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Bunuel
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Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot 23 Feb 2016, 02:52
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D
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87% (02:16) correct 13% (03:00) wrong based on 261 sessions

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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


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D
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BrentGMATPrepNow
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Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot 23 Feb 2016, 16:51
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Bunuel
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

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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

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Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot 23 Feb 2016, 10:12
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Bunuel
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


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hi,
two ways you can tackle these problems, although the concept/logic is same--
1) ratio--
clearly ratio between B:J:L=8:4:1..
since J:L=4:1 and B:J=2:1..
let the common ratio be x, so total=13x and x=78/13=6..
difference in B and L= (8-1)x=7*6=42..
D

2) Equations..
L+B+J=78..
Jim ate four times as many hot dogs as Leon
J=4L..
Jim ate half as many hot dogs as Billy
J=B/2 or B=2J..
since L+B+J=78.. L+4L+2*4L=78..
L=78/13=6..
so B=2*4L=8*6=48..

ans 48-6=42..
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Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot 23 Feb 2016, 10:25
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Since Leon has eaten the lowest number of htdgs, Let's consider,
the number of htdgs eaten by Leon= x
and htdgs etn by Jimmy=4x
And by Billy=2*4x=8x

Total number of htdgs= x+4x+8x = 13x

13x=78 => x=6

we need to find difference between Billy's and Leon's consumption, i.e. 8x-x = 7x

7*6=42

D is the answer.
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Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot 23 Feb 2016, 10:28
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Bunuel
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


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Let \(l\), \(b\) and \(j\) represent the number of hotdogs eaten by Leon, Billy and Jim, respectively.
Jim ate four times as many hot dogs as Leon.
so, \(j = 4l\)
But Jim ate half as many hot dogs as Billy
so, \(j = 1/2b\)
replace \(j = 4l\) in the above equation. we get:
\(4l = 1/2b\) or \(b = 8l\)

We know, \(j + l + b = 78\)
replace, \(j = 4l\) and \(b = 8l\) in the above equation, we get
\(4l + l + 8l = 78\)
This means, \(13l = 78\) or \(l = 6\)
Leon ate 6 hotdogs.
\(b = 8l\) = 8 x 6 = 48
Billy ate 48 hotdogs
How many more hot dogs did Billy eat than Leon?
= \(b - l\) = 48 - 6 = 42
Hence, D is the correct answer.
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Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot 23 Feb 2016, 12:52
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L+b+j=78
J=4l -> l=j/4
J=b/2 -> b=2j

J/4+2j+j=78
13j= 78×4
J=24
B=48
L=6

B-l=42
Ans:D
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Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot 27 Feb 2018, 10:42
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Bunuel
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
Show more

We can let the number of hot dogs eaten by Leon, Billy, and Jim = L, B, and J, respectively, and create the equations:

L + B + J = 78

and

J = 4L
J/4 = L

and

J = (1/2)B

2J = B

Substituting, we have:

J/4 + 2J + J = 78

J/4 + 3J = 78

Multiplying by 4 we have:

J + 12J = 312

13J = 312

J = 24

Thus, B = 2(24) = 48 and L = 24/4 = 6.

So Bill ate 48 - 6 = 42 more hot dogs than Leon.

Answer: D
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Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot 03 Dec 2019, 09:17
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Bunuel
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


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This is how i solved

Lets form the equation in terms of number of L. L has the least of Hot dogs
J = 4L and B= 2wice of J = 2* 4L

Therfore L+4L +8L = 78
13L = 78
L=6


SO IF L= 6 B= 8L = 8*6=48
B-L = 48-6 = 42 OR ( D )
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Leon, Billy, and Jim ate an astounding total of 78 hot dogs in a hot 10 Dec 2022, 03:08
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