AMC8 2008

AMC8 2008 · Q11

AMC8 2008 · Q11. It mainly tests Fractions, Counting & probability misc.

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?

林肯中学八年级的39名学生每人都有狗或猫或既有狗又有猫。有20名学生有狗，26名学生有猫。有多少名学生既有狗又有猫？

(A) 7 7

(B) 13 13

(D) 39 39

(E) 46 46

Answer

Correct choice: (A)

正确答案：（A）

Solution

The union of two sets is equal to the sum of each set minus their intersection. The number of students that have both a dog and a cat is $20+26-39 = \boxed{\textbf{(A)}\ 7}$.

两个集合的并集等于每个集合的大小之和减去它们的交集。既有狗又有猫的学生数量是$20+26-39=\boxed{\textbf{(A)}\ 7}$。

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