to another production plant to be completed. ) Also on Monday, the number of chips fed to the different production stages Q, R, S and T are 100, 300, 500 and 600 respectively.
Question 95
How many chips did not undergo any processing during Thursday ?
Show Answer
Solution
Since the work of P is independent of other stages and P
works to its full capacity on all days and all other units works on full
capacity on Monday, the starting point of production for each day is shown:
The capacity of Q on Tuesday is 300 but it is delivered only
200 units, thus 200 units will be processed by Q on Tuesday. The capacity of S
on Tuesday is 200 but it is delivered 300 units. So only 200 units are
processed by S on Tuesday, the remaining 100 units would be processed by S on
Wednesday. In this manner, the number of processed and unprocessed chips can be
calculated for each day. The table for
the processed chips is as shown:
The unfinished chips are shown in brackets.
From the table, we can see that 300 chips did not undergo any processing during Thursday.
correct answer:-
4
Instruction for set :
Anet is an electronic chip manufacturing company in India. The chip manufacturing is done in five production stages P, Q, R, S and T in the sequence P-Q-R-S-T. Each stage of production takes one working day and the product from one stage to another can be transferred only in the next day. The following table shows the number of chips that can processed in each day of the week in a certain production plant.
If a production process is delivered more chips that it can handle, then the unfinished chips are processed in the next day.
Production unit P works to its full capacity on all days of the week with no chips pending processing. (All unfinished products on Saturday is delivered to another production plant to be completed. ) Also on Monday, the number of chips fed to the different production stages Q, R, S and T are 100, 300, 500 and 600 respectively.
Question 96
What is the total number of products processed by R in a week ?
Show Answer
Solution
Since the work of P is independent of other stages and P
works to its full capacity on all days and all other units works on full
capacity on Monday, the starting point of production for each day is shown:
The capacity of Q on Tuesday is 300 but it is delivered only
200 units, thus 200 units will be processed by Q on Tuesday. The capacity of S
on Tuesday is 200 but it is delivered 300 units. So only 200 units are
processed by S on Tuesday, the remaining 100 units would be processed by S on
Wednesday. In this manner, the number of processed and unprocessed chips can be
calculated for each day. The table for
the processed chips is as shown:
The unfinished chips are shown in brackets.
From the table, we can see that R processes 1200 chips in a week.
correct answer:-
2
Instruction for set :
Six students, Anamika, Baishakhi, Chanakya, Divya, Eshan and Farha scored different marks in three different subjects - physics, chemistry and biology. They were ranked subject-wise according to the marks obtained by them in each subject. A higher rank means a lower numerical value. It is also known that:
1. No student got the same rank in two different subjects. Baishakhi and Chanakya got odd ranks in biology.
2. The highest rank that Eshan got across the three subjects was third. The sum of the ranks of Baishakhi and Divya in physics is even.
3. Baishakhi and Farha did not get the first rank in any of the subjects. The sum of the ranks of Anamika in all the three subjects is even.
4. Baishakhi got an inferior rank than Anamika in only one subject. The sum of the ranks of Farha in all the three subjects is the highest possible prime number.
5. The difference between the ranks of Divya and Eshan in biology is greater than 4. At least two students got inferior rank than Anamika in chemistry.
6. Chanakya, Baishakhi and Farha got the same rank in physics, chemistry and biology respectively.
Question 97
What is the sum of the ranks of Anamika, Divya and Farha in biology?
Show Answer
Solution
The difference between the ranks of Divya and Eshan in biology is greater than 4 and the highest rank that Eshan got is third. So, Divya must be first in biology and Eshan must be sixth in biology. Also, as Baishakhi and Farha did not get the first rank, Anamika and Chanakya must be first in physics and chemistry in any order.
Chanakya, Baishakhi and Farha got the same rank in physics, chemistry and biology respectively. If Chanakya would have gotten the first rank in physics, Farha would get first rank in biology. But, this is not possibe. So, Chanakya must be first in chemistry and Anamika must be first in physics. Baishakhi got inferior rank to Anamika in only one subject. That subject must be physics because Anamika got first in physics. Also, Baishakhi and Chanakya got odd ranks in biology. So, they must be third and fifth in any order. But, Baishakhi cannot be fifth in biology because Anamika's rank is inferior to Baishakhi's in biology. So, Baishakhi must be third, Chanakya must be fifth and Anamika must be fourth in biology.
