2019 AMC 8 第 11 题

先试着解答 2019 AMC 8 第 11 题,然后核对你的答案与视频与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2019 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

11.

Lincoln 中学八年级有 9393 名学生。每名学生上数学课、外语课,或两者都上。八年级有 7070 人上数学课,有 5454 人上外语课。有多少八年级学生只上数学课而不上外语课?
The eighth grade class at Lincoln Middle School has 9393 students. Each student takes a math class or a foreign language class or both. There are 7070 eighth graders taking a math class, and there are 5454 eighth graders taking a foreign language class. How many eighth graders take only a math class and not a foreign language class?
1616
2323
3131
3939
7070
答案:D
知识点:容斥原理韦恩图
小提示:
先求有多少学生被两类人数重复计算
First find how many students are counted twice
大提示:
只上数学课的人数等于数学课总人数减去两课都上的人数
Only math = math total minus both classes
视频讲解:
解答视频缩略图
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文字解答:
两门课都上的人数为 70+54−93=31。 70 + 54 - 93 = 31\text{。} 用上数学课的人数减去这个数,就得到只上数学课的人数。
所求人数为 70−31=3970 - 31 = 39。
正确答案是 D。
The number of kids that are taking both classes is 70+54−93=31. 70 + 54 - 93 = 31. Subtracting this from the number of kids taking a math class will give us the number of kids taking only a math class.
The desired number is 70−31=39.70 - 31 = 39.
Thus, the correct answer is D.
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