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**Instructions**

In each of the following questions a question is asked followed by three statements.You have to study the questions and all the given three statements and all the statements and decide whether any information provided in the statement are redundant and can be dispensed with while answering the questions ?

**Question 1:Â **8 men and 14 women are working together in a field. After working for 3 days, 5 men and 8 women leave the work. How many more days will be required to complete the work?

I. 19 men and 12 women together can complete the work in 18 days.

II. 16 men can complete two-third of the work in 16 days.

III. In a day, the work done by three men is equal to the work done by four women.

a)Â I only

b)Â II only

c)Â III only

d)Â II or III only

e)Â I or II or III

**Question 2:Â **what is the area of the given right angle triangle ?

I. Length of the hypotenuse is 5 cm

II.perimeter of the triangle is four times its base

III. one of the angles of the triangle is 60 degrees

a)Â I only

b)Â II only

c)Â II or III only

d)Â II and III both

e)Â Data inadequate

**Question 3:Â **Three friends J, K and Ljog around a circular stadium and complete one round in 12, 18 and 20 seconds respectively. In how many minutes will all the three meet again at the starting point

a)Â 5

b)Â 8

c)Â 12

d)Â 3

e)Â None of these

**Question 4:Â **The speed of a boat when travelling downstream is 32 Kms. / Hr. , whereas when travelling upstream it is 28 kms/hr. What is the speed of the boat in still water ?

a)Â 27 Kms./Hr.

b)Â 29 Kms./ Hr.

c)Â 31 Kms./ Hr.

d)Â Cannot be determined

e)Â None of these

**Question 5:Â **A pump can fill a tank with water in 2 hours. Because of a leak, it took 2$\frac{1}{3}$ hours to fill the tank. The leak can drain all the water of the tank in

a)Â 4$\frac{1}{3}$ hours

b)Â 7 hours

c)Â 8 hours

d)Â 14 hours

e)Â None of these

**Instructions**

Directions: Study the information carefully to answer these questions.

In a team, there are 240 members (males and females). Two-thirds of them are males. Fifteen per cent of males are graduates. Remaining males are non-graduates. Three-fourths of the females are graduates. Remaining females are non-graduates.

**Question 6:Â **What is the absolute difference between the number of females who are non-graduates and the number of males who are graduates?

a)Â 2

b)Â 24

c)Â 4

d)Â 116

e)Â 36

**Question 7:Â **What is the sum of the number of females who are graduates and the number of males who are non-graduates?

a)Â 184

b)Â 96

c)Â 156

d)Â 84

e)Â 196

**Question 8:Â **What is the ratio of the total number of males to the number of females who are non-graduates?

a)Â 6 : 1

b)Â 8 : 1

c)Â 8 : 3

d)Â 5 : 2

e)Â 7 : 2

**Question 9:Â **The ratio of the present age of Manisha and Deepali is 5 : X. Manisha is 9 years younger than Parineeta. Parineetaâ€™s age after 9 years will be 33 years. The difference between Deepaliâ€™s and Manishaâ€™s age is the same as the present age of Parineeta. What should come in place of X?

a)Â 23

b)Â 39

c)Â 15

d)Â Cannot be determined

e)Â None of these

**Question 10:Â **The average marks in English of a class of 24 students is 56. If the marks of three students were misread as 44, 45 and 61 in lieu of the actual marks 48, 59 and 67 respectively, then what would be the correct average?

a)Â 56.5

b)Â 59

c)Â 57.5

d)Â 58

e)Â None of these

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**Instructions**

In each of these question two equations I & II with variables a & b are given You have to solve both the equations to find the values of a & b

Mark answer if

a) a<b

</b

<b

</b

<b

b) $a\leq b$

c) relationship between a & b cannot be established

d) a>b

e) $a\geq b$

**Question 11:Â **I.$2a^{2}+a-1=0$

II.$12b^{2}-17b+6=0$

a)Â $a<b$

b)Â $a\leq b$

c)Â Relationship between $a$ & $b$ cannot be established

d)Â $a>b$

e)Â $a\geq b$

**Question 12:Â **I.$a^{2}-5a+6=0$

II. $2b^{2}-13b+21=0$

a)Â $a<b$

b)Â $a\leq b$

c)Â Relationship between $a$ & $b$ cannot be established

d)Â $a>b$

e)Â $a\geq b$

**Question 13:Â **I.$a^{2}+5a+6=0$

II.$b^{2}+7b+12=0$

a)Â $a<b$

b)Â $a \leq b$

c)Â Relationship between $a$ & $b$ cannot be established

d)Â $a>b$

e)Â $a \geq b$

**Question 14:Â **Seema bought 20 pens, 8 packets of wax colours, 6 calculators and 7 pencil boxes, The price of one pen is Rs. 7, one packet of wax colour is for Rs. 22, one calculator is for Rs.175 and one pencil box costs Rs. 14 more than the combined price of one pen and one packet of wax colours. How much amount did Seema pay to the shopkeeper?

