AMC 8 1991 Problem 23
AMC8 1991 年第 23 题
基本计数原理★★★☆☆
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
Pythagoras 高中乐队有 100 名女生和 80 名男生。Pythagoras 高中管弦乐团有 80 名女生和 100 名男生。有 60 名女生同时参加乐队和管弦乐团。共有 230 名学生参加乐队或管弦乐团或两者都参加。乐队中不在管弦乐团的男生人数是
- A.10
- B.20
- C.30
- D.50
- E.70
正确答案 · Correct Answer
A
解析 · Solution
Solution 1
There are 230 students in either band or orchestra, and 80+100=180 who are in orchestra. So, 230-180=50 students are in band but not orchestra.
Of the 100 female band members, 60 are in orchestra, so 100-60=40 are not in orchestra. Therefore, of the 50 students who are in band but not orchestra, 40 are female, so 50-40=10 are male.
By the principle of inclusion-exclusion, 100+80-60=120 female students are in either band or orchestra. So 230-120=110 male students are in either band or orchestra. Of these 110 male students, 100 are in orchestra, so 10 are in band but not orchestra.
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