SNAP 2011 - SOLVED PAPERS - How to Prepare for Quantitative Aptitude for CAT

How to Prepare for Quantitative Aptitude for CAT (2014)

SOLVED PAPERS

SNAP 2011

Note: The SNAP 2011 paper had 40 questions on the Quantitative Aptitude and Data Interpretation section. Apart from the solutions to the 31 questions in Quantitative Aptitude given here, the solutions to the 9 questions of data interpretation are available in my book—How to Prepare for Data Interpretation for the CAT also published by McGraw Hill.

1.

A train travelling at 36 kmph crosses a platform in 20 seconds and a man standing on the platform in 10 seconds. What is the length of the platform in meters?

(a) 240 meters

(b) 100 meters

(c) 200 meters

(d) 300 meters

2.

By walking at 4/5th of his usual speed, a man reaches office 10 minutes later than usual. What is his usual time?

(a) 20 min

(b) 40 min

(c) 30 min

(d) 50 min

3.

A man and a woman 81 miles apart from each other, start travelling towards each other at the same time. If the man covers 5 miles per hour to the women’s 4 mile per hour, how far will the woman have travelled when they meet?

(a) 27

(b) 36

(c) 45

(d) None of these

4.

Two people were walking in opposite directions. Both of them walked 6 miles forward then took right and walked 8 miles. How far is each from starting positions?

(a) 14 miles and 14 miles

(b) 10 miles and 10 miles

(c) 6 miles and 6 miles

(d) 12 miles and 12 miles

5.

Four men and three women can do a job in 6 days. When 5 men and 6 women work on the same job, the work gets completed in 4 days. How long will 2 women and 3 men take to do the job?

(a) 18

(b) 10

(c) 8.3

(d) 12

6.

Ram completes 60% of a task in 15 days and then takes the help of Rahim and Rachel. Rahim is 50% as efficient as Ram is and Rachel is 50% as efficient as Rahim is. In how many more days will they complete the work?

(a)

(b)

(c)

(d)

7.

A and B can do a piece of work in 21 and 24 days respectively. They start the work together and after some days A leaves the work and B completes the remaining work in 9 days. After how many days did A leave?

(a) 5

(b) 7

(c) 8

(d) 6

8.

A trader makes a profit equal to the selling price of 75 articles when he sells 100 of the articles. What % profit does he make in the transaction?

(a) 33.33%

(b) 75%

(c) 300%

(d) 150%

9.

In a 100 m race, if A gives B a start of 20 meters, then A wins the race by 5 seconds. Alternatively, if A gives B a start of 40 meters the race ends in a dead heat. How long does A take to run 200 m?

(a) 10 seconds

(b) 20 seconds

(c) 30 seconds

(d) 40 seconds

10.

A 4 cm cube is cut into 1cm cubes. What is the percentage increase in the surface area after such cutting?

(a) 4%

(b) 300%

(c) 75%

(d) 400%

11.

A number G236G0 can be divided by 36 if G is:

(a) 8

(b) 6

(c) 1

(d) More than one values are possible

12.

Amit can do a work in 12 days and Sagar in 15 days. If they work on it together for 4 days, then the fraction of the work that is left is:

(a) 3/20

(b) 3/5

(c) 2/5

(d) 2/20

13.

A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?

(a) 2.91 m

(b) 3 m

(c) 5.82 m

(d) None of these

14.

A bag contains 5 white and 3 black balls; another bag contains 4 white and 5 black balls. From any one of these bags a single draw of two balls is made. Find the probability that one of them would be white and other black.

(a) 275/504

(b) 5/18

(c) 5/9

(d) None of these

15.

Three parallel lines are cut by two transversals as shown in the given figure. If AB = 2 cm, BC = 4 cm and DE = 1.5 cm, then the length of EF is:

(a) 2 cm

(b) 3 cm

(c) 3.5 cm

(d) 4 cm

16.

log1010 + log10102 + …. + log1010n

(a) n2 + 1

(b) n2 – 1

(c)

(d)

17.

The sum of a number and its reciprocal is thrice the difference of the number and its reciprocal. The number is:

(a) ±

(b) ±

(c) ±

(d) ±

18.

The total number of natural numbers that lie between 10 and 300 and are divisible by 9 is

(a) 32

(b) 30

(c) 33

(d) 34

19.

If nCx = 56 and nPx = 336, find n and x.

(a) 7, 3

(b) 8, 4

(c) 8, 3

(d) 9, 6

20.

