Problem Solving

In a marketing survey for products A, B, and C, 1,000 people were asked which of the products, if any, they use. The three circular regions in the diagram above represent the numbers of people who use products A, B,
and C, according to the survey results. Of the people surveyed, a total of 400 use A, a total of 400 use B, and a total of 450 use C.

What percent of the people surveyed use product A or product B or both, but not product C?
(A) 12.5%
(B) 17.5%
(C) 30%
(D) 40%
(E) 60%


Hi,

I though the answer was D) but the correct answer is C) -- Can anyone explain?

From the given data you can find the value of A = 75, B = 100 and C = 150

They are asking for A or B or both but not C

So this means, Only A + AandB + OnlyB = 75 +125 +100 = 300

There were a 1000 people so % = 300/1000 = 30%

400 use A

Only A = 400 - (75+125+125) = 400 - 325 = 75

400 use B

Only B = 400 - (125 + 75 + 100) = 400 - 300 = 100

A+B but not C = 125 (as shown in the figure)

Hence A+B but not C = 75+100+125 = 300

300/1000 * 100 = 30%