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
[spoiler]OA=B[/spoiler]
Source: Veritas Prep
In a survey on three products – A, B, and C – 50% of those surveyed liked product A, 30% liked product B, 20% liked prod
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% of those that like A = 50%
% of those that like B = 30%
% of those that like C = 20%
% of those that liked all 3 products = 5%
% of those that liked at least one of the 3 products = 85%
Total % = % of A + % of B + % of C  % of those who like 2 products  2 (% of those who like 3 products) + % of those who like neither product = total %  % of those that liked at least one product
= 100%  85% = 15%
100% = 50% + 30% + 20%  20%  2(5%) + 15%
=> 100% = 100%  10% + 15%  x %
x = 105  100 = 5%
% of those who liked more than 1 product = % of those that liked 2 product + % of those who liked all 3
= 5 + 5 = 10%
Answer = B
% of those that like B = 30%
% of those that like C = 20%
% of those that liked all 3 products = 5%
% of those that liked at least one of the 3 products = 85%
Total % = % of A + % of B + % of C  % of those who like 2 products  2 (% of those who like 3 products) + % of those who like neither product = total %  % of those that liked at least one product
= 100%  85% = 15%
100% = 50% + 30% + 20%  20%  2(5%) + 15%
=> 100% = 100%  10% + 15%  x %
x = 105  100 = 5%
% of those who liked more than 1 product = % of those that liked 2 product + % of those who liked all 3
= 5 + 5 = 10%
Answer = B
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Solution:Gmat_mission wrote: ↑Wed Jun 24, 2020 7:53 amIn 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
[spoiler]OA=B[/spoiler]
The problem really asks for the percentage of people who liked 2 or 3 products.
We can create the following equation:
Total percentage of people = percentage who like product A + percentage who like product B + percentage who like product C  (percentage who like 2 products)  2(percentage who like 3 products) + percentage who like none of the products
Let’s represent the percentage who like 2 products as D and the percentage who like none of the products as N. Then:
100 = 50 + 30 + 20  D  2(5) + N
100 = 90  D + N
We are also given that 85% of the people surveyed liked at least one of the three products. Thus, 100  85 = 15 percent of the people liked none of the three products. So we have:
100 = 90  D + 15
D = 5
Thus, 5 + 5 = 10 percent of the people like more than one product.
Answer: B
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