GMAT Challenge Series (700+): Q5

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Question:

In racing over a given distance d at uniform speed, A can beat B by 20 yards, B can beat C by 10 yards, and A can beat C by 28 yards. Then d, in yards, equals?

A. Cannot be determined

B. 58

C. 100

D. 116

E. 120

MBA Wisdom's Answer:

$$\text{Moments:}$$ $$\textit{Moment 1: A crosses the line with B 20 yards behind and C 28 yards behind.}$$ $$\textit{Moment 2: B crosses the line with C 10 yards behind.}$$ $$$$ $$\text{Takeaways:}$$ $$\textit{Takeway 1: Between moment 1 and 2 B has gone 20 yards and C has gone 18 yards.}$$ $$\textit{Takeway 2: Between moment 1 and 2 B beats C by 2 yards.}$$ $$$$ $$\textit{Over the distance d, B beats C by 10 yards.}$$ $$\textit{d} = \left(\frac{10}{2}\right) \left({20}\right) = {100}$$

C. 100