Since, it has been found that Farha is second in biology, Chanakya and Baishakhi must be second in physics and chemistry respectively.The sum of the ranks of Anamika is even. So, her rank in chemistry must be odd. Also, at least two students got inferior ranks than Anamika in chemistry. So, she must be third in chemistry. Therefore, Eshan must be third in physics because the third place in chemistry and biology has already been taken.
The sum of the ranks of Baishakhi and Divya is even in physics. So, they must be fourth and sixth in physics in any order. Thus, Farha must be fifth in physics. The sum of the ranks of Farha is highest possible prime number i.e 13. So, she must be sixth in chemistry. Divya and Eshan must be fourth and fifth in any order. Thus, we get the final table as:
From the table we can see that the sum of the ranks of Anamika, Divya and Farha in biology is (4 + 1 + 2) = 7
Hence, 7 is the correct answer.
correct answer:-
7
Instruction for set :
Six students, Anamika, Baishakhi, Chanakya, Divya, Eshan and Farha scored different marks in three different subjects - physics, chemistry and biology. They were ranked subject-wise according to the marks obtained by them in each subject. A higher rank means a lower numerical value. It is also known that:
1. No student got the same rank in two different subjects. Baishakhi and Chanakya got odd ranks in biology.
2. The highest rank that Eshan got across the three subjects was third. The sum of the ranks of Baishakhi and Divya in physics is even.
3. Baishakhi and Farha did not get the first rank in any of the subjects. The sum of the ranks of Anamika in all the three subjects is even.
4. Baishakhi got an inferior rank than Anamika in only one subject. The sum of the ranks of Farha in all the three subjects is the highest possible prime number.
5. The difference between the ranks of Divya and Eshan in biology is greater than 4. At least two students got inferior rank than Anamika in chemistry.
6. Chanakya, Baishakhi and Farha got the same rank in physics, chemistry and biology respectively.
Question 98
What is the sum of the ranks of Chanakya in all the three subjects?
Show Answer
Solution
The difference between the ranks of Divya and Eshan in biology is greater than 4 and the highest rank that Eshan got is third. So, Divya must be first in biology and Eshan must be sixth in biology. Also, as Baishakhi and Farha did not get the first rank, Anamika and Chanakya must be first in physics and chemistry in any order.
Chanakya, Baishakhi and Farha got the same rank in physics, chemistry and biology respectively. If Chanakya would have gotten the first rank in physics, Farha would get first rank in biology. But, this is not possibe. So, Chanakya must be first in chemistry and Anamika must be first in physics. Baishakhi got inferior rank to Anamika in only one subject. That subject must be physics because Anamika got first in physics. Also, Baishakhi and Chanakya got odd ranks in biology. So, they must be third and fifth in any order. But, Baishakhi cannot be fifth in biology because Anamika's rank is inferior to Baishakhi's in biology. So, Baishakhi must be third, Chanakya must be fifth and Anamika must be fourth in biology.
Since, it has been found that Farha is second in biology, Chanakya and Baishakhi must be second in physics and chemistry respectively.The sum of the ranks of Anamika is even. So, her rank in chemistry must be odd. Also, at least two students got inferior ranks than Anamika in chemistry. So, she must be third in chemistry. Therefore, Eshan must be third in physics because the third place in chemistry and biology has already been taken.
The sum of the ranks of Baishakhi and Divya is even in physics. So, they must be fourth and sixth in physics in any order. Thus, Farha must be fifth in physics. The sum of the ranks of Farha is highest possible prime number i.e 13. So, she must be sixth in chemistry. Divya and Eshan must be fourth and fifth in any order. Thus, we get the final table as:
From the table we can see that the sum of the ranks of Chanakya in all the three subjects is (2 + 1 + 5) = 8
Hence, 8 is the correct answer.
correct answer:-
8
Instruction for set :
Six students, Anamika, Baishakhi, Chanakya, Divya, Eshan and Farha scored different marks in three different subjects - physics, chemistry and biology. They were ranked subject-wise according to the marks obtained by them in each subject. A higher rank means a lower numerical value. It is also known that:
1. No student got the same rank in two different subjects. Baishakhi and Chanakya got odd ranks in biology.
2. The highest rank that Eshan got across the three subjects was third. The sum of the ranks of Baishakhi and Divya in physics is even.
