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

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Math Expert
Joined: 02 Sep 2009
Posts: 43892
John, Karen, and Luke collected cans of vegetables for a food drive. [#permalink]

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15 Mar 2016, 22:46
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Difficulty:

25% (medium)

Question Stats:

76% (01:07) correct 24% (01:25) wrong based on 64 sessions

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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
[Reveal] Spoiler: OA

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

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17 Mar 2016, 06:44
1
KUDOS
John = (1/2)Karen --> Karen = 2(John)
John = 3(Luke) --> Luke = 3(John)

Total = 6(John)

Luke/Total = 3/6 = 1/2

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

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20 May 2017, 06:29
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Re: John, Karen, and Luke collected cans of vegetables for a food drive. [#permalink]

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20 May 2017, 10:19
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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John, Karen, and Luke collected cans of vegetables for a food drive. [#permalink]

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20 May 2017, 11:48
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 = $$\frac{3X}{6X}$$ = $$\frac{1}{2}$$

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

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20 May 2017, 11:53
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] 20 May 2017, 11:53
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