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In a consumer survey, 85% of those surveyed liked at least

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

A) 5

B) 10

C) 15

D) 20

E) 25

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-a-consumer-survey-85-of-those-surveyed-liked-at-least-98018.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Sep 2013, 11:20, edited 1 time in total.
Edited the question and added the OA
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 [#permalink] New post 22 Aug 2004, 14:42
I'm thinking B

more than 1 product is : 50 + 30 + 20 - 85 =15
but this 15% counts the a(intersection)b(intersection)c twice so the ans is
15 -5 = 10 ans
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Re: In a consumer survey, 85% of those surveyed liked at least [#permalink] New post 14 Sep 2013, 11:05
I'll go with B too.

85 = 50 + 30 + 20 - x - 2(5) + 0

x = 5

Then Liked more than 1 includes those who liked exactly 2 and those who liked exactly 3.

Liked exactly 2 ---> From x = 5
Liked exactly 3----> Given 5

Total 5+5 =10

Answerb (B)
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Re: In a consumer survey, 85% of those surveyed liked at least [#permalink] New post 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%) plus those who liked exactly three products (5%), so 5+5=10% liked more than one product.

Answer: B.

For more check ADVANCED OVERLAPPING SETS PROBLEMS

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-a-consumer-survey-85-of-those-surveyed-liked-at-least-98018.html
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Re: In a consumer survey, 85% of those surveyed liked at least   [#permalink] 14 Sep 2013, 11:21
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