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The third-place finisher of the Allen County hot dog eating

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by BTGmoderatorDC » Thu Oct 10, 2019 7:15 pm
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.

OA C

Source: Manhattan Prep
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Fri Oct 11, 2019 4:24 am
BTGmoderatorDC 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.

OA C

Source: Manhattan Prep
Say the total time given to each as many hot dogs is x seconds. Thus, the 3rd place finisher each x/15 hot dogs.

Let's take each statement one by one.

(1) The winner consumed 24 more hot dogs than did the third-place finisher.

No. of hot dogs the winner ate = 24 + x/15. Can't get the value. Insufficient.

(2) The winner consumed hot dogs at double the rate of the third-place finisher.

=> No. of hot dogs the winner ate = x/7.5. Can't get the value. Insufficient.

(1) and (2) together

x/7.5 = 24 + x/15

x = 15*24 = 360.

No. of hot dogs the winner ate = x/7.5 = 360/7.5 = 48. Sufficient

The correct answer: C

Hope this helps!

-Jay
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edited:

by deloitte247 » Sat Oct 12, 2019 7:14 am
Each contestant has equal amount of time to eat as many hot dogs as possible.
It requires an average of 15 seconds to consume 1 hotdog. So, how many hotdogs did the winner eat?
Statement 1: The winnner consumed 24 more hot dogs than the third-phase finisher.
Let hotm dogs consumed by the third-phase finisher = x
Therefore, third-phase finisher = x
Winner = x + 24
Since the value of x is unknown, statement 1 is NOT SUFFICIENT.

Statement 2: The winner consumed hot dogs at double rate of the third-place finisher.
So, let the rate of third-phase finisher = x
Winner = 2x
Since the value of x is unknown, statement 2 is also NOT SUFFICIENT.

Combining both statements together:
Statement 1: Winner = x + 24
Statement 2: Winner = 2x
Substituting the value of winner in statement 1 for the winner in statement 2;
We have,
Winner = x + 24
2x = x + 24
x = 24
Since the winner consumed 24 more hot dogs than the third-place finisher, winner = 24 + 24 = 48
Both statements combined together are SUFFICIENT.

Answer = option C
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