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GMAT Sample Questions » GMAT Sample Problem Soving Ability

Quantitative Section : GMAT Sample Problem Solving Ability

Choose the most correct answer from the given five options for each of the following problem solving question.

  1. Raven walks at a certain speed daily from his home to school. If the speed of raven is reduce by 3 / 7th part of his normal speed then, it takes 20 more minutes for Raven to reach his school. Calculate the time taken by Raven to reach his school when he walks at his usual speed?

    1. 15 minutes
    2. 20 minutes
    3. 25 minutes
    4. 30 minutes
    5. None of the above

    Correct answer: a

    Explanation:

    According to the data given in the question,

    Decrease in the usual speed of Raven = 3 / 7 …………i

    Now, let 'x' be the time taken by Raven to reach the school when he is walking at his normal speed ………………..ii

    But, as the speed is reduced by 3 / 7 of the regular speed,

    ∴ The time now taken by Raven to reach the school = 7 / 3 of the usual time.

    But, it is given that, it takes 20 minutes more than the normal time 'x' for Raven to reach the school with reduced speed.

    ∴ (7 / 3) x = x + 20
    ∴ 7x = 3x + 60
    ∴ 4x = 60
    ∴ x = 60 / 4 = 15 minutes

    Thus, it takes 15 minutes for Raven to reach his school when he is walking at his normal speed.

    Hence, the correct answer is option a.

  2. Rose leaves her home early in the morning so that she can reach her college on time. If she walks at the rate of 7 km / hr then she reaches her college 8 minutes late. But, if she walks at a speed of 8 km / hr, then she reaches her college 4 minutes early. What is the distance between Rose's house and her college?

    1. 10 km
    2. 11.2 km
    3. 11.5 km
    4.  12 km
    5. None of the above

    Correct answer: b

    Explanation:

    Time taken by Rose to cover a distance of say 1 km at a speed of 7 km / hr = 1 / 7 hr ……………..i

    Similarly, time taken by rose to cover a distance of say 1 km at a speed of 8 km / hr = 1 / 8 hr ……………ii

    Hence, the difference in both the time = 1 / 7 * 1 / 8 = 1 / 56 …………..iii

    Now, according to the data given in the question,

    When Rose walks at a speed of 7 km / hr she reaches late by 8 minutes

    And, when Rose walks at a speed of 8 km / hr she reaches early by 4 minutes

    ∴ The total difference of time in covering the entire distance (d) = (8 + 4) = 12 minutes = 1 / 5 hours.

    Now, if the time difference of 1 / 56, the distance covered by Rose is 1 km, then, the distance covered by Rose for a time difference of (1 / 5) hour = (1) * (1 / 5) / (1 / 56) = 56 / 5 = 11.2 km.

    Thus, the distance between Rose's house and college = 11.2 km.

    Hence, the correct answer is option b.

  3. In a hurdle race, Tom is beaten by Patrick by a distance of 25 meters or 10 seconds. How much time did Patrick take to finish the hurdle race of total 1 km?

    1. 5 minutes and 20 seconds
    2. 4 minutes and 20 seconds
    3. 6 minutes and 30 seconds
    4. 7 minutes and 20 seconds
    5. 8 minutes and 20 seconds

    Correct answer: c

    Explanation:

    According to the data given in the question,

    Tom covers a distance of 25 meters in 10 seconds.

    Total distance to be covered in the hurdle race = 1 km = 1000 m

    ∴ Time taken by Tom to complete the race = (10 / 25) * 1000 = 400 seconds

    ∴ Time taken by Patrick to complete the entire hurdle race = 400 – 10 = 390 seconds.

    Now, 390 seconds = 6 minutes and 30 seconds

    Hence, the correct answer is option c.

  4. Rose, Lilly and Jasmine participate in a km race. Rose gives a start of 20 meters to Lilly. Also, Jasmine is given a start of 350 meters by Rose. How many meters of start can be given by Lilly to Jasmine?

    1. 10.15 meters
    2. 15 meters
    3. 16.31 meters
    4. 15.31 meters
    5. None of the above

    Correct answer: d

    Explanation:

    Rose gives a start of 20 meters and 35 meters to Lilly and Jasmine means that, Lilly starts 20 meters ahead of Rose and Jasmine starts 35 meters ahead of Rose.

    Now, according to the data given in the question,

    Distance covered by Rose = 1000 meters ………..i

    Distance covered by Lilly = (1000 – 20) meters = 980 meters ………..ii

    Distance covered by Jasmine = (1000 – 35) meters = 965 meters ………..iii

    Now, when Lilly covers a distance of 980 meters, Jasmine covers a distance of 965 meters.

    ∴ When Rose covers a distance of 1000 meters, distance covered by Lilly = (965 / 980) * 1000 = 984.69 meters.

    ∴ Lilly can give a start of (1000 – 984.69) meters to Jasmine

    ∴ Lilly can give a start of 15.31 meters to Jasmine.

    Hence, the correct answer is option d.

  5. A, B and C are playing a game of billiards. In a game of 60 points, A can give B 15 points, while in a game of 90; A can give 20 points to C. How many points can C give to B in a game of 70 points?

    1. 5.5 points
    2. 6.5 points
    3. 8 points
    4. 7.5 points
    5. None of the above

    Correct answer: d

    Explanation:

    According to the data given in the question,

    In a game of billiards of 60 points, points given by A to B = 15 points ……….i

    ∴ If 60 points are scored by A, then points scored by B = 60 – 15 = 45 points ….ii

    In a game of billiards of 90 points, points given by A to C = 20 points ……….iii

    ∴ If 90 points are scored by A, then points scored by C = 90 – 20 = 70 points ……iv

    ∴ If A scores 60 points, then points scored by C = (70 / 90) * 60 = 420 / 9 points ….v

    Thus, we can say that, when C scores 420 / 9 points, then points scored by B = 45 points ………from equation i and v

    ∴ When C scores 70 points, then points scored by B = (45 * 70 * 9) / 420 = 67.5 points

    Thus, the points that C can give to B in a game of 70 = 67.5 / 9 = 7.5 points

    Hence, the correct answer is option d.

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GMAT Sample Problem Solving Ability Question Number : 1-5 | 6-10 | 11-15 | 16-20 | 21-25 | 26-30 | 31-35 | 36-40 | 41-45 | 46-50 | 51-55 | 56-60 | 61-65 | 66-70 | 71-75 | 76-80 | 81-85 | 86-90 | 91-95 | 96-100 | 101-105 | 106-110 | 111-115 | 116-120 | 121-125
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