CAT 2021 Slot 2 Quant — questions with answer key

1. A

   7

2. B

   4

3. C

   6

4. D

   8

In a football tournament, a player has played a certain number of matches and 10more matches are to be played. If he scores a total of one goal over the next 10matches, his overall average will be 0.15 goals per match. On the other hand, if hescores a total of two goals over the next 10 matches, his overall average will be 0.2goals per match. The number of matches he has played is

Let D and E be points on sides AB and AC, respectively, of a triangle ABC, such thatAD : BD = 2 : 1 and AE : CE = 2 : 3. If the area of the triangle ADE is 8 sq cm, thenthe area of the triangle ABC, in sq cm, is

A person buys tea of three different qualities at ₹ 800, ₹ 500, and ₹ 300 per kg, respectively, and the amounts bought are in the proportion 2 : 3 : 5. She mixes all the tea and sells one-sixth of the mixture at ₹ 700 per kg. The price, in INR per kg, at which she should sell the remaining tea, to make an overall profit of 50%, is

1. A

   688

2. B

   692

3. C

   653

4. D

   675

1. A

   

2. B

   

3. C

   

4. D

   

The number of ways of distributing 15 identical balloons, 6 identical pencils and 3identical erasers among 3 children, such that each child gets at least four balloonsand one pencil, is

Three positive integers x, y and z are in arithmetic progression. If y − x > 2 and xyz =5(x + y + z), then z − x equals

1. A

   8

2. B

   12

3. C

   10

4. D

   14

From a container filled with milk, 9 litres of milk are drawn and replaced with water.Next, from the same container, 9 litres are drawn and again replaced with water. Ifthe volumes of milk and water in the container are now in the ratio of 16 : 9, then thecapacity of the container, in litres, is

Raj invested ₹ 10000 in a fund. At the end of first year, he incurred a loss but hisbalance was more than ₹ 5000. This balance, when invested for another year, grew andthe percentage of growth in the second year was five times the percentage of loss inthe first year. If the gain of Raj from the initial investment over the two year period is35%, then the percentage of loss in the first year is

1. A

   10

2. B

   5

3. C

   70

4. D

   15

1. A

   

2. B

   

3. C

   

4. D

   

Two pipes A and B are attached to an empty water tank. Pipe A fills the tank while pipeB drains it. If pipe A is opened at 2 pm and pipe B is opened at 3 pm, then the tankbecomes full at 10 pm. Instead, if p ipe A is opened at 2 pm and pipe B is opened at 4pm, then the tank becomes full at 6 pm. If pipe B is not opened at all, then the time, inminutes, taken to fill the tank is

1. A

   264

2. B

   140

3. C

   120

4. D

   144

The sides AB and CD of a trapezium ABCD are parallel, with AB being the smaller side.P is the midpoint of CD and ABPD is a parallelogram. If the difference between theareas of the parallelogram ABPD and the triangle BPC is 10 sq cm, then the area, in sqcm, of the trapezium ABCD is

1. A

   40

2. B

   30

3. C

   25

4. D

   20

Two trains A and B were moving in opposite directions, their speeds being in the ratio 5 : 3. The front end of A crossed the rear end of B 46 seconds after the front ends of the trains had crossed each other. It took another 69 seconds for the rear ends of the trains to cross each other. The ratio of length of train A to that of train B is

1. A

   2 : 3

2. B

   5 : 3

3. C

   2 : 1

4. D

   3 : 2

A box has 450 balls, each either white or black, there being as many metallic whiteballs as metallic black balls. If 40% of the white balls and 50% of the black balls aremetallic, then the number of non-metallic balls in the box is

If a rhombus has area 12 sq cm and side length 5 cm, then the length, in cm, of its longer diagonal is

1. A

   

2. B

   

3. C

   

4. D

   

For a 4-digit number, the sum of its digits in the thousands, hundreds and tensplaces is 14, the sum of its digits in the hundreds, tens and units places is 15, andthe tens place digit is 4 more than the units place digit. Then the highest possible 4-digit number satisfying the above conditions is

1. A

   -2

2. B

   2

3. C

   -200

4. D

   200

Anil can paint a house in 60 days while Bimal can paint it in 84 days. Anil startspainting and after 10 days, Bimal and Charu join him. Together, they complete thepainting in 14 more days. If they are paid a total of ₹ 21000 for the job, then the shareof Charu, in INR, proportionate to the work done by him, is

1. A

   9100

2. B

   9150

3. C

   9000

4. D

   9200

Anil, Bobby and Chintu jointly invest in a business and agree to share the overallprofit in proportion to their investments. Anil’s share of investment is 70%. His shareof profit decreases by ₹ 420 if the overall profit goes down from 18% to 15%. Chintu’sshare of profit increases by ₹ 80 if the overall profit goes up from 15% to 17%. Theamount, in INR, invested by Bobby is

1. A

   2200

2. B

   2400

3. C

   1800

4. D

   2000

1. A

   3

2. B

   1

3. C

   4

4. D

   2