3. Baishakhi and Farha did not get the first rank in any of the subjects. The sum of the ranks of Anamika in all the three subjects is even.
4. Baishakhi got an inferior rank than Anamika in only one subject. The sum of the ranks of Farha in all the three subjects is the highest possible prime number.
5. The difference between the ranks of Divya and Eshan in biology is greater than 4. At least two students got inferior rank than Anamika in chemistry.
6. Chanakya, Baishakhi and Farha got the same rank in physics, chemistry and biology respectively.
Question 99
Who got the third rank in chemistry?
Show Answer
Solution
The difference between the ranks of Divya and Eshan in biology is greater than 4 and the highest rank that Eshan got is third. So, Divya must be first in biology and Eshan must be sixth in biology. Also, as Baishakhi and Farha did not get the first rank, Anamika and Chanakya must be first in physics and chemistry in any order.
Chanakya, Baishakhi and Farha got the same rank in physics, chemistry and biology respectively. If Chanakya would have gotten the first rank in physics, Farha would get first rank in biology. But, this is not possibe. So, Chanakya must be first in chemistry and Anamika must be first in physics. Baishakhi got inferior rank to Anamika in only one subject. That subject must be physics because Anamika got first in physics. Also, Baishakhi and Chanakya got odd ranks in biology. So, they must be third and fifth in any order. But, Baishakhi cannot be fifth in biology because Anamika's rank is inferior to Baishakhi's in biology. So, Baishakhi must be third, Chanakya must be fifth and Anamika must be fourth in biology.
Since, it has been found that Farha is second in biology, Chanakya and Baishakhi must be second in physics and chemistry respectively.The sum of the ranks of Anamika is even. So, her rank in chemistry must be odd. Also, at least two students got inferior ranks than Anamika in chemistry. So, she must be third in chemistry. Therefore, Eshan must be third in physics because the third place in chemistry and biology has already been taken.
The sum of the ranks of Baishakhi and Divya is even in physics. So, they must be fourth and sixth in physics in any order. Thus, Farha must be fifth in physics. The sum of the ranks of Farha is highest possible prime number i.e 13. So, she must be sixth in chemistry. Divya and Eshan must be fourth and fifth in any order. Thus, we get the final table as:
From the table we can see that Anamika got the third rank in chemistry.
Hence, option D is the correct answer.
correct answer:-
4
Instruction for set :
Six students, Anamika, Baishakhi, Chanakya, Divya, Eshan and Farha scored different marks in three different subjects - physics, chemistry and biology. They were ranked subject-wise according to the marks obtained by them in each subject. A higher rank means a lower numerical value. It is also known that:
1. No student got the same rank in two different subjects. Baishakhi and Chanakya got odd ranks in biology.
2. The highest rank that Eshan got across the three subjects was third. The sum of the ranks of Baishakhi and Divya in physics is even.
3. Baishakhi and Farha did not get the first rank in any of the subjects. The sum of the ranks of Anamika in all the three subjects is even.
4. Baishakhi got an inferior rank than Anamika in only one subject. The sum of the ranks of Farha in all the three subjects is the highest possible prime number.
5. The difference between the ranks of Divya and Eshan in biology is greater than 4. At least two students got inferior rank than Anamika in chemistry.
6. Chanakya, Baishakhi and Farha got the same rank in physics, chemistry and biology respectively.
Question 100
How many definite pairs of students are there such that one’s rank is either inferior or superior to the other across all subjects?
Show Answer
Solution
The difference between the ranks of Divya and Eshan in biology is greater than 4 and the highest rank that Eshan got is third. So, Divya must be first in biology and Eshan must be sixth in biology. Also, as Baishakhi and Farha did not get the first rank, Anamika and Chanakya must be first in physics and chemistry in any order.
Chanakya, Baishakhi and Farha got the same rank in physics, chemistry and biology respectively. If Chanakya would have gotten the first rank in physics, Farha would get first rank in biology. But, this is not possibe. So, Chanakya must be first in chemistry and Anamika must be first in physics. Baishakhi got inferior rank to Anamika in only one subject. That subject must be physics because Anamika got first in physics. Also, Baishakhi and Chanakya got odd ranks in biology. So, they must be third and fifth in any order. But, Baishakhi cannot be fifth in biology because Anamika's rank is inferior to Baishakhi's in biology. So, Baishakhi must be third, Chanakya must be fifth and Anamika must be fourth in biology.
