Question

在 Euler Middle School， $198$ 名学生对学校公投中的两个议题进行了投票，结果如下： $149$ 人支持第一个议题， $119$ 人支持第二个议题。如果正好有 $29$ 名学生两个议题都反对，那么有多少名学生两个议题都支持？

At Euler Middle School, $198$ students voted on two issues in a school referendum with the following results. $149$ voted in favor of the first issue and $119$ voted in favor of the second issue. If there were exactly $29$ students who voted against both issues, how many students voted in favor of both issues?

$49$

$70$

$79$

$99$

$149$

答案：D

知识点：容斥原理

难度评级：1100

视频讲解：

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文字解答：

因为 $29$ 名学生两个议题都反对，所以 $198-29 = 169$ 名学生至少支持一个议题。

已知 $149$ 人支持第一个议题， $119$ 人支持第二个议题，且 $169$ 人至少支持一个议题。由容斥原理，两个都支持的人数为 $149+119-169 = 99.$

所以正确答案是 D。

Since $29$ students voted against both, we know that $198-29 = 169$ people voted for at least one.

As we know that $149$ students voted for the first issue, and $119$ students voted for the second issue, and $169$ students that voted for at least one issue, we conclude that the number of students that voted for both is $149+119-169 = 99.$

Thus, the correct answer is D .

2015 AMC 8 第 15 题

答案：D

难度评级：1100

视频讲解：

文字解答：

其他年份的第 15 题