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GMAT Sample Questions » GMAT Sample Problem Soving Ability

Quantitative Section : GMAT Sample Problem Solving Ability

Select the correct answer from the given five options by solving the following questions.

  1. A piece of work is done by Tina in 10 days. The same piece of work is done by Amy in 15 days. In how many days will Tina and Amy finish the same amount of work if they work together?

    1. 10 days
    2. 6 days
    3. 12.5 days
    4. 13 days
    5. None of the above

    Correct answer: b

    Explanation:

    According to the data given in the question,

    Time taken by Tina to do the work = 10 days ………………i

    Time taken by Amy to do the work = 15 days ………………ii

    ∴ Work done by Tina in 1 day = 1 / 10 ………..iii

    Similarly, work done by Amy in 1 day = 1 / 15 …………iv

    ∴ Work done by both Tina and Amy in 1 day = (1 / 10) + (1 / 15)

    ∴ Work done by both of Tina and Amy in 1 day = 1 / 6 ……………v

    ∴ When Tina and Amy work together they can complete the work in (1 / (1 / 6)) = 6 days.

    Hence, the correct answer is option b.

  2. Which of the following algebraic formulae are true?

    1. Speed = Distance / Time
    2. Distance = speed * time
    3. Time = Distance / Speed
    4. Time = speed * distance

    1. Only statement (i) is true
    2. Only statements (i) and (ii) are true
    3. Only statements (i), (ii) and (iii) are true
    4. All statements are true
    5. all statements are false

    Correct answer: c

    Explanation:

    The formulae given in the statements (i), (ii) as well as (iii) are true.

    But, the formula given in the fourth statement is false.

    Hence, the correct answer is option c.

  3. Two trains X and Y are moving in opposite direction, one from station A to station B and the other from station B to station A. the train X reaches its destination i.e. station A in 14 hours and the train Y reaches its destination i.e. station B in 20 hours after the trains meet. If the speed of train X is 20 km per hour, then what is the speed of the train Y?

    1. 30 km per hour
    2. 35 km per hour
    3. 27 km per hour
    4. 38.57 km per hour
    5. None of the above

    Correct answer: d

    Explanation:

    According to the data given in the question,

    Train X travels at a speed of = 20 km / hr …………..i

    Train x reaches its destination station B in time = 14 hours ……………ii

    Train Y reaches its destination station A in time = 20 hours after they meet ………..iii

    Now, let the speed of train Y be x km per hour ………………..iv

    ∴ From equation (i), (ii), (iii) and (iv), we can say that,

    20 : x :: 14 : 20
    ∴ 20 / x = 14 / 20
    ∴ 20 * 20 = 14 * x
    ∴ x = 400 / 14
    ∴ x = 28.57 km / hr

    Thus, train B travels at a speed of 28.57 km per hour.

    Hence, the correct answer is option d.

  4. David observes that it takes 6 sec for a train to pass him when he is standing at the railway platform. But, to pass the platform the train takes 10 sec. If the length of the train is 150 meters, then what is the speed of the train?

    1. 20 km / hr
    2. 25 km / hr
    3. 30 km / hr
    4. 35 km / hr
    5. None of the above

    Correct answer: b

    Explanation:

    According to the data given in the question,

    Time taken by the train to cross David = 6 sec …………….i

    Time taken by the train to cross the platform = 10 sec ……………..ii

    Length of the train = 150 meters ……………iii

    The standard formula to calculate the speed of the train when it passes a stationary object without considerable length = length of the train / time taken by the train to pass the object

    ∴ Speed of the train = 150 / 6 = 25 km / hr

    Hence, the correct answer is option b.

  5. When the man rows a boat in still water his speed is 7 km / hr. But, if the river water runs at speed of 3 km / hr, then the man takes 1.5 hours to reach a certain place and come back. What is the distance covered by the man?

    1. 4.285 km
    2. 3.285 km
    3. 1.285 km
    4. 2.285 km
    5. None of the above

    Correct answer: a

    Explanation:

    According to the data given in the question,

    Speed of the man in still water = 7 km / hr ……………i

    Speed of the moving river water = 3 km / hr …………ii

    Time taken by the man to reach a certain place and come back = 1.5 hours = 1 hr and 30 min ………………….iii

    We have to find the distance covered by the man.

    Let this distance be 'x' km.

    The speed of man while going downstream = 7 + 3 = 10 km / hr ………iv

    The speed of man while upstream = 7 – 3 = 4 km / hr …………….v

    Total time taken by the man to row x km and come back = (x / 10) + (x / 4)

    But, the man takes 90 minutes or 1 hour and 30 min to cover this distance.

    ∴ (x / 10) + (x / 4) = 1.5
    ∴ 4x + 10x = 40 * 1.5
    ∴ 14x = 60
    ∴ x = 4.285 km = 4 km and 285 meters
    ∴ The total distance covered by man is 4.285 km

    Hence, the correct answer is option a.

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