How many three-digit numbers are divisible by 7?

(Hint: All three-digit numbers divisible by 7 form an AP. Find the smallest and largest such three-digit numbers.)

Smallest three-digit multiple of 7: $105 = 7 \times 15$

Largest three-digit multiple of 7: $994 = 7 \times 142$

These form an AP: 105, 112, 119, ..., 994.

Here, $a = 105$, $d = 7$, $l = 994$

Using $a_n = a + (n - 1)d$

$$994 = 105 + (n - 1)7$$

$$889 = 7(n - 1)$$

$$n - 1 = 127$$

$$n = 128$$

There are 128 three-digit numbers divisible by 7.