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?
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.
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