Question

How many numbers of two digit numbers are divisible by $6$?

Answer 1

The least $3$ digit no. is $100$

The least $3$ digit no divisible by $6$: $6\times 12=102$

The least $4$ digit no is $1000$

The largest $3$ digit no. divisible by $6$: $6\times 166=996$

Using identity $l=a+(n-1)d$ , where $l$ is the last term, $a$ is the first term, $n$ is total no of terms and $d$ is the common difference

Putting, $l=996$, $a=102$ and $d=6$

$996=102+(n-1)6$

$996=102+6n-6$

$996=96+6n$

$6n=900$

$n=150$

so, there are $150$, $3$ digits numbers which are divisible by $6$