Since, it has been found that Farha is second in biology, Chanakya and Baishakhi must be second in physics and chemistry respectively.The sum of the ranks of Anamika is even. So, her rank in chemistry must be odd. Also, at least two students got inferior ranks than Anamika in chemistry. So, she must be third in chemistry. Therefore, Eshan must be third in physics because the third place in chemistry and biology has already been taken.
The sum of the ranks of Baishakhi and Divya is even in physics. So, they must be fourth and sixth in physics in any order. Thus, Farha must be fifth in physics. The sum of the ranks of Farha is highest possible prime number i.e 13. So, she must be sixth in chemistry. Divya and Eshan must be fourth and fifth in any order. Thus, we get the final table as:
From the table we can see that only (A, E) and (C, E) are pairs in which one has got an inferior or a superior rank than the other in all the three subjects.
Hence, 2 is the correct answer.
Read the following information carefully and answer the questions that follow.
Players from five different nations- India, Australia, China, USA, and Britain- participated in a sporting carnival which has five different sporting events- Tennis, Sprinting, Swimming, Wrestling, and Shooting. Each country sent a total of at most 10 players to participate in the sporting carnival. No player participated in more than one event. The following information is also known-
(i) An equal number of players from Britain participated in sprinting, swimming, and wrestling.
(ii) The total number of players who participated in Sprinting, Swimming, Wrestling and Shooting was the same and it was twice the total number of players who participated in Tennis.
(iii) The number of players participating in the shooting is same for all the countries, with the exception of India.
(iv) Among all the USA player participating in different events, the number of players participating in Wrestling is the highest. Each country sent at least one player to participate in Sprinting and Wrestling.
(v) The total number of players from the USA who participated in various events is one less that of Australia, which in turn, is one less than that of China, which in turn, is one less than that of Britain, which in turn, is two less than that of India.
(vi) Other than the USA, at least one player from each country participated in Tennis. In all other events other than Tennis, at least one player from the USA participated.
(vii) No player from India participated in Swimming, and the number of players from India participating in different events is different.
Question 101
What is the sum of players from Australia and China who participated in Sprinting and Swimming put together? (Enter ‘-1’ if the answer cannot be determined)
Show Answer
Solution
Number of Indian participating in Swimming is 0. We also know that a different number of player participated in different events from India. Since the maximum number of players from each country can be 10, the number of players from India in different events are 0,1,2,3,4 (a total of 10). This means the total number of players participating in the carnival from different countries are- Ind 10, Aus 6, China 7, USA 5, and Bri (8) (Total of 36 players). Total number of players participating in tennis is exactly half of others. Let the number of players participating in tennis be a. This means that total number of player are 9a => 9a=36 or a=4.
In shooting, every country has the same number of players participating, except for India. This can happen in two ways- Ind=0 and every other country-2; Ind-4 and every other country 1. But the first case cannot happen as India as 0 players in Swimming already. Thus, in shooting, Ind=4 and every other country=1. Now the USA has the highest number of players participating in Wrestling. Thus USA(wrestling)=2 and USA(Sprinting)= USA(Sprinting)=1. Now since every country, except the USA, sends a player for tennis, number of players from each country participating in tennis should be 1. Now, an equal number of players from Britain participated in sprinting, swimming, and wrestling. This means that number of players participating in these events from Britain will be 2. Now if 3 players participate in Wrestling from India, either Aus or China has to be 0 in Wrestling, which can’t be possible. Thus, India(Wrestling)=2 and India(Sprinting)=3. This means that Aus(Sprinting)= China(Sprinting)= Aus(Wrestling)= China(Wrestling)=1. The rest of the players from Aus and China go to Swimming. We can tabulate the data in the following manner.
From the table, we can calculate the required sum as 1+2+1+3=7.
correct answer:-
7
Instruction for set :
Read the following information carefully and answer the questions that follow.
