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Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot d
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02 Apr 2021, 05:10
02 Apr 2021, 05:10
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Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot dog eating contest. If Jim ate four times as many hot dogs as Leon but half as many hot dogs as Billy, how many more hot dogs did Billy eat than Leon?
A. 13
B. 20
C. 39
D. 42
E. 60
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 13
B. 20
C. 39
D. 42
E. 60
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Joined: 10 Apr 2015
Posts: 6218
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Re: Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot d
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02 Apr 2021, 05:41
02 Apr 2021, 05:41
1
Carcass wrote:
Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot dog eating contest. If Jim ate four times as many hot dogs as Leon but half as many hot dogs as Billy, how many more hot dogs did Billy eat than Leon?
A. 13
B. 20
C. 39
D. 42
E. 60
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 13
B. 20
C. 39
D. 42
E. 60
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Let x = # of hot dogs that Jim ate
Jim ate four times as many hot dogs as Leon
In other words, Leon ate 1/4 as many hot dogs as Jim ate
So, x/4 = # of hot dogs that Leon ate
Jim ate half as many hot dogs as Billy
In other words, Billy ate twice as many hot dogs as Jim ate
So, 2x = # of hot dogs that Billy ate
In TOTAL they ate 78 hot dogs
So, x + x/4 + 2x = 78
Solve to get: x = 24
So...
Jim ate 24 hot dogs
Leon ate 6 hot dogs
Billy ate 48 hot dogs
How many more hot dogs did Billy eat than Leon?
48 - 6 = 42 = D
Cheers,
Brent
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot d
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02 Apr 2021, 05:49
02 Apr 2021, 05:49
1
Carcass wrote:
Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot dog eating contest. If Jim ate four times as many hot dogs as Leon but half as many hot dogs as Billy, how many more hot dogs did Billy eat than Leon?
A. 13
B. 20
C. 39
D. 42
E. 60
A. 13
B. 20
C. 39
D. 42
E. 60
Total \(= L + B + J = 78\)
\(J = 4L\)
\(\frac{J}{L} = \frac{4}{1}\)
\(J = \frac{1}{2}B\)
\(\frac{J}{B} = \frac{1}{2}\)
Let us make Js equal;
\(\frac{J}{L} = \frac{4}{1}\), \(\frac{J}{B} = \frac{1}{2}\)
\(\frac{J}{L} = \frac{4}{1}\), \(\frac{J}{B} = \frac{1(4)}{2(4)}\)
\(\frac{J}{L} = \frac{4}{1}\), \(\frac{J}{B} = \frac{4}{8}\)
Therefore, \(J : L : B = 4 : 1 : 8\)
The question asks \(B - L = \frac{(8 - 1)}{(4 + 1 + 8)}(78) = 42\)
Hence, option D
