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

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The third-place finisher of the Allen County hot dog eating [#permalink] New post 09 Jun 2012, 16:51
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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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Re: hot dog [#permalink] New post 09 Jun 2012, 17:02
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Interesting problem. We know that the 3rd place finisher had the same amount of time as everyone else and ate his/her hot dogs at an average pace of 15 seconds per dog. So third place finisher ate x/15 hot dogs. So in order to solve this problem, we need to know the value of x.

1)

The winner ate (x/15) + 24 hot dogs. We can't figure out the value of x from this.

So insufficient.

[strike]AD[/strike]
BCE

2)

This tells us that the winner ate 2 * (x/15) hot dogs. Again, not enough to know for sure.

Insufficient.

1+2)

We have two equations here that refer to the same thing...

(x/15) + 24 = 2 * (x/15)

We can solve for x! Sufficient.

Answer is C.
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Re: The third-place finisher of the Allen County hot dog eating [#permalink] New post 10 Jun 2012, 01:33
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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?

Information about 15 seconds is quite redundant. Say the third-place finisher ate T hot dogs and the winner ate W hot dogs.

(1) The winner consumed 24 more hot dogs than did the third-place finisher --> W=T+24 --> one equation two unknowns. Not sufficient.

(2) The winner consumed hot dogs at double the rate of the third-place finisher --> at double rate the winner would consume twice as many hot dogs, so W=2T --> one equation two unknowns. Not sufficient.

(1)+(2) We have two distinct linear equations with two unknowns, so we can get the single numerical values of T and W: T+24=2T --> T=24. Sufficient.

Answer: C.
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Re: The third-place finisher of the Allen County hot dog eating [#permalink] New post 15 Jul 2014, 23:49
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Re: The third-place finisher of the Allen County hot dog eating [#permalink] New post 17 Jul 2014, 07:44
Can you please tell why is it x/15? Thanks in advance
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Re: The third-place finisher of the Allen County hot dog eating [#permalink] New post 17 Jul 2014, 07:53
Expert's post
sri30kanth wrote:
Can you please tell why is it x/15? Thanks in advance


x is the total time given to each contestant to eat. Since the third-place finisher required an average of 15 seconds to consume each hot dog, then he/she ate x/15 hot dogs.

Another solution which does not use that bit of information is here: the-third-place-finisher-of-the-allen-county-hot-dog-eating-134234.html#p1095045

Hope it helps.
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Re: The third-place finisher of the Allen County hot dog eating   [#permalink] 17 Jul 2014, 07:53
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