According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
A. 15%
B. 20%
C. 25%
D. 0%
E. 35%
To MINIMIZE the percentage who like all 3 fruits, we must MAXIMIZE the percentage who like 2 of the fruits.
Since A=70, the maximum value of BC= 30.
Since B=75, the maximum value of AC = 25.
Since C=80, the maximum value of AB= 20.
Thus:
The MAXIMUM percentage who like 2 of the fruits = 30+25+20 = 75.
Thus:
The MINIMUM percentage who like all 3 fruits = 100-75 = 25.
The correct answer is
C.
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