In a survey on three products – A, B, and C – 50% of those surveyed liked product A, 30% liked product B, 20% liked prod

[Gmat_mission]

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

[deloitte247]

% 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

[Scott@TargetTestPrep]

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]

Solution:

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