How many two digits numbers are divisible by 3?

Two digit numbers which are divisible by 3 are :

12, 15, 18, 21, 24, ……, 99.

First number = a = 12 and common difference = d = 15 - 12 = 3.

Last number = 99.

By formula, a_n = a + (n - 1)d

⇒ 99 = 12 + 3(n - 1)
⇒ 99 = 12 + 3n - 3
⇒ 99 = 9 + 3n
⇒ 99 - 9 = 3n
⇒ 3n = 90
⇒ n = 30.

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