2024 AMC 12B 第 1 题

先试着解答 2024 AMC 12B 第 1 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 2024 AMC 12B 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。

1.

一长队人从左到右排列。从左数第 10131013 个人也是从右数第 10101010 个人。队伍中共有多少人?
In a long line of people arranged left to right, the 10131013th person from the left is also the 10101010th person from the right. How many people are in the line?
20212021
20222022
20232023
20242024
20252025
答案:B
知识点:区间内整数计数基本计数
小提示:
目标人物左边的人、右边的人,再加上这个人本身,组成整条队伍。
The people to the left of the target person and the people to the right, plus the person themself, make up the whole line
大提示:
左边有 10121012 人,右边有 10091009 人;再加上目标人物。
There are 10121012 people to the left and 10091009 to the right; add these to the target person
解答:
目标人物左边有 1013−1=10121013 - 1 = 1012 人,右边有 1010−1=10091010 - 1 = 1009 人。包括此人自己,总人数为 1012+1009+1=20221012 + 1009 + 1 = 2022。
所以正确答案是 B。
The target person has 1013−1=10121013 - 1 = 1012 people to the left and 1010−1=10091010 - 1 = 1009 people to the right. Including the person themself, the line has 1012+1009+1=20221012 + 1009 + 1 = 2022 people.
Thus, the correct answer is B.
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