2025 AMC 8 第 6 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。
6.
Sekou 写下 、、、、。擦掉其中一个数后，剩下四个数的和是 的倍数。他擦掉了哪个数？
Sekou writes the numbers After he erases one of the numbers, the sum of the remaining four numbers is a multiple of Which number did he erase?
小提示：
比较擦掉前后的总和模 的余数
Compare the total sum modulo before and after erasing
大提示：
被擦掉的数必须与原总和有相同的模四余数
The erased number must have the same remainder as the original total
视频讲解：
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文字解答：
这五个数除以 的余数分别为 、、、、。因此五个数的总和模 与 相同，余数为 （模 ）。要擦掉一个数后使总和余 （模 ），必须擦掉一个余数为 （模 ）的数，也就是 。所以答案是 C。
The remainders of the five numbers after dividing by are: and So, the sum of all five numbers modulo is the same as which has remainder modulo Therefore, in order to erase a single number and get a sum that is modulo we must erase the number which was modulo which was Therefore, the answer is C.
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