1971 AMC 12 第 16 题
先试着解答 1971 AMC 12 第 16 题，然后核对你的答案与精心整理的解答，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 1971 AMC 12 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。
16.
一名学生求出 个分数的平均数后，粗心地把这个平均数也加入原来的 个分数中，再求这 个数的平均数。第二次所得平均数与真实平均数之比为：
After finding the average of scores, a student carelessly included the average with the scores and found the average of these numbers. The ratio of the second average to the true average was:
以上都不是
None of these
小提示：
设原来的平均数为
Call the original average
大提示：
原来的总和为 ，额外加入的数也是
The original sum is , and the extra number is also
解答：
若真实平均数为 ，则原来的总和为 。再加入 本身后， 个数的总和为 ，所以新平均数仍为 。所求比为 。
因此，正确答案为 A。
If the true average is then the original sum is Including itself gives a sum of over numbers, so the new average is still The ratio is
Therefore, the correct answer is A.
其他年份的第 16 题
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