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OG Dignostic test question 6

Expert replies
by harikattamudi » Sun Jan 16, 2011 7:59 pm
A marketing firm determined that, of 200 households surveyed, 80 used neither brand A nor brand B soap, 60 used only brand A soap, and for every househols that used both brands of soap, 3 used only brand B soap. How many of the 200 households surveyed used both brands of soap?

A. 15
B. 20
C. 30
D. 40
E. 45

The officeial guids says answer as A.15.

120 = 60 + 3x +x.

But i feel the answer as C.30
120 = 60 +3x - x. (As x is commonly used brand shouldn't it be subtracted.)

Please advice.

thanks
-Hari
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Source: — Problem Solving |

by anshumishra » Sun Jan 16, 2011 8:05 pm
harikattamudi wrote:A marketing firm determined that, of 200 households surveyed, 80 used neither brand A nor brand B soap, 60 used only brand A soap, and for every househols that used both brands of soap, 3 used only brand B soap. How many of the 200 households surveyed used both brands of soap?

A. 15
B. 20
C. 30
D. 40
E. 45

The officeial guids says answer as A.15.

120 = 60 + 3x +x.

But i feel the answer as C.30
120 = 60 +3x - x. (As x is commonly used brand shouldn't it be subtracted.)

Please advice.

thanks
-Hari
I have solved it here : https://www.beatthegmat.com/venn-diagram ... 71795.html
Thanks
Anshu

(Every mistake is a lesson learned )
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by fitzgerald23 » Mon Jan 17, 2011 10:23 am
I always find these questions to be most easily solved by setting up a quick chart with columns of "A" and "Not A" with rows of "B" and "not B". Add down and across and you will quickly come up with the equation of

4x + 140 = 200
X=15[/list]
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