a)Â Rs. 491

b)Â Rs. 1,725

c)Â Rs. 1,667

d)Â Rs. 1,527

e)Â None of these

**Question 15:Â **An article was purchased for Rs.78,350. Its price was marked up by 30%. It was sold at a discount of 20% on the marked up price. What was the profit percent on the cost price?

a)Â 4

b)Â 7

c)Â 5

d)Â 3

e)Â 6

**Question 16:Â **Three men A, B and C start a business together. They invest Rs30000, Rs24000 and Rs42000 respectively in the beginning. After 4 months. B took out Rs6000 and C took out Rs10000. They get a profit of Rs11960 at the end of the year, Bâ€™s share in the profit (approximately) is

a)Â Rs2700

b)Â Rs2803

c)Â Rs2900

d)Â Rs2790

e)Â None of these

**Question 17:Â **A shopkeeper sells two watches for Rs308 each. On one he gets 12% profit and on the other 12% loss. His profit or loss in the entire transaction was

a)Â 1$\frac{11}{25}$% loss

b)Â 1$\frac{11}{25}$% gain

c)Â 3$\frac{2}{25}$%loss

d)Â 3$\frac{2}{25}$%gain

e)Â None of these

**Instructions**

An urn contains 6 red, 4 blue, 2 green and 3 yellow marbles.

**Question 18:Â **If four marbles are picked at random, what is the probability that at least one is blue ?

a)Â 4/11

b)Â 69/91

c)Â 11/15

d)Â 22/91

e)Â None of these

**Question 19:Â **If two marbles are picked at random, what is the probability that both are red ?

a)Â 1/6

b)Â 1/3

c)Â 2/15

d)Â 2/5

e)Â None of these

**Question 20:Â **If three marbles are picked at random, what is the probability that two are blue and one is yellow?

a)Â 3/91

b)Â 1/5

c)Â 18/455

d)Â 7/15

e)Â None of these

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**Answers & Solutions:**

**1)Â AnswerÂ (A)**

**2)Â AnswerÂ (B)**

To find the area of right angled triangle, we need to know the base and height or the length of any side if its aÂ 30-60-90 triangle

From statement I and III, two angles are 90Â° and 60Â°, => Third angle = 30Â°

In a 30-60-90 triangle, the hypotenuse is always twice as long as the side opposite the 30Â° angle and the side opposite the 60Â° angle isÂ âˆš3 times as long as the side opposite the 30Â° angle.

The ratio of sides opposite 30Â°, 60Â° and 90Â° angles =1Â : $\sqrt{3}$ : 2

LengthÂ of the side opposite the 90Â° angle (hypotenuse) = 5 cm

=> Length of side opposite the 30Â° angle = $\frac{5}{2}=2.5$ cm

and length of side opposite to 60Â° angle = $2.5 \sqrt{3}$ cm

$\therefore$ Area of triangle = $\frac{1}{2} \times 2.5 \times 2.5 \sqrt{3} = 3.125\sqrt{3}$ $cm^2$

Thus, statement II is redundant.

=> Ans – (B)

**3)Â AnswerÂ (D)**

All the three friends will meet at the starting point again after X seconds, such that X is the LCM of the times taken by J, K and L to complete one round.

=> LCM of 12, 18 and 20 = 180 seconds = 3 minutes.

Hence 3 minutes is the answer.

**4)Â AnswerÂ (E)**

Let the speed of boat in still water be v and the speed of water be x.

Boat speed while going upstream = v-x = 28

Boat speed while going downstream = v+x = 32

=> 2v = 60 => v = 30

Hence, none of these is the correct answer.

**5)Â AnswerÂ (D)**

Part of tank emptied in 1 hour by the

leak

$\frac{1}{2}$ – $\frac{2}{7}$ = $\frac{1}{14}$

The leak will empty the tank in 14 hours.

