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In a consumer survey 85% of respondents liked at least one

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In a consumer survey 85% of respondents liked at least one [#permalink] New post 14 Jul 2004, 09:04
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In a consumer survey 85% of respondents liked at least one of the three products 1, 2 and 3. 50% of respondents liked product 1, 30% of respondents liked pr.2, 20% of respondents liked pr.3. If 5 % of the people in the survey liked all three products, what percent of the respondents liked more than one of these products?
5, 10, 15, 20, 25
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 [#permalink] New post 14 Jul 2004, 10:09
n(AUBUC) = n(A)+n(B)+n(C)-n(A&B)-n(A&C)-n(B&C)+n(A&B&C)

therefore plugging in the values above
85 = 105-n(A&B)-n(A&C)-n(B&C)
=> n(A&B)+n(A&C)+n(B&C) = 20 (ans)
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 [#permalink] New post 14 Jul 2004, 10:49
The OA is different :roll:
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 [#permalink] New post 14 Jul 2004, 12:57
50+30+20-Both+10 (2*5) =100
110-B = 100
B=10%

10%i should be the answer. what is the OA
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 [#permalink] New post 14 Jul 2004, 13:11
pakoo wrote:
50+30+20-Both+10 (2*5) =100
110-B = 100
B=10%

10%i should be the answer. what is the OA


Pakoo, What is 10(2*5) ? Please elaborate your solution a bit, if you could.

:???
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 [#permalink] New post 14 Jul 2004, 13:19
X=people liking at least 2 products
50+30+20-X-5 = 85
X=10
But you have to add 5 because those 5 like more than 2 products.
Hence answer is 10+5=15
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 [#permalink] New post 14 Jul 2004, 18:01
pakoo wrote:
50+30+20-Both+10 (2*5) =100
110-B = 100
B=10%

10%i should be the answer. what is the OA

Pakoo, you failed to take into account the 15% of people who do not like any products
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 [#permalink] New post 14 Jul 2004, 19:20
Paul wrote:
X=people liking at least 2 products
50+30+20-X-5 = 85
X=10
But you have to add 5 because those 5 like more than 2 products.
Hence answer is 10+5=15


Paul, the equation should be like:

50+30+20- 2X-5 = 85
2X = 10
X=5

now, we will add 5% (all 3) = 5+5 = 10
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 [#permalink] New post 14 Jul 2004, 19:23
hmmm, I'm missing something here. What does the 2 in "2X" stand for?
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 [#permalink] New post 14 Jul 2004, 19:37
I used venn diagrams for this and got 10%. Took me a few minutes but was foolproof.

x+y+z+a+b+c+5= 85 eq 1

x+a+c+5 = 50
y+b+c+5 = 30
z+a+b+5 = 20
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x+y+z+2(a+b+c) + 15 = 100 eq 2
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eq2 - eq1 gives

a+b+c = 5

final answer is a+b+c+5 = 10%
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 [#permalink] New post 14 Jul 2004, 23:58
Ok this is quite simple....
like probability assume all possibilities and simply add

100= 50+30+20+5+x-15

thus x=10
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 [#permalink] New post 15 Jul 2004, 20:26
ashkg


Even though it takes doign the Venn diagram, it makes more sense, when you write that Venn diagram, Brings back school days!!! :lol:
  [#permalink] 15 Jul 2004, 20:26
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