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In a consumer survey, 85% of those surveyed liked at least one of thre [#permalink]
14 Jul 2004, 09:04

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Difficulty:

75% (hard)

Question Stats:

40% (02:57) correct
60% (02:07) wrong based on 52 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 one of thre [#permalink]
14 Jul 2004, 13:19

X=people liking at least 2 products
50+30+20-X-5 = 85
X=10
But you have to add 5 because those 5 like more than 2 products.
Hence answer is 10+5=15 _________________

Re: In a consumer survey, 85% of those surveyed liked at least one of thre [#permalink]
18 Jan 2015, 23:52

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Re: In a consumer survey, 85% of those surveyed liked at least one of thre [#permalink]
19 Jan 2015, 00:39

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boksana wrote:

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.

Answer: B.

For more check: formulae-for-3-overlapping-sets-69014.html (there is my post in the end of the first page about the formulas of 3 overlapping sets with theory, diagrams and examples).

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