### Quantitative Section : GMAT Sample Problem Solving Ability

**Speed, Time and Distance **

1. Rajesh traveled from city A to city B covering as much distance in the second part as he did in the first part of this journey. His speed during the second part was twice as that of the speed during the first part of the journey. What is his average speed of journey during the entire travel?

1. His average speed is the harmonic mean of the individual speeds for the two parts.

2. His average speed is the arithmetic mean of the individual speeds for the two parts.

3. His average speed is the geometric mean of the individual speeds for the two parts.

4. Cannot be determined.

Ans : B

2. Two boys begin together to write out a booklet containing 535 lines. The first boy starts with the first line, writing at the rate of 100 lines an hour; and the second starts with the last line then writes line 534 and so on, backward proceeding at the rate of 50 lines an hour. At what line will they meet?

1. 356

2. 277

3. 357

4. 267

Ans : C

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

1. 27

2. 36

3. 45

4. None of these.

Ans : B

4. The speed of a motor boat itself is 20 km/h and the rate of flow of the river is 4 km/h. Moving with the stream the boat went 120 km. What distance will the boat cover during the same time going against the stream?

1. 80 km

2. 180 km

3. 60 km

4. 100 km

Ans : A

5. Two friends A and B run around a circular track of length 510 metres, starting from the same point, simultaneously and in the same direction. A who runs faster laps B in the middle of the 5th round. If A and B were to run a 3 km race long race, how much start, in terms of distance, should A give B so that they finish the race in a dead heat?

1. 545.45 metres

2. 666.67 metres

3. 857.14 metres

4. Cannot be determined

Ans : B

6. I travel the first part of my journey at 40 kmph and the second part at 60 kmph and cover the total distance of 240 km to my destination in 5 hours. How long did the first part of my journey last?

1. 4 hours

2. 2 hours

3. 3 hours

4. 2 hours 24 minutes

Ans : C

7. By walking at 3/4th of his usual speed, a man reaches office 20 minutes later than usual. What is his usual time?

1. 30 min

2. 60 min

3. 70 min

4. 50 min

Ans : B

8. A passenger train covers the distance between stations X and Y, 50 minutes faster than a goods train. Find this distance if the average speed of the passenger train is 60 kmph and that of goods train is 20 kmph.

1. 20 kms

2. 25 kms

3. 45 kms

4. 40 kms

Ans : B

9. Yana and Gupta leave points x and y towards y and x respectively simultaneously and travel in the same route. After meeting each other on the way, Yana takes 4 hours to reach her destination, while Gupta takes 9 hours to reach his destination. If the speed of Yana is 48 km/hr, what is the speed of Gupta?

1. 72 kmph

2. 32 mph

3. 20 mph

4. None of these

Ans : C

10. Ram covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km. How many hours has been driving at 20 kmph?

1. 2 hours

2. 3 hours 20 minutes

3. 4 hours 40 minutes

4. 3 hours 12 minutes

Ans : D

**Speed, Time and Distance
**

1. Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 P.M. Train B traveling at 90 km/hr also leaves Mumbai for Delhi at 9 P.M. Train C leaves Delhi for Mumbai at 9 P.M. If all three trains meet at the same time between Mumbai and Delhi, what is the speed of Train C if the distance between Delhi and Mumbai is 1260 kms?

1. 60 km/hr

2. 90 km/hr

3. 120 km/hr

4. 135 km/hr

Ans : C

2. Two trains, 200 and 160 meters long take a minute to cross each other while traveling in the same direction and take only 10 seconds when they cross in opposite directions. What are the speeds at which the trains are traveling?

1. 21 m/s; 15 m/s

2. 30 m/s; 24 m/s

3. 18 m/s; 27 m/s

4. 15 m/s; 24 m/s

Ans : A

3. An express train traveling at 72 km/hr speed crosses a goods train traveling at 45 km/hr speed in the opposite direction in half a minute. Alternatively, if the express train were to overtake the goods train, how long will it take to accomplish the task. Assume that the trains continue to travel at the same respective speeds as mentioned in case 1.

1. Cannot be determined

2. 30 seconds

3. 150 seconds

4. 130 seconds

Ans : D

4. A train travels at an average speed of 90 km/hr without any stoppages. However, its average speed decrease to 60km/hr on account of stoppages. On an average, how many minutes per hour does the train stop?

