GMAT Quant Questions | GMAT Rates Q4

This GMAT Math practice question is from the topic rates, testing the concept of a race between two runners. A medium difficulty, GMAT 600 to 650 level sample question.

Question 4: A runs 25% faster than B and is able to give B a start of 7 meters to end a race in dead heat. What is the length of the race?

1. 10 meters
2. 25 meters
3. 45 meters
4. 15 meters
5. 35 meters

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Video Explanation

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Explanatory Answer | GMAT Races

Compute Length of Race

A runs 25% faster than B. Essentially, A runs 125% as much distance as B does in the same time.
i.e., if B runs 100 m in a given time, A will run 125 m in the same time.
Ratio of distances run between A and B in a given time is 125 : 100
Expressing the ratio in its lowest form, distance run by A : B = 5 : 4

In other words, if A runs 5 m in a given time, then B will run 4 m in the same time.

Therefore, if the length of a race is 5 m, then A can give B a start of 1 m (A can allow B to start 1 ahead of the starting point) so that they finish the race in a dead heat.
Ratio of length of start given : length of race :: 1 : 5

In this question, we know that the start given is 7 m.
Hence, the length of the race will be 7 × 5 = 35 m.

Choice E is the correct answer.