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% OA is C

Try to draw the lines in such a way that you minimize the overlap Answer = 15%+10% = 25% [spoiler]{C}[/spoiler]

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.

I would like a little more clarification for this question. How do you know the maximum percentages for liking 2 types of fruit?

outty wrote:I would like a little more clarification for this question. How do you know the maximum percentages for liking 2 types of fruit? Let the total = 100%. Since 70% like apples, the maximum percentage who could like only bananas and cherries = 100-70 = 30%. Since 75% like bananas, the maximum percentage who could like only apples and cherries = 100-75 = 25%. Since 80% like cherries, the maximum percentage who could like only apples and bananas = 100-80 = 20%. Thus: The maximum percentage who could like exactly 2 kinds of fruit = 30+25+20 = 75%.