Players from five different nations- India, Australia, China, USA, and Britain- participated in a sporting carnival which has five different sporting events- Tennis, Sprinting, Swimming, Wrestling, and Shooting. Each country sent a total of at most 10 players to participate in the sporting carnival. No player participated in more than one event. The following information is also known-
(i) An equal number of players from Britain participated in sprinting, swimming, and wrestling.
(ii) The total number of players who participated in Sprinting, Swimming, Wrestling and Shooting was the same and it was twice the total number of players who participated in Tennis.
(iii) The number of players participating in the shooting is same for all the countries, with the exception of India.
(iv) Among all the USA player participating in different events, the number of players participating in Wrestling is the highest. Each country sent at least one player to participate in Sprinting and Wrestling.
(v) The total number of players from the USA who participated in various events is one less that of Australia, which in turn, is one less than that of China, which in turn, is one less than that of Britain, which in turn, is two less than that of India.
(vi) Other than the USA, at least one player from each country participated in Tennis. In all other events other than Tennis, at least one player from the USA participated.
(vii) No player from India participated in Swimming, and the number of players from India participating in different events is different.
Question 102
Which event registered the highest number of players participating from a single country?
Show Answer
Solution
Number of Indian participating in Swimming is 0. We also know that a different number of player participated in different events from India. Since the maximum number of players from each country can be 10, the number of players from India in different events are 0,1,2,3,4 (a total of 10). This means the total number of players participating in the carnival from different countries are- Ind 10, Aus 6, China 7, USA 5, and Bri (8) (Total of 36 players). Total number of players participating in tennis is exactly half of others. Let the number of players participating in tennis be a. This means that total number of player are 9a => 9a=36 or a=4.
In shooting, every country has the same number of players participating, except for India. This can happen in two ways- Ind=0 and every other country-2; Ind-4 and every other country 1. But the first case cannot happen as India as 0 players in Swimming already. Thus, in shooting, Ind=4 and every other country=1. Now the USA has the highest number of players participating in Wrestling. Thus USA(wrestling)=2 and USA(Sprinting)= USA(Sprinting)=1. Now since every country, except the USA, sends a player for tennis, number of players from each country participating in tennis should be 1. Now, an equal number of players from Britain participated in sprinting, swimming, and wrestling. This means that number of players participating in these events from Britain will be 2. Now if 3 players participate in Wrestling from India, either Aus or China has to be 0 in Wrestling, which can’t be possible. Thus, India(Wrestling)=2 and India(Sprinting)=3. This means that Aus(Sprinting)= China(Sprinting)= Aus(Wrestling)= China(Wrestling)=1. The rest of the players from Aus and China go to Swimming. We can tabulate the data in the following manner.
From the table, we can see that 4 Indian players participated in Shooting which is the highest.
correct answer:-
3
Instruction for set :
Read the following information carefully and answer the questions that follow.
Players from five different nations- India, Australia, China, USA, and Britain- participated in a sporting carnival which has five different sporting events- Tennis, Sprinting, Swimming, Wrestling, and Shooting. Each country sent a total of at most 10 players to participate in the sporting carnival. No player participated in more than one event. The following information is also known-
(i) An equal number of players from Britain participated in sprinting, swimming, and wrestling.
(ii) The total number of players who participated in Sprinting, Swimming, Wrestling and Shooting was the same and it was twice the total number of players who participated in Tennis.
(iii) The number of players participating in the shooting is same for all the countries, with the exception of India.
(iv) Among all the USA player participating in different events, the number of players participating in Wrestling is the highest. Each country sent at least one player to participate in Sprinting and Wrestling.
(v) The total number of players from the USA who participated in various events is one less that of Australia, which in turn, is one less than that of China, which in turn, is one less than that of Britain, which in turn, is two less than that of India.
(vi) Other than the USA, at least one player from each country participated in Tennis. In all other events other than Tennis, at least one player from the USA participated.
(vii) No player from India participated in Swimming, and the number of players from India participating in different events is different.
Question 103
The number of players from India, who are participating in Sprinting, is what percentage more than the players from Australia, who are participating in Wrestling? (Round off the answer to two decimal digits if it is not an integer) (Enter ‘-1’ if the answer cannot be determined)
Show Answer
Solution
Number of Indian participating in Swimming is 0. We also know that a different number of player participated in different events from India. Since the maximum number of players from each country can be 10, the number of players from India in different events are 0,1,2,3,4 (a total of 10). This means the total number of players participating in the carnival from different countries are- Ind 10, Aus 6, China 7, USA 5, and Bri (8) (Total of 36 players). Total number of players participating in tennis is exactly half of others. Let the number of players participating in tennis be a. This means that total number of player are 9a => 9a=36 or a=4.
