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Venn Diagram problem

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Venn Diagram problem

by elgrower » Wed Mar 03, 2010 2:05 pm
In a consumer survey, 85% of those surveyed liked at least one of the three products: 1, 2, 3. 50% of those asked liked product 1, 30% liked product 2, 20% liked product 3. If 5% of the people liked more than one of the three products, what percentage of the survey participants like more one of the three products?

a) 5
b) 10
c) 15
d) 20
e) 25
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by papgust » Wed Mar 03, 2010 6:48 pm
Assume that there are 100 participants in the survey.

85 liked at least one of the 3 products. So, 15 did not like any of the products.

50% of 85 liked product 1 = 42 (roughly)
30% of 85 liked product 2 = 26 (roughly)
20% of 85 liked product 3 = 17

5% of 85 liked more than one of 3 products = 4 (roughly)

all 3 products = 'x'
5% of 85 exactly liked more than one of 3 products = 4-x

Total = (product 1) + (product 2) + (product 3) - (Exactly 2 products) - 2*(All 3)
85 = 42+26+17 - (4-x) - 2x
85 = 81 + x - 2x
x = 4

Percentage of survey participants which liked more than one of the three products = [spoiler]5% (approx)[/spoiler]

Not sure whether i'm right. OA please?
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by outreach » Fri Mar 05, 2010 12:57 am
For 3 sets A, B, and C:
Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither
100=50+30+20-(sum of 2-group overlaps)-2*5+15
(sum of 2-group overlaps)=5

found a post by stuart on the same
https://www.beatthegmat.com/three-overla ... tml#170757
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by yeahdisk » Fri Mar 05, 2010 2:24 am
elgrower wrote:If 5% of the people liked more than one of the three products, what percentage of the survey participants like more one of the three products?
If 'the people' = 'the survey participants', then the answer is A.
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