Question

If $abc$ is a three digit number, then the number $abc–a–b–c$ is divisible by

• A. $9$
• B. $90$
• C. $10$
• D. $11$

Answer 1

The correct option is A

$9$

Find the required number:

Given: $abc$ is a three-digit number.

Thus, $abc$ can be written as : $100a+10b+c$

$$\begin{gathered} abc–a–b–c \\ =100a+10b+c-a-b-c \\ =99a+9c \end{gathered}$$

Taking $9$ common we get

$=9(11a+c)$ which is a multiple of $9$

We can see that $abc–a–b–c$ can be written as $9(11a+c)$.

Hence, $abc–a–b–c$ is divisible by $9$.

Hence, option $A$ is the correct answer.