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

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In a consumer survey, 85% of those surveyed liked at least one of thre [#permalink]  14 Jul 2004, 09:04
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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
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Re: In a consumer survey, 85% of those surveyed liked at least one of thre [#permalink]  14 Jul 2004, 10:09
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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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Re: In a consumer survey, 85% of those surveyed liked at least one of thre [#permalink]  14 Jul 2004, 10:49
The OA is different
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Re: In a consumer survey, 85% of those surveyed liked at least one of thre [#permalink]  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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Re: In a consumer survey, 85% of those surveyed liked at least one of thre [#permalink]  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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Re: In a consumer survey, 85% of those surveyed liked at least one of thre [#permalink]  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.
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Re: In a consumer survey, 85% of those surveyed liked at least one of thre [#permalink]  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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Re: In a consumer survey, 85% of those surveyed liked at least one of thre [#permalink]  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.

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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Re: In a consumer survey, 85% of those surveyed liked at least one of thre [#permalink]  14 Jul 2004, 19:23
hmmm, I'm missing something here. What does the 2 in "2X" stand for?
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Re: In a consumer survey, 85% of those surveyed liked at least one of thre [#permalink]  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
_________________________
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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Re: In a consumer survey, 85% of those surveyed liked at least one of thre [#permalink]  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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Re: In a consumer survey, 85% of those surveyed liked at least one of thre [#permalink]  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!!!
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Re: In a consumer survey, 85% of those surveyed liked at least one of thre [#permalink]  18 Jan 2015, 23:52
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Re: In a consumer survey, 85% of those surveyed liked at least one of thre [#permalink]  19 Jan 2015, 00:39
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boksana 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 one of thre   [#permalink] 19 Jan 2015, 00:39
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