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i need some easy way to do this question

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by sana.noor » Tue Oct 29, 2013 9:29 am
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
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by theCodeToGMAT » Tue Oct 29, 2013 9:35 am
Try to draw the lines in such a way that you minimize the overlap

Answer = 15%+10% = 25% [spoiler]{C}[/spoiler]
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by GMATGuruNY » Tue Oct 29, 2013 11:49 am
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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by outty » Thu Oct 31, 2013 8:43 am
I would like a little more clarification for this question. How do you know the maximum percentages for liking 2 types of fruit?
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by GMATGuruNY » Thu Oct 31, 2013 9:35 am
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%.
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