2015 AMC 8考题15

AMC 8数学竞赛专为8年级及以下的初中学生设计，但近年来的数据显示，越来越多小学4-6年级的考生加入到AMC 8级别的考试行列中，而当这些学生能在成绩中取得“A”类标签，则是对孩子数学天赋的优势证明，不管是对美高申请还是今后在数学领域的发展都极其有利！那么接下来跟随小编来看一下AMC 8的官方真题以及官方解答吧：

Problem 15

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?

Solution 1

We can see that this is a Venn Diagram Problem.[SOMEBODY DRAW IT PLEASE]

First, we analyze the information given. There are 198 students. Let's use A as the first issue and B as the second issue.

149 students were for the A, and 119 students were for B. There were also 29 students against both A and B.

Solving this without a Venn Diagram, we subtract 29 away from the total, 198. Out of the remaining 169, we have 149 people for A and

119 people for B. We add this up to get 268 . Since that is more than what we need, we subtract 169 from 268 to get （D）99.

Solution 2

There are 198 people. We know that 29 people voted against both the first issue and the second issue. That leaves us with 169 people that voted for at least one of them. If 119 people voted for both of them, then that would leave 20 people out of the vote, because 149 is less than 169 people. 169-149 is 20, so to make it even, we have to take 20 away from the 119 people, which leaves us with （D）99.

Solution 3

Divide the students into four categories:

A. Students who voted in favor of both issues.

B. Students who voted against both issues.

C. Students who voted in favor of the first issue, and against the second issue.

D. Students who voted in favor of the second issue, and against the first issue.

We are given that:

A + B + C + D = 198.

B = 29.

A + C = 149 students voted in favor of the first issue.

A + D = 119 students voted in favor of the second issue.

We can quickly find that:

198 - 119 = 79 students voted against the second issue.

198 - 149 = 49 students voted against the first issue.

B + C = 79, B + D = 49, so C = 50, D = 20, A = 99.

The answer is （D）99.

以上就是小编对AMC 8数学竞赛官方真题以及解析的介绍，希望对你有所帮助，更多学习资料请持续关注AMC数学竞赛网！