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the pies problem

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the pies problem

by billzhao » Wed Feb 04, 2009 6:59 am
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


the answer is E:25.

i derived 5%

Can anyone help to explain?

Thanks!
Yiliang
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by Alara533 » Thu Feb 05, 2009 5:06 pm
Could you please explain how you got 5%?

I got 10 % :shock:

I used the following method. (Refer to attachment for figure)

Suppose 100 people participated in the Survey

We have the votes as
Product1 = 50, Product2 = 30 and Product3 = 20.

Also we know n = 5 (the % who liked all the three)

Now we need to find (a+b+c+n)/100.

From the figure we can get that
[50 + 30 + 20 - (a+b+c) - 2n] gives the total number of votes combined for product 1, product 2 and product 3, which is = 85
50 + 30 + 20 - (a+b+c) - 2n = 85
Solving it further we have
a + b + c + 2n = 15
a + b + c = 5

Which means, (a+b+c+n)/100 = 10%
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by billzhao » Thu Feb 05, 2009 11:47 pm
Alara533, your answer is correct.
using your figure:

The question asks us to find a+b+c+5% = ?
we have A+a+c+5%=50% -------(1)
B+b+a+5%=30%------------------(2)
C+c+b+5%=20%------------------(3)

(1)+(2)+(3) -> A+B+C+2(a+b+c)+25%=100%-----------(4)
Because A+B+C+(a+b+c)+5%=85%--------------(5)

(4)-(5) -> a+b+c=5%

So a+b+c+5%=10%, answer is (B)

What do you think of my approach?
Yiliang
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by Alara533 » Thu Feb 05, 2009 11:53 pm
Yiliang, your answer and approach looks absolutely fine to me!! :D
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by sam98034 » Fri Feb 06, 2009 1:46 am
Wait, so what's the E:25 all about?
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by billzhao » Fri Feb 06, 2009 3:22 am
The E: 25% is not correct.
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