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 form 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

`=>` 87 = 3n – 3

`=>` 3n = 87 + 3

`=>` 3n = 90

`=>` n = `90/3` = 30

Thus, 30 two-digit numbers are divisible by 3.