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In a consumer survey, 85% of those surveyed liked at least [#permalink]

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09 Jul 2011, 19:48

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A

B

C

D

E

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55% (hard)

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53% (02:15) correct
47% (01:13) wrong based on 72 sessions

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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?

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

Use the forumla ; Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither 100 = 50 + 30 + 20 - ( sum of 2) -2(5) +15 100 = 105-( sum of 2) 5 = sum of 2 so more than 1 = 10

Alchemist the answer has to be B i.e. 10% (A∪B∪C)=(A+B+C)-{(A∩B)+(B∩C)+(C∩A)}+(a∩b∩c) 85 = (50 + 30 + 20) - {(A∩B)+(B∩C)+(C∩A)} 5 {(A∩B)+(B∩C)+(C∩A)} = 20 But this intersection of groups counted (a∩b∩c) thrice thus we must subtract 3(a∩b∩c) from {(A∩B)+(B∩C)+(C∩A)} in order to calculate no of people who are part of exactly 2 groups. No of people who are exactly in 2 groups = {(A∩B)+(B∩C)+(C∩A)}-3(a∩b∩c) = 20 - 3(5)= 5 No of people who are either in exactly 2 groups or 3 groups = 5 +(a∩b∩c) = 5 + 5 = 10%

I hope this is clear.

Kindly Update the OA as B
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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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