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Data Sufficiency

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by RiyaR » Mon Sep 22, 2014 9:31 am
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.
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by Matt@VeritasPrep » Mon Sep 22, 2014 9:55 am
Let's suppose that the total time allotted to each contestant was 15t seconds. Hence the third-place finisher consumed t hot dogs.

S1 tells us that the winner consumed t + 24 hot dogs. We don't know what t is, however: NOT SUFFICIENT.

S2 tells us that the winner consumed TWICE as many hot dogs as did the third place finisher, for a total of 2t hot dogs. We don't know what t is, however: NOT SUFFICIENT.

S1 + S2 tells us that t + 24 = 2t. Hence t = 24, SUFFICIENT!
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by [email protected] » Mon Sep 22, 2014 11:51 am
Hi RiyaR,

Sometimes DS questions can be solved just by "playing around" with the given information and considering the possible outcomes.

Here, we're told that a 3rd place finisher at a contest averages 15 seconds per hot dog eaten. We're asked how MANY hot dogs the WINNER ate.

Fact 1: The winner ate 24 more hot dogs than the 3rd place finisher.

Let's TEST VALUES...
If Time = 60 seconds
3rd place = 4 hotdogs
1st place = 28 hotdogs

If Time = 120 seconds
3rd place = 8 hotdogs
1st place = 32 hotdogs

Fact 1 is INSUFFICIENT

Fact 2: The winner ate hot dogs at DOUBLE the rate of the 3rd place finisher

If Time = 60 seconds
3rd place = 4 hotdogs
1st place = 8 hotdogs

If Time = 120 seconds
3rd place = 8 hotdogs
1st place = 16 hotdogs

Fact 2 is INSUFFICIENT.

Combined, we know:
1st place ate 24 more hot dogs than 3rd place
1st place ate twice as many hot dogs as 3rd place
So for the difference to be 24 and the difference to be double, we have only one option:
3rd place = 24 hotdogs
1st place = 48 hotdogs
Combined, SUFFICIENT

Final Answer: C

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