Question

For the three digit number $8\underset{–}{}1$ to be divisible by $9,$ find the possible digit(s) that can be filled in the blank.

• A. 0
• B. 3
• C. 6
• D. 9

Answer 1

Answer: (A), (D)

9

Let the digit to be filled is $x.$
$\therefore 8+x+1=9+x$

For the number $8x1$ to be divisible by $9,9+x$ should be multiple of $9.$

$9+x=9\times n$

For $n=1,$
$9+x=9\times 1$
$\Rightarrow x=0$

For $n=2,$
$9+x=9\times 2$
$\Rightarrow x=9$

For $n=3,$
$9+x=9\times 3$
$\Rightarrow x=18$

$18$ is not a single digit.

$\therefore$ The possible digits that can fill in the blank are $0$ and $9.$