Question

数 $64$ 有一个性质：它能被自己的个位数字整除。 $10$ 到 $50$ 之间有多少个整数具有这个性质？

The number $64$ has the property that it is divisible by its unit digit. How many whole numbers between $10$ and $50$ have this property?

$15$

$16$

$17$

$18$

$20$

以 $1$ 、 $2$ 或 $5$ 结尾的数都满足条件，分别为 $11,21,31,41$ ， $12,22,32,42$ ，以及 $15,25,35,45$ 。这共有 $12$ 个数。

其余满足条件的数是 $24,33,36,44,48$ 。以 $0$ 结尾的数不行，因为除以 $0$ 没有定义。

因此共有 $12+5=17$ 个这样的数。

所以正确答案是 C。

Numbers ending in $1$ , $2$ , or $5$ all work in the ranges $11,21,31,41$ , $12,22,32,42$ , and $15,25,35,45$ . This gives $12$ numbers.

The remaining working numbers are $24,33,36,44,48$ . Numbers ending in $0$ do not work because division by $0$ is undefined.

Thus there are $12+5=17$ such numbers.

Thus, C is the correct answer.