Question

How many two digit numbers are divisible by 3?

Answer 1

The two digit numbers divisible by 3 are as follows:
12,15,18,21,............,99
Clearly, this forms an A.P with first term, a = 12
and common difference, d = 3
Last term = n^th term = 99
The general term of an A.P is given by
t_n = a + (n - 1)d
`=>` 99 = 12 + (n - 1)(3)
`=>` 99 = 12 + 3n - 3
`=>` 90 = 3n
`=>` n = 30
Thus, 30 two digit numbers are divisible by 3.