swerve wrote:In a survey on three products, A, B, and C, 50% of those surveyed liked product A, 30% liked product B, 20% liked product C, and 85% liked at least one of the three products. If 5% of those surveyed like all three products, then what percentage of those surveyed liked more than one of the products?
A. 5
B. 10
C. 15
D. 20
E. 25
The OA is B
Source: Veritas Prep
So we have
Percentage of surveyors who liked the products A, B, or C = 50%; it includes two products, and three products as well
Percentage of surveyors who liked the product A = A = 50%; it may include who liked B and C as well.
Percentage of surveyors who liked the product B = B = 30%; it may include who liked A and C as well.
Percentage of surveyors who liked the product C = C = 20%; it may include who liked B and A as well.
Say,
Percentage of surveyors who liked both products A and B, but not C = AB;
Percentage of surveyors who liked both products A and C, but not B = AC;
Percentage of surveyors who liked both products B and C, but not A = BC; and
Percentage of surveyors who liked all three products A, B and C = ABC = 5%
Thus, we have
85 = A + B + C - AB - AC - BC - 2*ABC
85 = 50 + 30 + 20 - (AB + AC + BC + 2*ABC)
85 = 100 - (AB + AC + BC + 2*5)
=> AB + AC + BC = 100 - 85 - 10 = 5%
=> those surveyed liked more than one of the products = AB + AC + BC + ABC = 5% + 5% = 10%
The correct answer:
B
Hope this helps!
-Jay
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