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Answer the following questions based on the given information:
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 ?
17.50%
22.50%
60%
40%
30%
17.50%
22.50%
60%
40%
30%
Solution
Total number of people surveyed = 1000
Number of people who use only A = Total people who use A − (people who use A & B) − (people who use A & C) − (people who use A , B & C)
= 400 − 125 − 125 − 75 = 75
Number of people who use only B = Total people who use B − (people who use A & B) − (people who use B & C) − (people who use A , B & C)
= 400 − 125 − 100 − 75 = 100
Number of people who use either product A or product B or both is
= (people who use only A) + (people who use only B) + (people who use A & B)
= 75 + 100 + 125 = 300
percent of the people surveyed use product A or product B or both, but not product C is
= (300/1000) × 100 = 30%