In shooting, every country has the same number of players participating, except for India. This can happen in two ways- Ind=0 and every other country-2; Ind-4 and every other country 1. But the first case cannot happen as India as 0 players in Swimming already. Thus, in shooting, Ind=4 and every other country=1. Now the USA has the highest number of players participating in Wrestling. Thus USA(wrestling)=2 and USA(Sprinting)= USA(Sprinting)=1. Now since every country, except the USA, sends a player for tennis, number of players from each country participating in tennis should be 1. Now, an equal number of players from Britain participated in sprinting, swimming, and wrestling. This means that number of players participating in these events from Britain will be 2. Now if 3 players participate in Wrestling from India, either Aus or China has to be 0 in Wrestling, which can’t be possible. Thus, India(Wrestling)=2 and India(Sprinting)=3. This means that Aus(Sprinting)= China(Sprinting)= Aus(Wrestling)= China(Wrestling)=1. The rest of the players from Aus and China go to Swimming. We can tabulate the data in the following manner.
India(Sprinting)=3 and Aus(Wrestling)=1
Thus the percentage is [(3-1)/1] X 100 = 200%
correct answer:-
200
Instruction for set :
Read the following information carefully and answer the questions that follow.
Players from five different nations- India, Australia, China, USA, and Britain- participated in a sporting carnival which has five different sporting events- Tennis, Sprinting, Swimming, Wrestling, and Shooting. Each country sent a total of at most 10 players to participate in the sporting carnival. No player participated in more than one event. The following information is also known-
(i) An equal number of players from Britain participated in sprinting, swimming, and wrestling.
(ii) The total number of players who participated in Sprinting, Swimming, Wrestling and Shooting was the same and it was twice the total number of players who participated in Tennis.
(iii) The number of players participating in the shooting is same for all the countries, with the exception of India.
(iv) Among all the USA player participating in different events, the number of players participating in Wrestling is the highest. Each country sent at least one player to participate in Sprinting and Wrestling.
(v) The total number of players from the USA who participated in various events is one less that of Australia, which in turn, is one less than that of China, which in turn, is one less than that of Britain, which in turn, is two less than that of India.
(vi) Other than the USA, at least one player from each country participated in Tennis. In all other events other than Tennis, at least one player from the USA participated.
(vii) No player from India participated in Swimming, and the number of players from India participating in different events is different.
Question 104
Find the number of instances where only 1 participant from a country participated in an event? (Enter ‘-1’ if the answer cannot be determined)
Show Answer
Solution
Number of Indian participating in Swimming is 0. We also know that a different number of player participated in different events from India. Since the maximum number of players from each country can be 10, the number of players from India in different events are 0,1,2,3,4 (a total of 10). This means the total number of players participating in the carnival from different countries are- Ind 10, Aus 6, China 7, USA 5, and Bri (8) (Total of 36 players). Total number of players participating in tennis is exactly half of others. Let the number of players participating in tennis be a. This means that total number of player are 9a => 9a=36 or a=4.
In shooting, every country has the same number of players participating, except for India. This can happen in two ways- Ind=0 and every other country-2; Ind-4 and every other country 1. But the first case cannot happen as India as 0 players in Swimming already. Thus, in shooting, Ind=4 and every other country=1. Now the USA has the highest number of players participating in Wrestling. Thus USA(wrestling)=2 and USA(Sprinting)= USA(Sprinting)=1. Now since every country, except the USA, sends a player for tennis, number of players from each country participating in tennis should be 1. Now, an equal number of players from Britain participated in sprinting, swimming, and wrestling. This means that number of players participating in these events from Britain will be 2. Now if 3 players participate in Wrestling from India, either Aus or China has to be 0 in Wrestling, which can’t be possible. Thus, India(Wrestling)=2 and India(Sprinting)=3. This means that Aus(Sprinting)= China(Sprinting)= Aus(Wrestling)= China(Wrestling)=1. The rest of the players from Aus and China go to Swimming. We can tabulate the data in the following manner.
