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In a consumer survey, 85% of those surveyed liked at least [#permalink]
22 Aug 2004, 13:04

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Difficulty:

55% (hard)

Question Stats:

55% (02:54) correct
45% (01:26) wrong based on 104 sessions

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?

Re: In a consumer survey, 85% of those surveyed liked at least [#permalink]
14 Sep 2013, 11:21

Expert's post

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

As 85% of those surveyed liked at least one of three products then 15% liked none of three products.

Total = {liked product 1} + {liked product 2} + {liked product 3} - {liked exactly two products} - 2*{liked exactly three product} + {liked none of three products}

\(100=50+30+20-x-2*5+15\) --> \(x=5\), so 5 people liked exactly two products. More than one product liked those who liked exactly two products, (5%) plusthose who liked exactly three products (5%), so 5+5=10% liked more than one product.

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