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

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Intern
Joined: 19 May 2004
Posts: 7
Location: Denver, CO
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In a consumer survey, 85% of those surveyed liked at least [#permalink]  19 May 2004, 14:10
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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

Does anyone have a good formula to use when there are more than two possible combinations of overlap?
SVP
Joined: 30 Oct 2003
Posts: 1794
Location: NewJersey USA
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Hi,

There is a formula but this problem cannot be solved using that formula.

Here is my solution.

Let products be X,Y,Z
From the stem we know that x+y+z+xy+xz+yz+xyz = 85
So x+y+z+xy+xz+yz = 85-xyz = 80 because xyz=5

X = x + xy + xz + xyz = 50 hence
x + xy + xz = 45
Similarly
y + xy + yz = 30-5 = 25
z + xz + yz = 20-5 = 15

x+y+z+xy+xz+yz = 85
= 80+xy+xz+yz = 85
Hence xy+xz+yz = 5

No of people who like more than one product
= xy+xz+yz +xyz = 5+5 = 10

Senior Manager
Joined: 02 Mar 2004
Posts: 328
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Re: Need help with PS question [#permalink]  19 May 2004, 20:12
Given |A| = 50
|B| = 30
|C| = 20
|ABC| = 5
|AUBUC| = 85

Find |AUB|+|BUC|+|AUC|-2|ABC|

|AUBUC| = |A|+|B|+|C|-|AUB|-|BUC|-|CUA|+|ABC|

Manager
Joined: 10 Mar 2004
Posts: 64
Location: Dallas,TX
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i think making a Venn Diagram for this will be simpler. I find it that way to be simpler. Answer remains the same.

cheers
Manager
Joined: 27 Feb 2004
Posts: 187
Location: illinois
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As an extension to the above problem....

How many people(or %) of people Liked ONLY 1 but NOT 2 and NOT 3...

How can we modify the formula then...

Halle How did you get 2AB...Please clarify...
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