Question

How many two-digits numbers are divisible by 3?

Answer 1

The two-digit numbers divisible by 3 are 12, 15, 18, ..., 99.

Clearly, these number are in AP.

Here, a = 12 and d = 15 – 12 = 3

Let this AP contain n terms. Then,

a_n = 99

⇒ 12 + (n – 1) × 3 = 99   ...[a_n = a + (n – 1)d]

⇒ 3n + 9 = 99

⇒ 3n = 99 – 9 = 90

⇒ n = 30

Hence, there are 30 two-digit numbers divisible by 3.