**6)Â AnswerÂ (C)**

Total members = 240

Total males = 160

Total Females = 80

15% of males are graduates => 24 male graduates

75% of females are graduates => 60 female graduates

Absolute Difference between number of females who are non-graduates and number of males who are graduates = 24 – 20 = 4

**7)Â AnswerÂ (E)**

Total members = 240

Total males = 160

Total Females = 80

15% of males are graduates => 24 male graduates => 136 male non-graduates

75% of females are graduates => 60 female graduates => 20 female non-graduates

=>Â sum of the number of females who are graduates and the number of males who are non-graduates = 136 + 60 = 196

**8)Â AnswerÂ (B)**

Total members = 240

Total males = 160

Total Females = 80

15% of males are graduates => 24 male graduates => 136 male non-graduates

75% of females are graduates => 60 female graduates => 20 female non-graduates

Ratio of total number of males to number of female non-graduates = 160 : 20 = 8 : 1

**9)Â AnswerÂ (E)**

Parineetaâ€™s present age = 33 – 9 = 24 yrs.

Manishaâ€™s present age = 24 – 9 = 15yrs

Difference between Manisha and Deepali’s prresent ages = Parineeta’s present age

Deepaliâ€™s present age = Parineeta’s present age + Manisha’s present age = 24 + 15 = 39 yrs.

Ratio of the present age of Manisha and Deepali = 15 : 39 = 5 : 13

x = 13

**10)Â AnswerÂ (E)**

Total marks = 24 x 56 = 1344

Sum of actual marks = 1344 – (44 + 45 + 61) + (48 + 59 + 67) = 1368

Actual Average = $\frac{1368}{24}$ = 57

**11)Â AnswerÂ (A)**

$2a^{2}+a-1=0$

We get the factor as:

a=-1, a=0.5

$12b^{2}-17b+6=0$

Solving, we get the factor as,

b= 1.5, b= .75

Hence, b>a

Option A is correct option.

**12)Â AnswerÂ (B)**

Soving the quadratic equations we get,

$a^{2}-5a+6=0$

i.e (a-2)(a-3)=0

i.e a=2, a=3

$2b^{2}-13b+21=0$

i.e (b-3.5)(b-3)=0

i.e b= 3.5 and b=3

Hence, we can deduce that $a\leq b$

Therefore, option B is correct.

**13)Â AnswerÂ (E)**

$a^{2}+5a+6=0$

i.e (a+2)(a+3)=0

i.e a=-2, a=-3

.$b^{2}+7b+12=0$

i.e (b+4)(b+3)=0

i.e b=-4, b=-3

Hence, we can deduce that $a \geq b$.

Therefore, option E is correct.

**14)Â AnswerÂ (C)**

Total amount = 20 x 7 + 8 x 22 + 6 x 175 + 7 x 43

= 140 + 176 + 900 + 301

= Rs1,667

**15)Â AnswerÂ (A)**

Marked price = 78,350 + 30% of 78,350 = Rs 1,01,855

Price after discount = 101855 -20% of 101855 = Rs 81,484

Profit = Rs 3,134

**16)Â AnswerÂ (B)**

The profits are divided in the ratio of [Investment X time period]

So, this number for A is 30k X 12 = 360k

For B it is 24k X 4 + 18k X 12 = 240k

For C it is 42k X 4 + 32k X 8 = 424k

So, B’s share in the profit will be $\frac{240}{360+240+424} \times 11960 = 2803.125 \approx 2803$

**17)Â AnswerÂ (A)**

Loss percent

= [$\frac{loss}{10}$]^{2} %

= [$\frac{12}{10}$]^{2Â }%

= $\frac{36}{25}$ %

= 1$\frac{11}{25}$ %

**18)Â AnswerÂ (B)**

Probability that at least 1 is blue => 1 – (probability that none is blue) => 1 – $(\frac{^{11}C_4}{^{15}C_4})$ = $\frac{69}{91}$

**19)Â AnswerÂ (E)**

Number of ways of selecting 2 red balls in 2 chances = $^{6}C_2$

Probability of 2 red balls in 2 chances = $\frac{^{6}C_2}{^{15}C_2}$ = $\frac{1}{7}$

**20)Â AnswerÂ (C)**

Number of ways of selecting 2 blue urns and 1 yellow urn = $^{4}C_2* ^{3}C_1$ = 18

Probability of selecting 2 blue urns and 1 yellow urn Â = $\frac{18}{^{15}C_3}$ = $\frac{18}{455}$