How many 2 - digit numbers are divisible by 3?

To Find : 2 - digit numbers divisible by 3.

First 2 - digit number divisible by 3 is 12

Second 2 - digit number divisible by 3 is 15 and

Last 2 - digit number divisible by is 99 .

Given: The AP is $12,15,18, \ldots \ldots \ldots \ldots, 99$

$a_{1}=12, a_{2}=15, d=15-12=3$ and $a_{n}=99$

(Where $a=a_{1}$ is First term, $a_{2}$ is Second term, $a_{n}$ is nth term and $d$ is common difference of given $\mathrm{AP}$ )

Formula Used: $a_{n}=a+(n-1) d$

$99=12+(n-1) 3$

$87=(n-1) 3$

$29=(n-1)$

$n=30$

So, There are total of 30 two - digit number which is divisible by 3.