How many two-digit numbers are divisible by 6?

Question:

How many two-digit numbers are divisible by 6?

Solution:

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

Clearly, these number are in AP.

Here, = 12 and d = 18 − 12 = 6

Let this AP contains n terms. Then,

$a_{n}=96$

$\Rightarrow 12+(n-1) \times 6=96 \quad\left[a_{n}=a+(n-1) d\right]$

$\Rightarrow 6 n+6=96$

$\Rightarrow 6 n=96-6=90$

$\Rightarrow n=15$

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

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