CAT 2021 Question Paper Slot 1 with Solutions, Download PDF

Instructions

Ganga, Kaveri, and Narmada are three women who buy four raw materials (Mango, Apple, Banana and Milk) and sell five finished products (Mango smoothie, Apple smoothie, Banana smoothie, Mixed fruit smoothie and Fruit salad). Table-1 gives information about the raw materials required to produce the five finished products. One unit of a finished product requires one unit of each of the raw materials mentioned in the second column of the table.

One unit of milk, mango, apple, and banana cost ₹5, ₹3, ₹2, and ₹1 respectively. Each unit of a finished product is sold for a profit equal to two times the number of raw materials used to make that product. For example, apple smoothie is made with two raw materials (apple and milk) and will be sold for a profit of ₹4 per unit. Leftover raw materials are sold during the last business hour of the day for a loss of ₹1 per unit.

The amount, in rupees, received from sales (revenue) for each woman in each of the four business hours of the day is given in Table-2.

The following additional facts are known.
1. No one except possibly Ganga sold any Mango smoothie.
2. Each woman sold either zero or one unit of any single finished product in any hour.
3. Each woman had exactly one unit each of two different raw materials as leftovers.
4. No one had any banana leftover.

Question 31

What BEST can be concluded about the number of units of fruit salad sold in the first hour?

Video Solution

Solution

Given that each item is sold for a profit of 2 times the number of materials required for the dish.

Hence for different finished products: The cost price and selling price are :

Given that in any hour only either zero or one unit of a single finished product is sold. Hence the price distribution for the first three hours sales distribution is given by :

Additionally, it has been mentioned that no one except Ganga possibly sold Mango smoothies.

Considering Apple Smoothie : (AS), Mango Smoothie : ( M.S), Banana Smoothie : (B. S), Mixed Fruit : (M.F), Fruit Salad : (F.S)

In the last one hour everyone had one unit each of two different materials as leftovers:

Each leftover item is sold at Re1 less than their cost price. Hence

One unit of milk, mango, and apple will cost ₹4, ₹2, ₹1,

The three possible combinations for the last hour in which raw materials can be sold is :

One unit of milk+ One unit of mango = Rs 4+2 = Rs 6.

One unit of milk+ One unit of apple = Rs 4+1 = Rs 5.

One unit of mango+ One unit of apple = Rs 2+1 = Rs 3.

In the last one hour :

Total sale of Ganga is Rs 30. This is the total cost earned by considering selling the finished items and raw materials :

Hence the possible cases are :

(24 + 6) or (25 + 5) or ( 27 + 3). It is not possible to earn 25 and 27 by selling finished products.

Hence she earns Rs 24 which is possible by selling one ( M.S + F.S) and one raw unit of milk and mango each.

Total sale of Kaveri is Rs 27. This is the total cost earned by considering selling the finished items and raw materials :

Hence the possible cases are :

(21 + 6) or (22+5) or (24+3).

Since Kaveri cannot sell mango smoothies the possible cases are :

(21+6) Selling one apple smoothie and one banana smoothie and one raw unit of Milk and Mango.

(22+5) Selling one Banana smoothie and Fruit Salad, one unit of raw milk, and one unit of Raw Apple.

Total sale for Narmada is Rs 22. The possible cases are :

(16+6), (17+5), (19+3).

Among these, the only possible case is 19 + 3. Selling one unit Mixed Fruit, and one raw unit of Mango and Apple.

Case 1 :

case 2 :

In the first one hour, either one or two fruit salads are sold.

Question 32

Which of the following is NECESSARILY true?

Video Solution

Solution

Given that each item is sold for a profit of 2 times the number of materials required for the dish.

Hence for different finished products: The cost price and selling price are :

Given that in any hour only either zero or one unit of a single finished product is sold. Hence the price distribution for the first three hours sales distribution is given by :

Additionally, it has been mentioned that no one except Ganga possibly sold Mango smoothies.

Considering Apple Smoothie : (AS), Mango Smoothie : ( M.S), Banana Smoothie : (B. S), Mixed Fruit : (M.F), Fruit Salad : (F.S)

In the last one hour everyone had one unit each of two different materials as leftovers:

Each leftover item is sold at Re1 less than their cost price. Hence

One unit of milk, mango, and apple will cost ₹4, ₹2, ₹1,

The three possible combinations for the last hour in which raw materials can be sold is :

One unit of milk+ One unit of mango = Rs 4+2 = Rs 6.

One unit of milk+ One unit of apple = Rs 4+1 = Rs 5.

One unit of mango+ One unit of apple = Rs 2+1 = Rs 3.

In the last one hour :

Total sale of Ganga is Rs 30. This is the total cost earned by considering selling the finished items and raw materials :

Hence the possible cases are :

(24 + 6) or (25 + 5) or ( 27 + 3). It is not possible to earn 25 and 27 by selling finished products.

Hence she earns Rs 24 which is possible by selling one ( M.S + F.S) and one raw unit of milk and mango each.

Total sale of Kaveri is Rs 27. This is the total cost earned by considering selling the finished items and raw materials :

Hence the possible cases are :

(21 + 6) or (22+5) or (24+3).

