Question

How many two-digit numbers are divisible by 6? [CBSE 2011]

Answer 1

The two-digit numbers divisible by 6 are 12, 18, 24, ..., 96.

Clearly, these number are in AP.

Here, a = 12 and d = 18 − 12 = 6

Let this AP contains n terms. Then,

$$\begin{gathered} a_n=96 \\ \Rightarrow 12+\left(n-1\right)\times 6=96\left[a_n=a+\left(n-1\right)d\right] \\ \Rightarrow 6n+6=96 \\ \Rightarrow 6n=96-6=90 \\ \Rightarrow n=15 \end{gathered}$$

Hence, there are 15 two-digit numbers divisible by 6.