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GMAT Prep Overlapping Sets problem

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GMAT Prep Overlapping Sets problem [#permalink] New post 20 May 2011, 10:47
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Question Stats:

86% (01:34) correct 13% (00:52) wrong based on 1 sessions
I am interested to seeing the different approaches to solving this problem:

A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?

a. 1/10
b. 3/10
c. 1/2
d. 7/10
e. 9/10
[Reveal] Spoiler: OA
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Re: GMAT Prep Overlapping Sets problem [#permalink] New post 20 May 2011, 11:18
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C+M+B-CM-MB-CB-2CMB = 100

C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.

the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.

50 + 40 + B-CB-MB-20-2CMB = 100

B-CB-MB-2CMB = 30

hence the probability = 30/100 = 3/10.

B
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Re: GMAT Prep Overlapping Sets problem [#permalink] New post 20 May 2011, 11:59
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probability that the buyer selected will be one who purchases neither cake mix nor muffin mix = 30/100 = 3/10
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Re: GMAT Prep Overlapping Sets problem   [#permalink] 20 May 2011, 11:59
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