alchemist009 wrote:
The third-place finisher of the Allen County hot dog eating contest, in which each contestant was given an equal amount of time to eat as many hot dogs as possible, required an average of 15 seconds to consume each hot dog. How many hot dogs did the winner eat?
(1) The winner consumed 24 more hot dogs than did the third-place finisher.
(2) The winner consumed hot dogs at double the rate of the third-place finisher.
There are several ways to achieve sufficiency in solving this rate problem, so the question cannot be rephrased in a useful manner.
(1) INSUFFICIENT: This statement provides the difference between the number of hot dogs consumed by the third-place finisher (let’s call this t) and the number of hot dogs consumed by the winner (let’s call this w). We now know that w = t + 24, but this does not provide sufficient information to solve for w.
(2) INSUFFICIENT: The third-place finisher consumed one hot dog per 15 seconds. To simplify the units of measure in this problem, let’s restate this rate as 4 hot dogs per minute. Statement (2) tells us that the winner consumed 8 hot dogs per minute. This does not provide sufficient information to solve for w.
(1) AND (2) SUFFICIENT: The rate of consumption multiplied by elapsed time equals the number of hot dogs consumed. This equation can be restated as time = hot dogs/rate. Because the elapsed time is equal for both contestants, we can set the hot dogs/rate for each contestant equal to one another:
w/8 = t/4
w = 2t
Substituting w – 24 for t yields
w = 2(w – 24)
w = 2w – 48
48 = w
The correct answer is C