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# GMAT Prep Overlapping Sets problem

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Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 128
Concentration: Finance, General Management
GMAT 1: 720 Q49 V40
Followers: 13

Kudos [?]: 372 [0], given: 210

GMAT Prep Overlapping Sets problem [#permalink]

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20 May 2011, 10:47
00:00

Difficulty:

15% (low)

Question Stats:

86% (01:56) correct 14% (00:57) wrong based on 44 sessions

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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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Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1345
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Kudos [?]: 250 [1] , given: 10

Re: GMAT Prep Overlapping Sets problem [#permalink]

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20 May 2011, 11:18
1
KUDOS
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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Senior Manager
Joined: 03 Mar 2010
Posts: 439
Schools: Simon '16 (M)
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Kudos [?]: 284 [1] , given: 22

Re: GMAT Prep Overlapping Sets problem [#permalink]

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20 May 2011, 11:59
1
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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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