2015 AMC 8 第 13 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
13.
从集合 中可以移除多少个不同的二元素子集，使剩余九个数的平均数为 ？
How many subsets of two elements can be removed from the set so that the mean (average) of the nine remaining numbers is
小提示：
求剩余九个数必须有的总和
Find the sum the remaining nine numbers must have.
大提示：
因此被移除的两个数必须有固定的和
So the two removed numbers must have a fixed sum.
视频讲解：
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文字解答：
原集合的和为 。移除两个数后剩下 个数，平均数要为 ，所以剩余数总和必须是 。
因此被移除的两个数之和必须是 。可能的二元素子集为 、、、、，共有 种。
所以正确答案是 D。
The original set has sum After removing two numbers, numbers remain and must have mean so their sum must be
Therefore the two removed numbers must have sum The possible two-element subsets are so there are choices.
Thus, D is the correct answer.
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