AMC 8 2008 Problem 11
AMC8 2008 年第 11 题
基本计数原理★★★☆☆
Each of the 39 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 26 students have a cat. How many students have both a dog and a cat?
林肯中学八年级总共有 39 名学生，每名学生都有一条狗，或者一只猫，或者两者兼具。已知有 20 名学生有狗，有 26 名学生有猫。那么有多少名学生既有猫又有狗？
- A.7
- B.13
- C.19
- D.39
- E.46
正确答案 · Correct Answer
A
解析 · Solution
Solution 1
The number of cat owners plus the number of dog owners is 20 + 26 = 46 20+26=46. Because there are only 39 39 students in the class, there are 46 − 39 46−39 = 7 =7 students who have both. OR OR Because each student has at least a cat or a dog, there are 39 − 20 = 19 39−20=19 students with a cat but no dog, and 39 − 26 = 13 39−26=13 students with a dog but no cat. So there are 39 − 13 − 19 = 7 39−13−19=7 students with both a cat and a dog. Answer: 𝐴 A .
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