Question

数 $N$ 是一个两位数，满足以下性质：

第一个条件是 $N$ 除以 $9$ 的余数为 $1$ ；第二个条件是 $N$ 除以 $10$ 的余数为 $3$ 。

$N$ 除以 $11$ 的余数是多少？

The number $N$ is a two-digit number with the following properties:

When $N$ is divided by $9,$ the remainder is $1.$
When $N$ is divided by $10,$ the remainder is $3.$

What is the remainder when $N$ is divided by $11?$

$0$

$2$

$4$

$5$

$7$

答案：E

知识点：模运算系统列举

难度评级：940

视频讲解：

Click to load, then click again to play

文字解答：

第二个条件说明 $N$ 的个位数字是 $3$ ，所以可能的数为 $13,23,33,43,53,63,73,83,93$ 。其中只有 $73$ 除以 $9$ 余 $1$ ，因为它的各位数字之和是 $10$ 。最后， $73=6\cdot11+7$ ，所以所求余数是 $7$ 。

所以正确答案是 E。

The second condition says that $N$ ends in $3$ , so the possibilities are $13,23,33,43,53,63,73,83,93.$ Of these, only $73$ leaves remainder $1$ when divided by $9$ , because its digit sum is $10$ . Finally, $73=6\cdot11+7$ , so the requested remainder is $7$ .

Thus, E is the correct answer.

2016 AMC 8 第 5 题

答案：E

难度评级：940

视频讲解：

文字解答：

其他年份的第 5 题