1.3 Marks

A truck travelling at 70 kilometres per hour uses 30% more diesel to travela certain distance than it does when it travels at the speed of 50kilometres per hour. If the truck can travel 19.5 kilometres on a litre ofdiesel at 50 kilometres per hour, how far can the truck travel on 10 litres ofdiesel at a speed of 70 kilometres per hour?

[CAT 2000]

1) 130

2) 140

3) 150

4) 175

Solution:At 50 km/hr, truck covers 19.5 km in 1 litre diesel.

∴ The truck will use 1.3 litre diesel to cover 19.5 km at 70 km/hr.

∴ At 70 km/hr, in 10 litres of diesel, the truck will cover (19.5 × 10)/1.3 =150 km

Hence, option 3.

Group Question

Answer the following questions based on the information given below.

The batting average (BA) of a test batsman is computed from runs scored andinnings played-completed innings and incomplete innings (not out) in thefollowing manner:

r1 = number of runs scored in completed innings; n1 = number of completed

innings

r2 = number of runs scored in incomplete innings; n2 = number of incomplete

innings

To better assess batsman's accomplishments, the ICC is considering twoother measures MBA1 and MBA2 defined as follows:

Collapse All

Section I

[CAT 2001]

2.3 Marks

Based on the information provided which of the following is true?

1) MBA1 ≤ BA ≤ MBA2

2) BA ≤ MBA2 ≤ MBA1

3) MBA2 ≤ BA ≤ MBA1

4) None of these

Solution:

Whatever may be the values, MBA1 < BA

Similarly, we can observe that MBA2 ≤ BA

Hence, option 4.

3.3 Marks

An experienced cricketer with no incomplete innings has a BA of 50.The next time he bats, the innings is incomplete and he scores 45runs. It can be inferred that:

1) BA and MBA1 will both increase

2) BA will increase and MBA2 will decrease

3) BA will increase and not enough data is available toassess change in MBA1 and MBA2

4) None of these

Solution:

As 45 is less than his current average of 50, MBA2 goes down. But

with any incomplete innings, BA increases.

Hence, option 2.

4.3 Marks A can complete a piece of work in 4 days. B takes double the time taken by A,C takes double that of B, and D takes double that of C to complete the sametask. They are paired in groups of two each. One pair takes two thirds the timeneeded by the second pair to complete the work. Which is the first pair?

[CAT 2001]

1) A, B

2) A, C

3) B, C

4) A, D

Solution:

If A takes 4 days then, B will take 8 days, C will take 16 days and D will take 32days.

∴ The pairs are (A, D) and (B, C).

Hence, option 4.

5.3 Marks

There's a lot of work in preparing a birthday dinner. Even after the turkey isin oven, there are still the potatoes and gravy, yams, salad, andcranberries, not to mention setting the table. Three friends, Asit, Arnold,and Afzal, work together to get all of these chores done. The time it takesthem to do the work together is six hours less than Asit would have takenworking alone, one hour less than Arnold would have taken, and half thetime Afzal would have taken working alone.

How long did it take them to do these chores working together?

[CAT 2001]

1) 20 minutes

2) 30 minutes

3) 40 minutes

4) 50 minutes

Solution:

Suppose Asit, Arnold and Afzal finish the work together in x hours.

Then Asit, Arnold and Afzal will take x + 6, x + 1 and 2x hour respectively.

3x2 + 7x – 6 = 0

(x + 3)(3x − 2) = 0

∵ Number of hours cannot be negative.

Hence, option 3.

6.3 Marks

Three friends went for a picnic. First brought five apples and the secondbrought three. The third friend however brought only Rs. 8. What is theshare of the first friend?

