GRE数学题（详见补充）A survey of 100 persons revealed that 72 of them had eaten at restaurant P and that 52 of them had eaten at restaurant Q.Which of the following could not be the number of persons in the surveyed group who had eaten at bo

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GRE数学题（详见补充）
A survey of 100 persons revealed that 72 of them had eaten at restaurant P and that 52 of them had eaten at restaurant Q.Which of the following could not be the number of persons in the surveyed group who had eaten at both P and
A.20 B.24 C.30 D.50 E.52

72人有去过P
52人有去过Q
设X是P+Q都去过的人数
(72-X)是只去过P
(52-X)是只去过Q
列出不等式:(总人数须少於或等於100),另外X须少於等於52
X+72-X+52-X

如果时间充足，还可以慢慢推算。
A.20个人在P,Q都吃过，那么52个人只在P吃过，32个人只在Q吃过，这样20+52+32=104，但是调查的人只有100个，就不符了。
B.24个人在P,Q都吃过，那么48个人只在P吃过，28个人只在Q吃过，这样24+48+28=100，刚好在调查的数字范围内。
后面的一次类推。
所以A是不可能的。...

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如果时间充足，还可以慢慢推算。
A.20个人在P,Q都吃过，那么52个人只在P吃过，32个人只在Q吃过，这样20+52+32=104，但是调查的人只有100个，就不符了。
B.24个人在P,Q都吃过，那么48个人只在P吃过，28个人只在Q吃过，这样24+48+28=100，刚好在调查的数字范围内。
后面的一次类推。
所以A是不可能的。

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