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Sets : Atleast 2 or more products

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Sets : Atleast 2 or more products

by gmatrant » Tue Jun 01, 2010 3:31 am
In a recent consumer survey, 85% of those surveyed liked at least one of three products: 1, 2 and 3. 50% of those liked product 1. 30% liked 2, and 20% liked 3. if 5 % of the people in the survey liked all three products, what percentage of the survey participants liked more than one of the three products?

What is the answer. I believe OA is 10. I am not sure though
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by Patrick_GMATFix » Tue Jun 01, 2010 4:00 am
Answer: [spoiler]10%[/spoiler]
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by selango » Tue Jun 01, 2010 4:00 am
IMO 10 only

P(AUBUC)=P(A)+P(B)+P(C)-2P(Exactly 2 sets)+P(AnBnC)

85=50+30+20-2x+5

x=10
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by Patrick_GMATFix » Tue Jun 01, 2010 4:06 am
Selango,

I like your solution better!
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by jube » Sat Jun 12, 2010 6:44 am
selango wrote:IMO 10 only

P(AUBUC)=P(A)+P(B)+P(C)-2P(Exactly 2 sets)+P(AnBnC)

85=50+30+20-2x+5

x=10
hey, why have you put 2 there?

thanks.
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by kevincanspain » Sat Jun 12, 2010 10:14 am
Remember that all elements must be counted exactly once.

IF you add |A| + |B| + |C| , some elements (the ones in exactly two sets) have been counted twice (suppose that x have been counted exactly twice) and others (the ones in all three sets) have been counted three times (we are told that there are 5 of these)

85 = 50 + 30 + 20 - x - 2(5) , where x is the number counted exactly twice.

We are asked for the value of x+5

Since x=5, the answer is 10%
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