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# A certain manufacturer of cake, muffin, and bread mixes has

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Intern
Joined: 08 Nov 2005
Posts: 11

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Location: Beijing, China

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24 Apr 2006, 06:35
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A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchase 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 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

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Director
Joined: 13 Nov 2003
Posts: 788

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Location: BULGARIA

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24 Apr 2006, 06:43
Hallo,
If 20 purchase both mixtures then 30 purchase cake mix only, 20 purchase muffin mix only. Then the number of people who buy neither is 30.
required prob is 30/100=3/10
IMO
regards

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Manager
Joined: 13 Dec 2005
Posts: 224

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Location: Milwaukee,WI

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24 Apr 2006, 07:09
3/10

C- cake, M muffine, B -banana

C -50 ,M 40 ,C & M =20 so B =100- (50+40 -20) =30

so B =30 , total buyers 100
probablity of choosing one of B's is 30/100 =3/10

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GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5032

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Location: Singapore

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24 Apr 2006, 17:46
From a venn diagram, we can find:

Muffin purchase = 20
Muffin + Cake purchase = 20
Cake purchase = 30

Kudos [?]: 457 [0], given: 0

24 Apr 2006, 17:46
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