One side of an equilateral triangle is 24 cm. The midpoints of its sides are joined to form another triangle whose midpoints are in turn joined to form still another triangle. This process continues indefinitely. Find the sum of the perimeters of all the triangles.

(a) 144 cm

(b) 72 cm

(c) 536 cm

(d) 676 cm

21.

The probability that a leap year selected at random contains either 53 Sundays or 53 Mondays, is:

(a) 17/53

(b) 1/53

(c) 3/7

(d) None of these

22.

Find the intercepts made by the line 3x + 4y – 12 = 0 on the axes:

(a) 2 and 3

(b) 4 and 3

(c) 3 and 5

(d) None of these

23.

The average of 4 distinct prime numbers a, b, c, d is 35, where a < b < c < d. a and d are equidistant from 36 and b and c are equidistant from 34 and a, b are equidistant from 30 and c and d are equidistant from 40. The difference between a and d is:

(a) 30

(b) 14

(c) 21

(d) Cannot be determined

24.

Ramsukh bhai sells rasgulla (a favourite Indian sweets) at ` 15 per kg. A rasgulla is made up of flour and sugar in the ratio 5 : 3. The ratio of price of sugar and flour is 7 : 3 (per kg). Thus he earns 66 % profit. What is the cost price of sugar?

(a) ` 10/kg

(b) ` 9/kg

(c) ` 18/kg

(d) ` 14/kg

25.

A reduction of 20% in the price of sugar enables a person to purchase 6 kg more for ` 240. What is the original price per kg of sugar?

(a) ` 10/kg

(b) ` 8/kg

(c) ` 6/kg

(d) ` 5/kg

26.

A solid sphere is melted and recast into a right circular cone with a base radius equal to the radius of the sphere. What is the ratio of the height and radius of the cone so formed?

(a) 4 : 3

(b) 2 : 3

(c) 3 : 4

(d) None of these

27.

The speed of scooter, car and train are in the ratio of 1 : 4 : 16. If all of them cover equal distance then the ratio of time taken/velocity for each of the vehicle is:

(a) 256 : 16 : 1

(b) 1 : 4 : 16

(c) 16 : 4 : 1

(d) 16 : 1 : 4

28.

B is twice efficient as A and A can do a piece of work in 15 days. A started the work and after a few days B joined him. They completed the work in 11 days, from the starting. For how many days did they work together?

(a) 1 day

(b) 2 days

(c) 6 days

(d) 5 days

29.

A, B, C and D purchased a restaurant for ` 56 lakhs. The contribution of B, C and D together is 460% that of A, alone. The contribution of A, C and D together is 366.66% that of B’s contribution and the contribution of C is 40% that of A, B and D together. The amount contributed by D is:

(a) 10 lakhs

(b) 12 lakhs

(c) 16 lakhs

(d) 18 lakhs

30.

The salary of Raju and Ram is 20% and 30% less than the salary of Saroj respectively. By what percent is the salary of Raju more than the salary of Ram?

(a) 33.33%

(b) 50%

(c) 15.18%

(d) 14.28%

31.

The radius of a wire is decreased to one-third and its volume remains the same. The new length is how many times the original length?

(a) 2 times

(b) 4 times

(c) 5 times

(d) 9 times

ANSWER KEY

1. (b)

2. (b)

3. (b)

4. (b)

5. (c)

6. (c)

7. (b)

8. (b)

9. (c)

10. (b)

11. (a)

12. (c)

13. (b)

14. (a)

15. (b)

16. (d)

17. (a)

18. (a)

19. (c)

20. (a)

21. (c)

22. (b)

23. (b)

24. (d)

25. (a)

26. (d)

27. (a)

28. (b)

29. (d)

30. (d)

31. (d)

Solutions

1.The speed of the train in m/s would be 36 × 5 ÷ 18 = 10 m/s. If the train takes 10 seconds to cross a man on the platform, it means that the length of the train = 10 × 10 = 100 m.

Also, while crossing the platform, the distance traveled by the train is equal to: Length of Train + Length of Platform.

Hence, Length of Platform + 100 = 20 × 10 Æ Length of Platform = 100 meters. Option (b) is the correct answer.

2.As the distance is constant, the speed and time are inversely proportional to each other. Walking at 4/5th of his usual speed would mean that the man would take 5/4th of his usual time. Thus, the extra time taken = 5/4th of tt= 1/4th of t (where t = normal time taken).

