2008 AMC 8 第 11 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
11.
林肯中学八年级的 名学生中，每人养一只狗、一只猫，或狗和猫都养。有二十名学生养狗， 名学生养猫。有多少名学生狗和猫都养？
Each of the students in the eighth grade at Lincoln Middle School has one dog or one cat or both a dog and a cat. Twenty students have a dog and students have a cat. How many students have both a dog and a cat?
答案：A
小提示：
把养狗人数和养猫人数相加时，同时养两种宠物的学生被数了两次
Adding dog owners and cat owners counts students with both pets twice.
大提示：
用容斥原理，总人数就是并集大小
Use inclusion-exclusion with the total number of students as the union.
解答：
同时养两种动物的人数等于养猫人数加养狗人数，再减去至少养一种动物的人数。
因此同时养两种动物的人数为
所以正确答案是 A。
The number of people that have both animals is equal to the number of people that own a cat plus the number of people that own a dog minus the number of people that own either.
Therefore, the number of people who own both is
Thus, the answer is A .
其他年份的第 11 题
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