# Choose the correct answer in each of the following questions:

Question:

Choose the correct answer in each of the following questions:

How many three-digit numbers are divisible by 9?

(a) 86

(b) 90

(c) 96

(d) 100

Solution:

The three-digit numbers divisible by 9 are 108, 117, 126, ..., 999.

Clearly, these numbers are in AP.

Here, = 108 and d = 117 − 108 = 9

Let this AP contains n terms. Then,

$a_{n}=999$

$\Rightarrow 108+(n-1) \times 9=999 \quad\left[a_{n}=a+(n-1) d\right]$

$\Rightarrow 9 n+99=999$

$\Rightarrow 9 n=999-99=900$

$\Rightarrow n=100$

Thus, there are 100 three-digit numbers divisible by 9.

Hence, the correct answer is option D.