2020 AMC 8 第 20 题
先试着解答 2020 AMC 8 第 20 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 2020 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。
20.
一位科学家穿过森林时，把排成一行的 棵树的高度记录为整数。她观察到每棵树要么是右边那棵树的两倍高，要么是右边那棵树的一半高。不幸的是，雨水让笔记中的一些数据丢失了。她的笔记如下，空白表示缺失数字。根据观察，科学家能够恢复丢失数据。树的平均高度是多少米？
A scientist walking through a forest recorded as integers the heights of trees standing in a row. She observed that each tree was either twice as tall or half as tall as the one to its right. Unfortunately some of her data was lost when rain fell on her notebook. Her notes are shown below, with blanks indicating the missing numbers. Based on her observations, the scientist was able to reconstruct the lost data. What was the average height of the trees, in meters?
小提示：
整数高度迫使 的相邻树高度都是
Integer heights force the neighbors of to be
大提示：
平均数以 结尾意味着总和除以 余
The average ending in means the total ends in mod
视频讲解：
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文字解答：
第 棵树高 米。由于相邻两棵树高度相差因子 ，且高度都是整数，第 棵和第 棵都必须高 米。
前三棵树总高为 米。第 棵和第 棵的可能整数高度对为 、、。
这三种情况对应的平均数分别为 、、。笔记表明平均数以 结尾，所以只能是 。
正确答案是 B。
Tree is meters tall. Since all heights are integers and neighboring trees differ by a factor of trees and must both be meters tall.
The first three trees total meters. The possible integer pairs for trees and are and
These give averages and respectively. The notebook shows that the average ends in so it must be
Thus, the correct answer is B.
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