Counting the number of 1’s in the table, we get the required instances as 14.
correct answer:-
14
Instruction for set :
Read the information given below carefully and answer the questions which follow.
Sunil appeared for Civil Services prelims examination. The examination consisted of 5 different sections. The partial details of Sunil’s attempts are given below.
It is known that
1. In the exam, each correct answer is awarded 3 marks and each incorrect answer attracts a penalty of 1 mark. Half (.5) mark is deducted for each unattempted question.
2. Sunil attempted 125 questions in the paper and scored a total of 201 marks.
3. Out of the total incorrect answers by Sunil, one-sixth were in the CA section.
4. The number of incorrect questions in Geography is half the number of incorrect questions in CA.
5. The net score of Sunil in Geography section is two times his net score in Economics.
Question 105
What is the total number of questions which Sunil got wrong in the paper?
Show Answer
Solution
From the table we can see that there is a total of 185 questions. Out of these 185, Sunil attempted 125. Hence he left 60 questions which means that he has a negative of 30 marks already. His final score was 201. Let the number of incorrect questions be x, then
125*3 - 30 - 4x = 201 ( Each wrong question results in a loss of 4 marks, 3 marks for the question + 1 negative)
So we have
4x = 375 - 201 - 30 = 144
=> x = 36
Hence total incorrect questions are 36. Thus, correct questions = 89
From 3 and 4, 6 incorrect questions will be in CA and 3 will be in geography.
In economics, correct attempts = 11
Hence marks in economics = 33 - 9 - 6 = 18
=> Marks in geography = 36
Number of unattempted in CA + Correct in CA = 34
Let c be the no. of correct answers, then
3c - (34 - c)*.5 - 6 = 33
=> 3c - 17 + .c = 39
=> 3.5c = 56
=> c = 16
Thus, unattempted must be 18.
Marks in geography = 18
Incorrect in geography = 3.
Let s be the correct answers in geography, so we have
3s - (27 - s)*.5 - 3 = 36
=> 3.5s = 52.5
=> s = 15
Hence unattempted in geography = 12
We know that total correct answers = 89
Hence correct answers in History = 17
Hence we can get the final table as follows
correct answer:-
36
Instruction for set :
Read the information given below carefully and answer the questions which follow.
Sunil appeared for Civil Services prelims examination. The examination consisted of 5 different sections. The partial details of Sunil’s attempts are given below.
It is known that
1. In the exam, each correct answer is awarded 3 marks and each incorrect answer attracts a penalty of 1 mark. Half (.5) mark is deducted for each unattempted question.
2. Sunil attempted 125 questions in the paper and scored a total of 201 marks.
3. Out of the total incorrect answers by Sunil, one-sixth were in the CA section.
4. The number of incorrect questions in Geography is half the number of incorrect questions in CA.
5. The net score of Sunil in Geography section is two times his net score in Economics.
Question 106
In which section did Sunil get the maximum questions wrong?
Show Answer
Solution
From the table we can see that there is a total of 185 questions. Out of these 185, Sunil attempted 125. Hence he left 60 questions which means that he has a negative of 30 marks already. His final score was 201. Let the number of incorrect questions be x, then
125*3 - 30 - 4x = 201 ( Each wrong question results in a loss of 4 marks, 3 marks for the question + 1 negative)
So we have
4x = 375 - 201 - 30 = 144
=> x = 36
Hence total incorrect questions are 36. Thus, correct questions = 89
From 3 and 4, 6 incorrect questions will be in CA and 3 will be in geography.
In economics, correct attempts = 11
Hence marks in economics = 33 - 9 - 6 = 18
=> Marks in geography = 36
Number of unattempted in CA + Correct in CA = 34
Let c be the no. of correct answers, then
3c - (34 - c)*.5 - 6 = 33
=> 3c - 17 + .c = 39
=> 3.5c = 56
=> c = 16
Thus, unattempted must be 18.
Marks in geography = 18
Incorrect in geography = 3.
Let s be the correct answers in geography, so we have
3s - (27 - s)*.5 - 3 = 36
=> 3.5s = 52.5
=> s = 15
Hence unattempted in geography = 12
We know that total correct answers = 89
Hence correct answers in History = 17
Hence we can get the final table as follows
correct answer:-
1
Instruction for set :
Read the information given below carefully and answer the questions which follow.