Since Kaveri cannot sell mango smoothies the possible cases are :

(21+6) Selling one apple smoothie and one banana smoothie and one raw unit of Milk and Mango.

(22+5) Selling one Banana smoothie and Fruit Salad, one unit of raw milk, and one unit of Raw Apple.

Total sale for Narmada is Rs 22. The possible cases are :

(16+6), (17+5), (19+3).

Among these, the only possible case is 19 + 3. Selling one unit Mixed Fruit, and one raw unit of Mango and Apple.

Case 1 :

case 2 :

In both, cases Ganga did not sell any leftover apples. The other options are not necessarily true.

Question 33

What BEST can be concluded about the total number of units of milk the three women had in the beginning?

Video Solution

Solution

Given that each item is sold for a profit of 2 times the number of materials required for the dish.

Hence for different finished products: The cost price and selling price are :

Given that in any hour only either zero or one unit of a single finished product is sold. Hence the price distribution for the first three hours sales distribution is given by :

Additionally, it has been mentioned that no one except Ganga possibly sold Mango smoothies.

Considering Apple Smoothie : (AS), Mango Smoothie : ( M.S), Banana Smoothie : (B. S), Mixed Fruit : (M.F), Fruit Salad : (F.S)

In the last one hour everyone had one unit each of two different materials as leftovers:

Each leftover item is sold at Re1 less than their cost price. Hence

One unit of milk, mango, and apple will cost ₹4, ₹2, ₹1,

The three possible combinations for the last hour in which raw materials can be sold is :

One unit of milk+ One unit of mango = Rs 4+2 = Rs 6.

One unit of milk+ One unit of apple = Rs 4+1 = Rs 5.

One unit of mango+ One unit of apple = Rs 2+1 = Rs 3.

In the last one hour :

Total sale of Ganga is Rs 30. This is the total cost earned by considering selling the finished items and raw materials :

Hence the possible cases are :

(24 + 6) or (25 + 5) or ( 27 + 3). It is not possible to earn 25 and 27 by selling finished products.

Hence she earns Rs 24 which is possible by selling one ( M.S + F.S) and one raw unit of milk and mango each.

Total sale of Kaveri is Rs 27. This is the total cost earned by considering selling the finished items and raw materials :

Hence the possible cases are :

(21 + 6) or (22+5) or (24+3).

Since Kaveri cannot sell mango smoothies the possible cases are :

(21+6) Selling one apple smoothie and one banana smoothie and one raw unit of Milk and Mango.

(22+5) Selling one Banana smoothie and Fruit Salad, one unit of raw milk, and one unit of Raw Apple.

Total sale for Narmada is Rs 22. The possible cases are :

(16+6), (17+5), (19+3).

Among these, the only possible case is 19 + 3. Selling one unit Mixed Fruit, and one raw unit of Mango and Apple.

Case 1 :

case 2 :

In except fruit salad, all the other finished products require one unit of milk :

For case 1: a minimum of 19 units of milk and a maximum of 20 units of milk can be used.

For case 2: a minimum of 18 units of milk and a maximum of 19 units of milk is used

Question 34

If it is known that three leftover units of mangoes were sold during the last business hour of the day, how many apple smoothies were sold during the day?

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Video Solution

Solution

Given that each item is sold for a profit of 2 times the number of materials required for the dish.

Hence for different finished products: The cost price and selling price are :

Given that in any hour only either zero or one unit of a single finished product is sold. Hence the price distribution for the first three hours sales distribution is given by :

Additionally, it has been mentioned that no one except Ganga possibly sold Mango smoothies.

Considering Apple Smoothie : (AS), Mango Smoothie : ( M.S), Banana Smoothie : (B. S), Mixed Fruit : (M.F), Fruit Salad : (F.S)

In the last one hour everyone had one unit each of two different materials as leftovers:

Each leftover item is sold at Re1 less than their cost price. Hence

One unit of milk, mango, and apple will cost ₹4, ₹2, ₹1,

The three possible combinations for the last hour in which raw materials can be sold is :

One unit of milk+ One unit of mango = Rs 4+2 = Rs 6.

One unit of milk+ One unit of apple = Rs 4+1 = Rs 5.

One unit of mango+ One unit of apple = Rs 2+1 = Rs 3.

In the last one hour :

Total sale of Ganga is Rs 30. This is the total cost earned by considering selling the finished items and raw materials :

Hence the possible cases are :

(24 + 6) or (25 + 5) or ( 27 + 3). It is not possible to earn 25 and 27 by selling finished products.

Hence she earns Rs 24 which is possible by selling one ( M.S + F.S) and one raw unit of milk and mango each.

Total sale of Kaveri is Rs 27. This is the total cost earned by considering selling the finished items and raw materials :

Hence the possible cases are :

(21 + 6) or (22+5) or (24+3).

Since Kaveri cannot sell mango smoothies the possible cases are :

(21+6) Selling one apple smoothie and one banana smoothie and one raw unit of Milk and Mango.

