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.
OAC
Hi Experts ,
Please explain.
Many thanks in advance.
SJ
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Let W = the number of hot dogs consumed by the winner.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.
and c
Let T = the number of hot dogs consumed by the third-place finisher.
Statement 1: The winner consumed 24 more hot dogs than did the third-place finisher.
W = T + 24.
No way to solve for W.
INSUFFICIENT.
Statement 2: The winner consumed hot dogs at double the rate of the third-place finisher.
Since the winner ate twice as fast, he consumed TWICE the number of hot dogs:
W = 2T.
No way to solve for W.
INSUFFICIENT.
Statement combined:
Since we have two variables and two distinct linear equations, we can solve for each variable.
SUFFICIENT.
The correct answer is C.
The rate given for the third-place finisher -- 15 seconds per hot dog -- is irrelevant.
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Hi jain2016,
In this DS question, we're told the rate of the 3rd place finisher in a contest (4 hotdogs per minute). We are asked how many total hotdogs the winner (1st place) ate. Before you start this question, consider all of the things that you DON'T KNOW (don't know how long the contest was, don't know the winner's rate of eating hotdogs).
Fact 1 tells us that the winner ate 24 more hotdogs than the 3rd place finisher. We don't know how many the 3rd place finisher ate though, so....
Fact 1 is INSUFFICIENT
Fact 2 tells us the winner ate at twice the rate of the 3rd place finisher. This tells us that the winner ate 8 hotdogs per minute, but we still don't know how long the contest was.
Fact 2 is INSUFFICIENT
COMBINED, we know the difference in the rates (8 per minute vs. 4 per minute) and we know the actual difference (24 hotdogs). This helps us to figure out how long the contest was:
If X = the number of minutes in the contest, then
8X - 4X = 24 hotdogs
4X = 24 hotdogs
X = 6 minutes
With the 1st place finishers rate (8 per minute) and the number of minutes (6 minutes), we can get the answer (48 hotdogs, but we really don't have to figure that out to know that.....)
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
In this DS question, we're told the rate of the 3rd place finisher in a contest (4 hotdogs per minute). We are asked how many total hotdogs the winner (1st place) ate. Before you start this question, consider all of the things that you DON'T KNOW (don't know how long the contest was, don't know the winner's rate of eating hotdogs).
Fact 1 tells us that the winner ate 24 more hotdogs than the 3rd place finisher. We don't know how many the 3rd place finisher ate though, so....
Fact 1 is INSUFFICIENT
Fact 2 tells us the winner ate at twice the rate of the 3rd place finisher. This tells us that the winner ate 8 hotdogs per minute, but we still don't know how long the contest was.
Fact 2 is INSUFFICIENT
COMBINED, we know the difference in the rates (8 per minute vs. 4 per minute) and we know the actual difference (24 hotdogs). This helps us to figure out how long the contest was:
If X = the number of minutes in the contest, then
8X - 4X = 24 hotdogs
4X = 24 hotdogs
X = 6 minutes
With the 1st place finishers rate (8 per minute) and the number of minutes (6 minutes), we can get the answer (48 hotdogs, but we really don't have to figure that out to know that.....)
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
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We know that
Work = Rate * Time
Here, Work = # of hot dogs consumed. Let's start with the third place finisher.
W = 15 * T
Now let's go to S1.
(W + 24) = R * T
This helps, but isn't sufficient, since we still need one of the two rates (either the third place guy's or the first place guy's).
S2 tells us that R = 2 * 15 = 30. By itself this isn't enough, since we need a number of hot dogs, and we only have two rates in terms of each other.
Together, though we're set!
W = 15T
W + 24 = 30T
So 15T = 24, T = 24/15, and the winner ate 30 * (24/15) = 48 hot dogs.
Work = Rate * Time
Here, Work = # of hot dogs consumed. Let's start with the third place finisher.
W = 15 * T
Now let's go to S1.
(W + 24) = R * T
This helps, but isn't sufficient, since we still need one of the two rates (either the third place guy's or the first place guy's).
S2 tells us that R = 2 * 15 = 30. By itself this isn't enough, since we need a number of hot dogs, and we only have two rates in terms of each other.
Together, though we're set!
W = 15T
W + 24 = 30T
So 15T = 24, T = 24/15, and the winner ate 30 * (24/15) = 48 hot dogs.
