How many three-digit numbers are divisible by 7?

1. 128

2. 124

3. 136

4. 132

The three-digit numbers divisible by 7 form an Arithmetic Progression (A.P.) :

105, 112, 119, ……,994.

a = 105

l = 994

d = 7

Let no. of terms be n.

∴ T_n = a + (n - 1)d

⇒ 994 = 105 + (n - 1)7

⇒ 994 - 105 = (n - 1)7

⇒ 889 = (n - 1)7

⇒ $\dfrac{889}{7}$ = n - 1

⇒ 127 = n - 1

⇒ n = 127 + 1

⇒ n = 128.

Hence, option 1 is the correct option.