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Sets

by crackgmat007 » Thu Jul 16, 2009 7:31 am
In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?

A) 5

B) 10

C) 15

D) 20

E) 25
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by yogami » Thu Jul 16, 2009 8:01 am
The formula for three set situation is
Total = A + B + C + A intersect B intersect C + none - (A intersect B + B intersect C + C intersect A)
intersect => common between two sets

We know that the total of the sets is 85 % and 15 % are in the nothing category.
So
85 = A + B + C + (A int B int C) - (A int B + B int C + C int A)
85 = 50 + 30 + 20 + 5 - (people who like two things)
so people who like two things = 20.,
But the dang question asks to give a percentage of people who like more than 1 i.e. 2 or 3 things which is annoying because some of us can simply list the answer as 20. I don't know what GMAC wants to test by asking something like "more than one". Are they trying to be picky on those people who do not give attention to detail??? I really hate that and thats why I dont like standardized tests. This forces us to reread the question for some stupid things hidden in it. In this case you have to add extra 5% (people who like three things) in the final answer because three is also more than one. HATE IT HATE IT HATE IT
So answer is 25.
But again I dont have the right words to express my anger at such kind of questions. Its silly to test people on such stupid things. This question is a little bit matured version of the following question " You are riding a bus of forty people - 20 get off the first stop, 40 get in - 30 get off the next stop, 10 get off. What is the name of the driver??"
200 or 800. It don't matter no more.
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