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John, Karen, and Luke collected cans of vegetables for a food drive.

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Bunuel
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John, Karen, and Luke collected cans of vegetables for a food drive. [#permalink] New post   15 Mar 2016, 23:46
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John, Karen, and Luke collected cans of vegetables for a food drive. The number of cans that John collected was 1/2 the number of cans that Karen collected and 1/3 the number of cans that Luke collected. The number of cans that Luke collected was what fraction of the total number of cans that John, Karen, and Luke collected?

(A) 1/5
(B) 1/3
(C) 2/5
(D) 1/2
(E) 2/3
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John, Karen, and Luke collected cans of vegetables for a food drive. [#permalink] New post   20 May 2017, 12:48
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John, Karen, and Luke collected cans of vegetables for a food drive. The number of cans that John collected was 1/2 the number of cans that Karen collected and 1/3 the number of cans that Luke collected. The number of cans that Luke collected was what fraction of the total number of cans that John, Karen, and Luke collected?

Let cans collected by John be X.
John collected \(\frac{1}{2}\) of the number of cans that Karen collected, ie; Karen's cans = 2X
John collected \(\frac{1}{3}\) of the number of cans that Luke collected, ie; Luke's cans = 3X
Total number of cans collected by Luke, John and Karen = X + 2X + 3X = 6X
Required fraction = Luke's cans/Total cans = \(\frac{3X}{6X}\) = \(\frac{1}{2}\)
Answer D...

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Re: John, Karen, and Luke collected cans of vegetables for a food drive. [#permalink] New post   17 Mar 2016, 07:44
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John = (1/2)Karen --> Karen = 2(John)
John = 3(Luke) --> Luke = 3(John)

Total = 6(John)

Luke/Total = 3/6 = 1/2

Answer: D
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Re: John, Karen, and Luke collected cans of vegetables for a food drive. [#permalink] New post   20 May 2017, 11:19
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Assume number of cans John collected = 1
Then, number of cans Karen collected = 2
and number of cans Luke collected = 3

Total = 1+2+3=6

Cans with Luke as a fraction of total = 3/6 = 1/2

Hence D
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Re: John, Karen, and Luke collected cans of vegetables for a food drive. [#permalink] New post   20 May 2017, 12:53
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The best way is to find assume numbers and do the following problem

Given, number of cans of John was half the cans that Karen collected.
This number is also 1/3rd of the cans that Luke collection.
If 10 is the number of cans that John, collected.
Karen collected 20 cans and Luke, 30 cans.

Luke collected 30 out of total cans(10+20+30), which is 30/60 or 1/2(Option D)
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Re: John, Karen, and Luke collected cans of vegetables for a food drive. [#permalink] New post   04 Apr 2019, 18:38
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Bunuel wrote:
John, Karen, and Luke collected cans of vegetables for a food drive. The number of cans that John collected was 1/2 the number of cans that Karen collected and 1/3 the number of cans that Luke collected. The number of cans that Luke collected was what fraction of the total number of cans that John, Karen, and Luke collected?

(A) 1/5
(B) 1/3
(C) 2/5
(D) 1/2
(E) 2/3


We can create the equations:

J = K/2

2J = K

And

J = L/3

3J = L

So the fraction that Luke collected was:

L/(J + K + L) = 3J/(J + 2J + 3J) = 3J/6J = 1/2

Alternate Solution:

Let’s assume that John collected 5 cans. Since he collected half as many cans as Karen collected, then she collected 10 cans. Since John collected 1/3 the number of cans that Luke collected, then Luke collected 15 cans. Thus, the total number of cans collected was 5 + 10 + 15 = 30. So Luke collected 15/30 = ½ of all the cans collected.

Answer: D
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Re: John, Karen, and Luke collected cans of vegetables for a food drive. [#permalink] New post   24 Mar 2024, 17:27
Hello from the GMAT Club BumpBot!

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Re: John, Karen, and Luke collected cans of vegetables for a food drive. [#permalink]
24 Mar 2024, 17:27
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