But the extra time taken is given as 10 minutes. Hence, t/4 = 100 Æ t = 40 minutes.

Hence, Option (b) is correct.

3.Their relative speed would be equal to 9 miles per hour (as they are approaching each other). Thus, they would meet in 81 ÷ 9 = 9 hours. The woman would travel 9 × 4 = 36 miles in that time. Hence, Option (b) is correct.

4.Since both have them have taken a 90o turn, it clearly implies that 6 miles and 8 miles (the distances they have walked) would be the base and height of a right-angled triangle. Their distance from the starting point would be calculated by the hypotenuse of each right-angled triangle. The appropriate Pythagoras triplet would be 6, 8, 10 and hence their distance from the start would be 10 miles each.

Hence, Option (b) is correct.

5.24 man days + 18 woman days = 20 man days + 24 woman days Æ 1 man-day = 1.5 woman days.

In terms of woman days the total work would be:

24 man days + 18 woman days = 36 woman days + 18 woman days = 54 woman days.

2 women and 3 men would be equivalent to 2 women + 4.5 women = 6.5 women.

The number of days required would be:

54/6.5 = 8.3 days. Hence, Option (c) is correct.

6.Since Ram has completed 60% of the task in 15 days – this gives us two pieces of information –

(i)That 40% of the task is left;

(ii)Ram’s rate of work is 4% per hour.

Then, from the information in the problem we can see that Rahim’s work rate would be 2% per annum, while Rachel’s work rate would be 1% per annum. Thus, their combined rate of work would be 7% per hour giving us 40/7 as the required answer.

Option (c) is correct.

7.In the 9 days that he works alone, B would do of the work. This means that A and B together have done of the work. Thus,

Solving the above equation we get d = 7.

Hence, Option (b) is correct.

8.The profit percent = × 100 = 75. Hence, Option (b) is correct.

9.From the second statement, we have that in the time A runs 100 m, B would run 60 m. Thus, their ratio of speeds is 5:3. From this point you can start checking with the options in order to get to the correct answer.

If we check for Option (a) we see that, A’s speed = 20m/s, B’s speed = 12 m/s. This would satisfy the second condition – i.e., if A gives B a start of 40 meters the race ends in a dead heat.

We need to see whether these values satisfy the first condition too – i.e., if A gives B a start of 20 meters, then A wins the race by 5 seconds.

A would complete the race in 5 seconds and B at that time would have reached from 20 m to 80 m (as he would simultaneously have traveled 60 m in 5 seconds @ 12 m/s). To cover the remaining 20 m, A would not be taking 5 seconds. Hence, we can reject this option.

The same thinking can be applied to the other options to get the correct answer.

For Option (c): A’s speed = 6.666 m/s, B’s speed = 4 m/s

We need to see whether these values satisfy the first condition too – i.e., if A gives B a start of 20 meters, then A wins the race by 5 seconds.

A would complete the race in 15 seconds and B at that time would have reached from 20 m to 80 m (as he would simultaneously have traveled 60 m in 15 seconds @ 4 m/s). To cover the remaining 20 m, A would be taking 5 seconds. Hence, this option is correct.

Option (c) is the correct answer.

10.The initial surface area = 6 × 4 × 4 = 96 sq. cm. The new surface area = 64 × 6 × 1 × 1 = 384 sq. cm. The surface area is becoming 4 times the original, which means that there is a 300% increase in the surface area. Hence, Option (b) is correct.

11.With G = 8, divisibility can be verified. Hence, Option (a) is correct.

12.Amit’s work per day = 8.33%, Sagar’s work per day = 6.66%. Combined work per day = 15%. In 4 days they would complete 15 × 4 = 60% work. Fraction of work left = 40 out of 100 or 2 out of 5. Hence, Option (c) is correct.

13.The total area of the field is 2400 sq. m. If we try to keep the width of the road as 3 m, we can see that the total area of the roads = 3 × 60 + 3 × 40 – 3 × 3 = 291sq. m. – leaving 2109 sq. m for the lawn. Hence, Option (b) is correct.

14.The event definition would be:

First bag & white ball & black ball OR First bag & black ball & white ball

OR

Second bag & white ball & black ball OR Second bag & black ball & white ball

=

=

15.The ratio of AB to BC would be equal to the ratio of DE to EF. Since, BC is twice the value of AB, EF would also be twice the value of DE and hence, EF = 3 cm. Hence, Option (b) is correct.

16.The value of the expression = 1 + 2 + 3 +…n = sum of the first n natural numbers . Hence, Option (d) is correct.

