The number of all three-digit numbers that are divisible by 7 is :

The correct answer is (B) 128.

Step-by-step arithmetic progression solution:

• Three-digit numbers range from 100 to 999.
• The smallest 3-digit number divisible by 7 is $105$ ($7$$\times$ 15).
• The largest 3-digit number divisible by 7 is $994$ ($7$$\times$ 142).
• The sequence is an AP: $105, 112, 119,$$\dots$, 994 with $a = 105, d = 7, a_n = 994$.
• $a_n = a + (n - 1)d$$\implies$ 994 = 105 + (n - 1)7 $\implies$ 889 = 7(n - 1).
• $n - 1 =$$\frac{889}{7}$ = 127 $\implies$ n = 128.
• Therefore, there are 128 three-digit numbers divisible by 7.