Sunil appeared for Civil Services prelims examination. The examination consisted of 5 different sections. The partial details of Sunil’s attempts are given below.
It is known that
1. In the exam, each correct answer is awarded 3 marks and each incorrect answer attracts a penalty of 1 mark. Half (.5) mark is deducted for each unattempted question.
2. Sunil attempted 125 questions in the paper and scored a total of 201 marks.
3. Out of the total incorrect answers by Sunil, one-sixth were in the CA section.
4. The number of incorrect questions in Geography is half the number of incorrect questions in CA.
5. The net score of Sunil in Geography section is two times his net score in Economics.
Question 107
How many questions did Sunil attempt in Geography? (Enter -1 if the answer cannot be determined)
Show Answer
Solution
From the table we can see that there is a total of 185 questions. Out of these 185, Sunil attempted 125. Hence he left 60 questions which means that he has a negative of 30 marks already. His final score was 201. Let the number of incorrect questions be x, then
125*3 - 30 - 4x = 201 ( Each wrong question results in a loss of 4 marks, 3 marks for the question + 1 negative)
So we have
4x = 375 - 201 - 30 = 144
=> x = 36
Hence total incorrect questions are 36. Thus, correct questions = 89
From 3 and 4, 6 incorrect questions will be in CA and 3 will be in geography.
In economics, correct attempts = 11
Hence marks in economics = 33 - 9 - 6 = 18
=> Marks in geography = 36
Number of unattempted in CA + Correct in CA = 34
Let c be the no. of correct answers, then
3c - (34 - c)*.5 - 6 = 33
=> 3c - 17 + .c = 39
=> 3.5c = 56
=> c = 16
Thus, unattempted must be 18.
Marks in geography = 18
Incorrect in geography = 3.
Let s be the correct answers in geography, so we have
3s - (27 - s)*.5 - 3 = 36
=> 3.5s = 52.5
=> s = 15
Hence unattempted in geography = 12
We know that total correct answers = 89
Hence correct answers in History = 17
Hence we can get the final table as follows
correct answer:-
18
Instruction for set :
Read the information given below carefully and answer the questions which follow.
Sunil appeared for Civil Services prelims examination. The examination consisted of 5 different sections. The partial details of Sunil’s attempts are given below.
It is known that
1. In the exam, each correct answer is awarded 3 marks and each incorrect answer attracts a penalty of 1 mark. Half (.5) mark is deducted for each unattempted question.
2. Sunil attempted 125 questions in the paper and scored a total of 201 marks.
3. Out of the total incorrect answers by Sunil, one-sixth were in the CA section.
4. The number of incorrect questions in Geography is half the number of incorrect questions in CA.
5. The net score of Sunil in Geography section is two times his net score in Economics.
Question 108
What is Sunil’s net score in Aptitude? (Enter -1 if the answer cannot be determined)
Show Answer
Solution
From the table we can see that there is a total of 185 questions. Out of these 185, Sunil attempted 125. Hence he left 60 questions which means that he has a negative of 30 marks already. His final score was 201. Let the number of incorrect questions be x, then
125*3 - 30 - 4x = 201 ( Each wrong question results in a loss of 4 marks, 3 marks for the question + 1 negative)
So we have
4x = 375 - 201 - 30 = 144
=> x = 36
Hence total incorrect questions are 36. Thus, correct questions = 89
From 3 and 4, 6 incorrect questions will be in CA and 3 will be in geography.
In economics, correct attempts = 11
Hence marks in economics = 33 - 9 - 6 = 18
=> Marks in geography = 36
Number of unattempted in CA + Correct in CA = 34
Let c be the no. of correct answers, then
3c - (34 - c)*.5 - 6 = 33
=> 3c - 17 + .c = 39
=> 3.5c = 56
=> c = 16
Thus, unattempted must be 18.
Marks in geography = 18
Incorrect in geography = 3.
Let s be the correct answers in geography, so we have
3s - (27 - s)*.5 - 3 = 36
=> 3.5s = 52.5
=> s = 15
Hence unattempted in geography = 12
We know that total correct answers = 89
Hence correct answers in History = 17
Hence we can get the final table as follows