(22+5) Selling one Banana smoothie and Fruit Salad, one unit of raw milk, and one unit of Raw Apple.

Total sale for Narmada is Rs 22. The possible cases are :

(16+6), (17+5), (19+3).

Among these, the only possible case is 19 + 3. Selling one unit Mixed Fruit, and one raw unit of Mango and Apple.

Case 1 :

case 2 :

3 units of leftover mangoes were available in case 1 and in here a total of 6 apple shakes were sold.

Instructions

Amudha, Bharatan, Chandran, Dhinesh, Ezhil, Fani and Gowtham are seven people in a town. Any pair of them could either be strangers, acquaintances, or friends. All relationships are mutual. For example, if Amudha is a friend of Bharatan, then Bharatan is also a friend of Amudha. Similarly, if Amudha is a stranger to Bharatan, then Bharatan is also a stranger to Amudha.

Partial information about the number of friends, acquaintances, and strangers of each of these people among them is given in the table below.

The following additional facts are also known.
1. Amudha, Bharatan, and Chandran are mutual strangers.
2. Amudha, Dhinesh, and Fani are Ezil's friends.
3. Chandran and Gowtham are friends.
4. Every friend of Amudha is an acquaintance of Bharatan, and every acquaintance of Bharatan is a friend of Amudha.
5. Every friend of Bharatan is an acquaintance of Amudha, and every acquaintance of Amudha is a friend of Bharatan.

Question 35

Who are Gowtham’s acquaintances?

Video Solution

Solution

Since A, B, C are mutual strangers,( B, C )are strangers for A, (A, C) are strangers for B, (A, B) are strangers for C.

Since the total number of strangers+ acquaintances+ friends for any among the 7 is 6.

The number of friends for Amudha is 1, the number of friends for Gowtham is 1.

Using statement 3 Chandran and Gowtham are friends.

Using statement 2: Amudha, Dinesh, and Fani are Ezil’s friends. Similarly, Ezil is a friend of Amudha, Dhinesh, and Fani.

Using statement 4 Every friend of Bharatan is an acquaintance of Amudha, and every acquaintance of Amudha is a friend of Bharatan, Hence the number of acquaintances of Bharatan is equal to the number of friends of Amudha.

Using statement 5 Every friend of Amudha is an acquaintance of Bharatan, and every acquaintance Bharatan is a friend of Amudha, Hence the number of acquaintances of Amudha is equal to the number of friends of Bharatan.

Hence Bharatan has one friend, 1 Acquaintance, 4 strangers.

For Amudha we are yet to find a relationship with Dhinesh, Fani, and Gowtham. Any among the three can be the stranger for Amudha, considering the three different cases.

Case 1 :

Considering Fani as an acquaintance of Amudha, then Dhinesh and Gowtham are strangers to Amudha.

Every acquaintance of Amudha is a friend of Bharathan and since the friend and acquaintance of Bharatan are known the strangers are found for Bharatan.

Fani is an acquaintance of Amudha, hence Amudha is an Acquaintance of Fani, Fani is a friend of Bharathan and hence Bharathan is a friend of Fani. But Fani has only one friend and Ezhil is already a friend of Fani.

Hence this case fails.

Case 2 :

Considering Gowtham as an acquaintance of Amudha, then Dhinesh and Fani are strangers to Amudha.

Every acquaintance of Amudha is a friend of Bharathan and since the friend and acquaintance of Bharatan are known the strangers are found for Bharatan.Since Gowtham is a friend of Bharatan, Bharatan must be a friend of Gowtham. But Gowtham can only have one friend and it already mentioned that Chandran is a friend of Gowtham and hence this case fails.

Case 3 :

Considering Dhinesh as an acquaintance of Amudha, then Fani and Gowtham are strangers to Amudha.

Every acquaintance of Amudha is a friend of Bharathan and since the friend and acquaintance of Bharatan are known the strangers are found for Bharatan.

Since Fani, Gowtham are strangers to Amudha, Bharatan. Amudha, Bharatan are strangers to Fani, Gowtham.

The 2 strangers to Gowtham and his only friend are known. Hence his three acquaintances are (Dhinesh, Ezhil, Fani).

Hence Gowtham is an acquaintance of Dhinesh, Ezhil, and Fani.

Dhinesh is an acquaintance of Amudha and hence Amudha must be an acquaintance of Dhinesh.

Dhinesh is a friend of Bharatan and hence Bharatan is a friend of Dhinesh.

Ezhil is an acquaintance of Bharatan and hence Bharatan is an acquaintance of Ezhil. The only stranger to Ezhil who is left is Chandran. Hence Ezhil is a stranger to Chandran.

The two strangers to Dhinesh who are left are Chandran and Fani. Chandran is a stranger to Dhinesh and hence Dhinesh is a stranger to Chandran.

The only acquaintance of Chandran who is left is Fani.

The remaining relationships with Fani are Dhinesh and Chandran. Dhinesh is a stranger to Fani and Chandran is an acquaintance of Fani.

Gowtham's Acquaintances are Ghinesh, Ezhil, Fani.

Question 36

Which of these pairs share the same type of relationship?