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

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Manager
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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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Difficulty:

55% (hard)

Question Stats:

54% (01:17) correct 46% (01:20) wrong based on 78 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?

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 21 Aug 2012, 08:00, edited 2 times in total.
Edited the question and OA.

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09 Jul 2011, 21:38
Are you sure the answer is D ? I'm getting B as answer.

So we have :

P1 + x + z + 5 = 50

P2 + x + y + 5 = 30

P3 + z + y + 5 = 20

P1 + P2 + P3 + x + y + z + 5 = 85

We need to find x + y + z + 5 = ?

So P1 + P2 + P3 + 2(x + y + z) + 15 - (P1 + P2 + P3 + x + y + z + 5) = 100 - 85

=> x+y+z + 10 = 15

=> x + y + z + 5 = 10

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09 Jul 2011, 21:38
Alchemist1320 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

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

Im getting 10 , ru sure on the OA?

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10 Jul 2011, 20:31
Soln: n(1U2U3) = n(1) + n(2) + n(3) - n(1n2) - n(2n3) - n(1n3) + n (1n2n3)
85=50+30+20- [n(1n2) + n(2n3) + n(1n3)] +5
[n(1n2) + n(2n3) + n(1n3)] = 20
Answer = 20+5 = 25 so E

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10 Jul 2011, 20:45
apologies...I had initially put in D as an asnwer...but now I think its E...

let me know if you think its not correct

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21 Aug 2012, 07:55
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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Re: In a consumer survey, 85% of those surveyed liked at least [#permalink]

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21 Aug 2012, 08:05
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Expert's post
Alchemist1320 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%) plus those who liked exactly three products (5%), so 5+5=10% liked more than one product.

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).

Hope it helps.

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] 21 Aug 2012, 08:05
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