Question

Pythagoras 高中的乐队有 $100$ 名女生和 $80$ 名男生。Pythagoras 高中的管弦乐队有 $80$ 名女生和 $100$ 名男生。有 $60$ 名女生同时属于乐队和管弦乐队。总共有 $230$ 名学生属于乐队或管弦乐队或两者都属于。属于乐队但不属于管弦乐队的男生人数是

The Pythagoras High School band has $100$ female and $80$ male members. The Pythagoras High School orchestra has $80$ female and $100$ male members. There are $60$ females who are members in both band and orchestra. Altogether, there are $230$ students who are in either band or orchestra or both. The number of males in the band who are NOT in the orchestra is

$10$

$20$

$30$

$50$

$70$

答案：A

知识点：容斥原理韦恩图

难度评级：1200

解答：

属于乐队或管弦乐队的女生人数为 $100 + 80 - 60 = 120$ 。所以属于至少一个团体的男生人数为 $230 - 120 = 110$ 。

乐队有 $80$ 名男生，管弦乐队有 $100$ 名男生，因此两个团体都有的男生人数是 $80 + 100 - 110 = 70$ 。属于乐队但不属于管弦乐队的男生有 $80 - 70 = 10$ 人。

所以正确答案是 A。

Females in band or orchestra: $100 + 80 - 60 = 120.$ So males in at least one group: $230 - 120 = 110.$

With $80$ males in band and $100$ in orchestra, the males in both are $80 + 100 - 110 = 70.$ Hence males in band but not orchestra: $80 - 70 = 10.$

Thus, the correct answer is A .

1991 AMC 8 第 23 题

答案：A

难度评级：1200

解答：

其他年份的第 23 题