selango wrote: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
Please see the attached Venn diagram.
We have 100 people.
The total of the 3 circles is 85.
If we add Circle X + Circle Y + Circle Z = 50 + 30 + 20 = 100, we've double-counted everything contained in 2 circles and triple-counted everything contained in all 3 circles.
So the number contained in 2 circles has to be subtracted from the total once, the number contained in all 3 circles has to be subtracted from the total
twice.
Let B = number in 2 circles.
85 = 50 + 30 + 20 - B - (2*5)
85 = 90 - B
B = 5
So 5 are in 2 circles, 5 are in all 3 circles.
5 + 5 = 10 who liked more than 1 product.
10/100 = 10%.
The correct answer is B.
When you have groups with a double and triple overlap, remember this rule:
The number contained in 2 out of the 3 groups has to be subtracted once from the total.
The number contained in all 3 groups has to be subtracted twice from the total.
Hope this helps!
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