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 Post subject: GMAT Overlapping Sets
PostPosted: Fri Apr 16, 2010 12:53 pm 
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In a consumer survey, 85 percent of those surveyed liked at least one of three products. 50 percent of those surveyed liked Product 1, 30 percent liked Product 2, and 20 percent liked Product 3. If 5 percent of the people in the survey liked all three of the products, what percent of the survey participants liked more than one of the three products?

A. 5%
B. 10%
C. 15%
D. 20%
E. 25%


For better understanding we can use vienn diagram:
Image


(B)Overall, 85% of the surveyed people like at least one product, but when we add up the percent of people who like each product individually, we get a sum that is more than 85%:
50% + 30% + 20% = 100%

These two figures differ because the people that like all three products are counted three times in the 100% figure, and the people that like exactly two products are counted twice.

To correct for the triple-counting, we can subtract 2 times the number of people that like all three products, so these people are now counted just once. We can also correct for the double-counting by subtracting the number of people that were double counted, so they are now counted just once.

The equation will look like this:
85% = 100% – 2(like all three) – (like exactly 2).
85% = 100% – 2(5%) – (like exactly 2)
85% = 90% – (like exactly 2)
5% = the number of people that like exactly 2 products.

Since 5% like all three products, and 5% like exactly 2 products, 10% like more than one product.

The correct answer is choice (B).
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