the pies problem

[billzhao]

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!

[Alara533]

Could you please explain how you got 5%?

I got 10 %

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%

[billzhao]

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?

[Alara533]

Yiliang, your answer and approach looks absolutely fine to me!!

[sam98034]

Wait, so what's the E:25 all about?

[billzhao]

The E: 25% is not correct.