Question

Clara 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?

$45$

$46$

$47$

$48$

$49$

答案：A

知识点：位值整除性

难度评级：1020

视频讲解：

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文字解答：

如果这个分数的后两位是 $10a+b$ ，交换后得到 $10b+a$ 。差为因此错误总和与正确总和之差必须是 $9$ 的倍数。 $\begin{aligned} &(10a+b)-(10b+a) \\ &= 9(a-b), \end{aligned}$

选项中只有 $45$ 能被 $9$ 整除。

所以正确答案是 A。

If the last two digits of the score are $10a+b$ , then reversing those digits gives $10b+a$ . The difference is $\begin{aligned} &(10a+b)-(10b+a) \\ &= 9(a-b), \end{aligned}$ so the incorrect sum must differ from the correct sum by a multiple of $9$ .

Among the answer choices, only $45$ is divisible by $9$ .

Thus, A is the correct answer.

2013 AMC 8 第 13 题

答案：A

难度评级：1020

视频讲解：

文字解答：

其他年份的第 13 题