1. 12 minutes

2. 18 minutes

3. 24 minutes

4. 20 minutes

Ans : D

5. Two trains A and B start simultaneously from stations X and Y towards each other respectively. After meeting at a point between X and Y, train A reaches station Y in 9 hours and train B reaches station X in 4 hours from the time they have met each other. If the speed of train A is 36 km/hr, what is the speed of train B?

1. 24 km/hr

2. 54 km/hr

3. 81 km/hr

4. 16 km/hr

Ans : B

6. A man moves from A to B at the rate of 4 km/hr. Had he moved at the rate of 3.67 km/hr, he would have taken 3 hours more to reach the destination. What is the distance between A and B?

1. 33 kms

2. 132 kms

3. 36 kms

4. 144 kms

Ans : B

7. A ship develops a leak 12 km from the shore. Despite the leak, the ship is able to move towards the shore at a speed of 8 km/hr. However, the ship can stay afloat only for 20 minutes. If a rescue vessel were to leave from the shore towards the ship, and it takes 4 minutes to evacuate the crew and passengers of the ship, what should be the minimum speed of the rescue vessel in order to be able to successfully rescue the people aboard the ship?

1. 53 km/hr

2. 37 km/hr

3. 28 km/hr

4. 44 km/hr

Ans : B

8. A man driving his bike at 24 kmph reaches his office 5 minutes late. Had he driven 25% faster on an average he would have reached 4 minutes earlier than the scheduled time. How far is his office?

1. 24 km

2. 72 km

3. 18 km

4. Data Insufficient

Ans : C

9. When an object is dropped, the number of feet N that it falls is given by the formula N = ½gt2 where t is the time in seconds from the time it was dropped and g is 32.2. If it takes 5 seconds for the object to reach the ground, how many feet does it fall during the last 2 seconds?

1. 64.4

2. 96.6

3. 161.0

4. 257.6

Ans : D

10. If the wheel of a bicycle makes 560 revolutions in travelling 1.1 km, what is its radius?

1. 31.25 cm

2. 37.75 cm

3. 35.15 cm

4. 11.25 cm

Ans : A

Time and Work

1. Two workers A and B manufactured a batch of identical parts. A worked for 2 hours and B worked for 5 hours and they did half the job. Then they worked together for another 3 hours and they had to do (1/20)th of the job. How much time does B take to complete the job, if he worked alone?

1. 24 hours

2. 12 hours

3. 15 hours

4. 30 hours

Ans : C

2. Pipe A can fill a tank in ‘a’ hours. On account of a leak at the bottom of the tank it takes thrice as long to fill the tank. How long will the leak at the bottom of the tank take to empty a full tank, when pipe A is kept closed?

1. (3/2)a hours

2. (2/3)a

3. (4/3)a

4. (3/4)a

Ans : A

3. A and B working together can finish a job in T days. If A works alone and completes the job, he will take T + 5 days. If B works alone and completes the same job, he will take T + 45 days. What is T?

1. 25

2. 60

3. 15

4. None of these

Ans : C

4. A man can do a piece of work in 60 hours. If he takes his son with him and both work together then the work is finished in 40 hours. How long will the son take to do the same job, if he worked alone on the job?

1. 20 hours

2. 120 hours

3. 24 hours

4. None of these

Ans : B

5. A, B and C can do a work in 5 days, 10 days and 15 days respectively. They started together to do the work but after 2 days A and B left. C did the remaining work (in days)

1. 1

2. 3

3. 5

4. 4

Ans : D

6. X alone can do a piece of work in 15 days and Y alone can do it in 10 days. X and Y undertook to do it for Rs. 720. With the help of Z they finished it in 5 days. How much is paid to Z?

1. Rs. 360

2. Rs. 120

3. Rs. 240

4. Rs. 300

Ans : B

7. Ram starts working on a job and works on it for 12 days and completes 40% of the work. To help him complete the work, he employs Ravi and together they work for another 12 days and the work gets completed. How much more efficient is Ram than Ravi?

1. 50%

2. 200%

3. 60%

4. 100%

Ans : D

8. A red light flashes 3 times per minute and a green light flashes 5 times in two minutes at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?

1. 30

2. 24

3. 20

4. 60

Ans : A

9. A and B can do a piece of work in 21 and 24 days respectively. They started 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?

1. 5

2. 7

3. 8

4. 6

Ans : B

10. Ram, who is half as efficient as Krish, will take 24 days to complete a work if he worked alone. If Ram and Krish worked together, how long will they take to complete the work?

1. 16 days

2. 12 days

3. 8 days

4. 18 days

Ans : C

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