Question

How many two digits numbers are divisible by 3?

Answer 1

The first two-digit number that is divisible by 3 is 12
So, the series starts from 12
And the highest two-digit number that is divisible by 3 is 99
So, the sequence becomes:
12, 15, ..., 99.

We, need to find the numbers in the given sequence
Using a_n = `"a" + (n-1)d`
a is the first term, d is the common difference, n is the number of terms and a_n  is the nth term 
a = 12, d = 3, a_n= 99 substituting the values we get

`99 = 12 + (n - 1)3`
`99 = 12 + 3n - 3`
`90 = 3n`

`n =90/3` 

`n = 30`.
Therefore, there are total 30 two digit numbers that are divisible by 3.