[CAT 2002]

1) 8

2) 7

3) 1

4) None of these

Solution:There are 8 apples available for 3 friends. So, share of apples of eachperson = 8/3

The 1st person gives out 5 − 8/3 apples = 7/3 apples to 3rd person

The 2nd person gives out 3 − 8/3 apples = 1/3 apples to 3rd person

∴ 3rd person will distribute Rs. 8 in the ratio 7 : 1 to 1st and 2nd personrespectively and thus Rs. 7 and Rs. 1 are given to them respectively.

∴ Share of 1st friend is Rs. 7.

Hence, option 2.

7.3 Marks

It takes 6 technicians a total of 10 hours to build a new server from DirectComputer, with each working at the same rate. If six technicians start tobuild the server at 11 a.m. and one technician per hour is added beginningat 5 p.m., at what time will the server be complete?

[CAT 2002]

1) 6:40 p.m.

2) 7:00 p.m.

3) 7:20 p.m.

4) 8:00 p.m.

Solution:6 technicians → 10 hours to 1 job

∴ 1 technician → 60 hours to 1 job

In the hour after 5p.m.,

∴ At the end of 9th hour i.e. 8:00 p.m. the work is complete.

Hence, option 4.

8.3 Marks

Three small pumps and one large pump are filling a tank. Each of the three

small pumps works at 2/3rd the rate of the large pump. If all 4 pumps workat the same time, then they should fill the tank in what fraction of time that itwould have taken the large pump alone?

[CAT 2002]

1)

2)

3)

4)

Solution:

Work done by the large pump = 3 units

∴ Work done by the 3 small pumps = 2 × 3 = 6 units

∴ Work done by all 4 pumps together = 9 units

Rate of work is inversely proportional to time taken for completing thework.

Hence, option 2.

9.3 Marks

Let a, b, c, d and e be integers such that a = 6b = 12c, and 2b = 9d = 12e.Then which of the following pairs contains a number that is not an integer?

[CAT 2003 Re-Test]

1)

2)

3)

4)

Solution:

Since a = 6b = 12c and 2b = 9d = 12e

∴ a : b : c = 12 : 2 : 1 and b : d : e = 18 : 4 : 3

∴ a : b : c : d : e = 108 : 18 : 9 : 4 : 3

∴ a = 108k; b = 18k; c = 9k; d = 4k and e = 3k where ‘k’ is an integer

Hence, option 4.

10.3 Marks

A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he hassold. What is the current proportion of water to milk?

[CAT 2004]

1) 2 : 3

2) 1 : 2

3) 1 : 3

4) 3 : 4

Solution:

The quantity of milk and water is as shown in the table.

∴ Current proportion of water and milk is 40 : 60 = 2 : 3

Hence, option 1.

11.3 Marks

[CAT 2004]

1)

2) –1

3)

4)

Solution:

By property of equal ratios,

Assuming (a + b + c ≠ 0),

If a + b + c = 0, a = –(b + c)

Hence, option 3.

12.3 Marks

A chemical plant has four tanks (A, B, C, and D), each containing 1000litres of a chemical. The chemical is being pumped from one tank toanother as follows:

From A to B @ 20 litres/minute

From C to A @ 90 litres/minute

From A to D @ 10 litres/minute

From C to D @ 50 litres/minute

From B to C @ 100 litres/minute

From D to B @ 110 litres/minute

Which tank gets emptied first and how long does it take (in minutes) to getempty after pumping starts?

[CAT 2005]

1) A, 16.66

2) C, 20

3) D, 20

4) D, 25

Solution:

The change in the amount of chemical in each tank after every minute is asfollows:

A: −20 – 10 + 90 = 60

B: −100 + 110 + 20 = 30

C: −50 − 90 + 100 = −40

D: −110 + 10 + 50 = −50

Since tank D loses the maximum amount of chemical in a minute, it will beemptied first.

Let n minutes be the time taken by tank D to get empty.

∴ 1000 – 50n = 0

∴ n = 20 minutes

Hence, option 3.

13.3 Marks

[CAT 2006]

1)

2)

3)

4)

5)

Solution:

Hence, option 1.