2. 外语
  3. A language class has 155 students. 80 of them can speak English, 40 of them can speak Russian, and 60 of them can speak French.

A language class has 155 students. 80 of them can speak English, 40 of them can speak Russian, and 60 of them can speak French.

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问题 A language class has 155 students. 80 of them can speak English, 40 of them can speak Russian, and 60 of them can speak French. There are 50 of them can speak exactly two languages, and 10 can speak all three kind languages. What is the number of the student that can speak none of the language?
选项 A、7
B、10
C、15
D、45
E、25
答案D
解析 按照集合的理论：设集合A为speaking English，集合B为speaking Russian，集合C为speaking French，则A=80，B=40，C=60，A∩B∩C=10，Total=155，有些考生认为A∩B+A∩C+B∩C=50，这也是做错本题的原因，注意There are 50 of them can speak exactly two languages，并不包括能够说all three kind languages的10人，所以实际上A∩B+A∩C+B∩C=50+3×10。
A∪B∪C=A+B+C-(A∩B+A∩C+B∩C)+A∩B∩C
=80+40+60-(50+3×10)+10
=180-50-2×10=110
不能说任何一门语言的人=Total-A∪B∪C=155-110=45，选择D。
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