Question

Choose the digit(s) that can fill in the blank of a four-digit number $\underset{–}{}531$ to make it divisible by $9.$

• A. $0$
• B. $1$
• C. $6$
• D. $9$

Answer 1

The correct option is D $9$

Let the digit to be filled is $x.$
$\therefore x+5+3+1=x+9$

For the number $x531$ to be divisible by $9,9+x$ should be multiple of $9.$

$x+9=9\times n$

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

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

However, for $x=0,x531,$ i.e., $0531$ is a three digit number.

$\therefore$ The possible digit that can fill in the blank is $9.$