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!
the pies problem
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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%
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%
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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?
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