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in a consumer survey , 85% of those surveyed likes at least

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Intern
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in a consumer survey , 85% of those surveyed likes at least [#permalink] New post 28 Mar 2007, 10:21
in a consumer survey , 85% of those surveyed likes at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% like product 3. if 5 % of the people in the survey likes all 3 of products, what % of the survey participants likes more than one of the three products?

5
10
15
20
25
Manager
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 [#permalink] New post 28 Mar 2007, 12:38
B for me.

50% of 85 = 42.5
30% of 85 = 25.5
20% of 85 = 17

5% = 5 (question says 5% of the ppl in the survey, not 5% of the 85 % surveyed)

so our equation:
85 = 42.5 + 25.5 +17 - (x) + 5
x= 5

add the other 5 who liked all 3 products and we get
10
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 [#permalink] New post 28 Mar 2007, 17:03
B.

I drew a venn-diagram :)
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 [#permalink] New post 29 Mar 2007, 02:08
rico, I tried to draw a venn-diagram for this question.....but :oops:

Could you please describe how did you do that in this question?

Thanks!
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 [#permalink] New post 29 Mar 2007, 02:34
Thanks rico...

I tried again and this time I was able to draw a venn diagram for this sum and solve it :-D
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 [#permalink] New post 29 Mar 2007, 08:15
Here is another way to look at the question.

100 participants

5 like both products

50 % + 30% + 20 %= 100%

100 votes

-15 votes for all three (5 percent of 100)

85 votes from 80 voters (85 voters-5 voters who voted for all three)

5 voted for more than on 5 for all three

10 or 10%
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 [#permalink] New post 29 Mar 2007, 11:30
yet another way. change all the percentages to actual people.

85 voted.
50 liked 1
30 liked 2
20 liked 3

85 = 50+30+20 - (anyone who like voted for more than one) - (anyone who voted for all three)
85 = 100 - (anyone who voted for more than one) - 5
10 = anyone who voted for more than one
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Re: venn diagram set theory question 2 [#permalink] New post 29 Mar 2007, 19:35
pman wrote:
in a consumer survey , 85% of those surveyed likes at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% like product 3. if 5 % of the people in the survey likes all 3 of products, what % of the survey participants likes more than one of the three products?

5
10
15
20
25


shouldn't the answer be 15?

let union = union of sets
int = intersection of sets

so

n(A union B union C) = n(A) + n(B) + n(C) - n(A union B) - n(B union C) - n(C union A) + n(A int B int C)

putting values
0.85 = 1 - [n(A union B) + n(B union C) + n(C union A)] + 0.05

or [n(A union B) + n(B union C) + n(C union A)] = 0.20

so people who like more than 2 is obtained by

[n(A union B) + n(B union C) + n(C union A)] - 2 [A int B int C]
= 25 - 10
= 15

What do you guys think?
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 [#permalink] New post 30 Mar 2007, 03:05
My equation will be :

n(A U B U C) = n(A) + n(B) +n(C) - n(A U B)- n(B U C)- n(C U A) + n(A int B int C)

85= 50+30+20 -[n(A U B)+ n(B U C)+ n(C U A)] + 5

[n(A U B)+ n(B U C)+ n(C U A)] = 20

No. of people liked more than one of the three products =
[n(A U B)+ n(B U C)+ n(C U A)] + n(A int B int C) = 20 +5 = 25
Answer is 'E'
  [#permalink] 30 Mar 2007, 03:05
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