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GMAT Prep Overlapping Sets Problem

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by tonebeeze » Fri May 20, 2011 9:54 am
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 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 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

OA = B
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Source: — Problem Solving |

by Frankenstein » Fri May 20, 2011 10:17 am
Hi,
C(Cake)= 50, M(Muffin)= 40, C&M(Cake and Muffin)= 20
So, C or M = C+M-(C&M)= 50+40-20 = 70
Neither C nor M = 100-(C or M) = 100-70=30

Hence, the probability that buyer selected purchases neither cake nor muffin = 30/100 =3/10

Hence B

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by manpsingh87 » Fri May 20, 2011 10:19 am
tonebeeze wrote: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 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 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

OA = B
total no. of buyers= cake mix buyers+ muffin mix buyers- both cake and muffin mix buyers+ other(bread buyers);
100=50+40-20+other;
other=30;
hence required probability is 30/100=3/10 hence B
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by Brent@GMATPrepNow » Sat May 21, 2011 6:25 am
You can also solve this question using the Double Matrix Method.
I recently wrote some articles for Beat The GMAT about this.
Here's part 1: https://www.beatthegmat.com/mba/2011/05/ ... question-1

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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