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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]

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09 Jun 2012, 17:51
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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: The third-place finisher of the Allen County hot dog eating [#permalink]

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10 Jun 2012, 02:33
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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.

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09 Jun 2012, 18:02
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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.

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.

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Re: The third-place finisher of the Allen County hot dog eating [#permalink]

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16 Jul 2014, 00:49
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Re: The third-place finisher of the Allen County hot dog eating [#permalink]

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17 Jul 2014, 08:44
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Re: The third-place finisher of the Allen County hot dog eating [#permalink]

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17 Jul 2014, 08:53
sri30kanth wrote:

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]

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11 Feb 2016, 02:27
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Re: The third-place finisher of the Allen County hot dog eating [#permalink]

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06 Oct 2016, 06:45
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.

I thought that I was looking at 700 lvl question..and did not believe it could be that simple...
1 and 2 alone are not sufficient.
1 - we don't know how many hot dogs the third place finisher ate
2 - we don't have any piece of absolute value.

1+2
we have the rate of 1st place, and we have a piece of absolute value

should be sufficient. C
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The third-place finisher of the Allen County hot dog eating [#permalink]

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29 Oct 2016, 23:01
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.

From 1 + 2

$$\frac{(X+24)}{(30)} = \frac{(X)}{(15)}$$

15x +360 = 30x
15x=360
x=24

Note : Catch is, we have to equate the times of both contestants.

All the best.
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Re: The third-place finisher of the Allen County hot dog eating [#permalink]

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29 May 2017, 10:56
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.

The goal is to find the number of hot dogs that the winner ate. Incidentally, the average time per hot dog is not actually relevant to the problem.

Statement 1) W = T + 24

The winner ate 24 more hotdogs than the third place finisher. However, we don't know the value of either. Insufficient.

Statement 2) W = 2T. We know this fact is true because the time for each is the same. So if the winner has twice the rate of the third place finisher, then he did twice as much work (eating hot dogs) in the same amount of time. So he ate twice as many hotdogs. However, similar to statement 1, this statement is insufficient.

Statements 1+2) W = T + 24 and W = 2T.

Sufficient. We have two equations and two unknowns.
Re: The third-place finisher of the Allen County hot dog eating   [#permalink] 29 May 2017, 10:56
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