Question

How many two digits numbers are divisible by 3?

Answer 1

Two digit numbers divisible by 3 are:
12, 15, ..... , 99

$$\begin{gathered} \mathrm{Given}: \\ a=12 \\ d=15-12 \\ =3 \\ {a}_n=99 \\ \mathrm{Now}, \\ {a}_n=a+\left(n-1\right)d \\ \Rightarrow 99=12+\left(n-1\right)\left(3\right) \\ \Rightarrow 99=12+3n-3 \\ \Rightarrow 99=9+3n \\ \Rightarrow 99-9=3n \\ \Rightarrow 3n=90 \\ \Rightarrow n=30 \end{gathered}$$

Hence, 30 two digits numbers are divisible by 3.