2013 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.
克拉拉计算总分时，不小心把其中一个分数的个位数字和十位数字写反了。她的错误总和与正确总和可能相差下列哪一个数？
When Clara totaled her scores, she inadvertently reversed the units digit and the tens digit of one score. By which of the following might her incorrect sum have differed from the correct one?
小提示：
交换十位和个位会使一个数改变 的倍数
Reversing tens and units changes a number by a multiple of .
大提示：
检查哪个选项能被 整除
Check which answer choice is divisible by .
视频讲解：
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文字解答：
如果这个分数的后两位是 ，交换后得到 。差为 因此错误总和与正确总和之差必须是 的倍数。
选项中只有 能被 整除。
所以正确答案是 A。
If the last two digits of the score are , then reversing those digits gives . The difference is so the incorrect sum must differ from the correct sum by a multiple of .
Among the answer choices, only is divisible by .
Thus, A is the correct answer.
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