How many two - digit numbers are divisible by 3?

The two digit numbers divisible by 3 are 12, 15, 18, 21, …., 99.

This forms an AP with first term a = 12

and common difference = d = 3

Last term is 99.

Now, number of terms in this AP are given as:

99 = a + (n - 1)d

⇒ 99 = 12 + (n - 1)3

⇒ 99 - 12 = 3n - 3

⇒ 87 + 3 = 3n

⇒ 90 = 3n

⇒ n = 30

There are 30 two - digit numbers that are divisible by 3.