Question

How many two-digit numbers are divisible by $4$ ?

Answer 1

Step $1$ : Identify the pattern.

Two-digit numbers divisible by $4$ are $12,16,20,\dots 96.$

This is an A.P. with $a=12$, $a_n=96$ and common difference $d=4$.

Step $2$ : Find the total number of terms in A.P.

We know that, n^th term of an A.P. is given by :

$a_n=a+(n-1)d$

$$\begin{gathered} \Rightarrow 96=12+(n-1)4 \\ \Rightarrow 84=(n-1)4 \\ \Rightarrow 21=n-1 \\ \Rightarrow n=22 \end{gathered}$$

Hence, $22$ two-digit numbers are divisible by $4$.