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

Question

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.

Bunuel · Accepted Answer

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.

geometric · Answer

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.

AD 
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.

sri30kanth · Answer

Can you please tell why is it x/15? Thanks in advance

Bunuel · Answer

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.

mvictor · Answer

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

deekshant111 · Answer

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.

mbaapp1234 · Answer

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.

mangamma · Answer

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

mangamma · Answer

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.

hero_with_1000_faces · Answer

The winner ate at the rate of double the third place finisher. Which means he ate double quantity compared to third place finisher.

Both were given equal time, as winner ate 24 more, hence he ate 48. double of 24.

sanjeevsinha082 · Answer

(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

ANS is C

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

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