How many two-digit numbers are divisible by 3

• Arithmetic Progression (C10)

How many two-digit numbers are divisible by 3?

Solution

The list of two-digit numbers divisible by 3 is:

12, 15, 18, ... , 99

It is an AP with

a = 12

d = 3

a_n = 99

a_n = a + (n – 1)d

99 = 12 + (n – 1) × 3

87 = (n – 1) × 3

n – 1 = 87/3 = 29

n = 29 + 1 = 30

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