17.Solve through options by checking for the given conditions. The value of fits the conditions. Hence, Option (a) is the correct answer.

18.We need to find the number of terms in the series:

18, 27, 36, … 297

There are 32 terms in this series since it starts with 9 × 2 and ends with 9 × 33.

Hence, Option (a) is correct.

19.We know that the value of nCx × r! = nPx

Since, the value of nPx is 6 times the value of nCx, we know that r = 3. Checking the options, we can see that n = 8 and r = 3 fits the given values. Hence, Option (c) is the correct answer.

20.The second perimeter would be half the first perimeter. In order to get the answer to this question, we need the infinite sum of the geometric progression: 72 +36 +18 + 9 +….. This is a GP with a = 72 and r = ½ . The infinite sum of the given series = 144. Hence, Option (a) is correct.

21.A leap year has 366 days, which means that it has 52 completed weeks + 2 extra days. Thus, if 1st January is a Saturday, 30th December would also be a Saturday. For a 53rd Sunday or Monday, the year should start either from a Saturday, Sunday or a Monday in which case, the last two days of the year would be (Saturday, Sunday) or (Sunday, Monday) or (Monday, Tuesday) respectively. The required probability is 3/7. Hence, Option (c) is correct.

22.For the x-intercept y = 0 and hence the x-intercept = 4. Similarly, for the y-intercept, the value of x = 0 and hence the y-intercept = 3. Hence, Option (b) is correct.

23.A quick look at the various prime numbers between the 20s to the 40s gives us the following list: 23, 29, 31, 37, 39, 41, 43, 47. The given conditions are satisfied by the set of numbers: 29, 31, 37 and 43. Thus, a = 29 and d = 43 and hence the required difference between and d is 14. Hence, Option (b) is correct.

24.8 kg of rasgulla would give a revenue of `120 and a cost of `72. (Note: Cost should be 3/5 of the revenue for a profit of 66.66%.) 8 kg of the sweet would also require 5 kg of flour and 3 kg of sugar. Thus, the cost of 5 kg flour + 3 kg sugar = `72. The price of sugar that satisfies this condition in association with the additional condition that the ratio of the price of sugar to flour is 7:3 is `14/kg.

Hence, Option (d) is correct.

25.Reduction of 20% in the price of sugar would increase the quantity by 25% = increase of 6 kg (for the same cost). Thus, the original quantity = 24 kg and the new quantity = 30 kg. The price of sugar (original) = 240 ÷ 24 = `10/ kg.

26.The volume of the sphere = . The volume of a right circular cone = .

Since the radii of the sphere and the cone are equal, when we equate the two volumes we get 4r = h. Hence, the ratio of height to radius for the right circular cone is 4:1. Hence, Option (d) is correct.

27.If the speeds are 1 kmph, 4 kmph and 16 kmph respectively, they would cover a distance of (say 16 km) in 16 hours, 4 hours and 1 hour respectively. The ratio of time taken to velocity would be (16/1): (4/4) : (1/16) = 16:1:1/16 = 256:16:1. Hence, Option (a) is correct.

28.A’s work = 6.66% per hour. Thus, B’s work = 13.33% per hour. Combined work = 20% per hour. Checking the options: Option (a) does not work because 10 × 6.66 + 20 × 1 π 100.

For Option (b) we get: 9 × 6.66 + 2 × 20 = 60 +40 = 100%.

Hence, Option (b) is correct.

29.From the given statements we can work out the values of the individual investments as follows:

Statement: The contribution of B, C and D together is 460% that of A, alone means that A’s investment = 56 ÷ 5.6 = 10 lakhs.

Statement: The contribution of A, C and D together is 366.66% that of B’s contribution means that B’s investment = 56 ÷ 4.6666 = 12 lakhs.

Statement: The contribution of C is 40% that of A, B and D together implies that C’s investment = 56 × 40 ÷ 140 (unitary method) = 16 lakhs

Hence, D’s investment = 56 –10 – 12 – 16 = 18 lakhs.

Hence, Option (d) is correct.

30.If Saroj is taken as 100, Raju would be 80 and Ram would be 70. The salary of Raju would be 14.28% more than the salary of Ram. Hence, Option (d) is correct.

31.If the wire is 1/3rd in terms of the radius, per unit length the volume of material required would be 1/9th. Thus, the length of the wire—if the volume has to be kept the same—would be 9 times the original length. Hence, Option (d) is correct.