Question

有多少个三位数能被 $13$ 整除？

How many three-digit numbers are divisible by $13?$

$7$

$67$

$69$

$76$

$77$

要求有多少个 $k$ 使得 $13k$ 是三位数。

最小的 $k$ 满足 $13k \gt 99$ ，因此 $k = 8$ 。

最大的 $k$ 满足 $13k \lt 1000$ ，因此 $k = 76$ 。

所以 $k$ 可以从 $8$ 到 $76$ 共有 $69$ 个 $k$ 。

所以正确答案是 C。

We want to find how many $k$ exist such that $13k$ is a three-digit number.

The smallest possible $k$ such that $13k \gt 99$ is $k = 8.$

The largest possible $k$ such that $13k \lt 1000$ is $k = 76.$

This tells us that $k$ can range from $8$ to $76,$ which gives us $69$ values for $k.$

Thus, C is the correct answer.