Question

If the sum of the digits of any number between $100$ and $1000$ be subtracted from that number, by what number is the result divisible?

• A. $0$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

A three digit number is represented by $100x+10y+z$

where, $x$ is the digit at the hundreds' place, $y$ at tens' place and $z$ at ones' place.
Now, $100x+10y+z-(x+y+z)=99x+9y=9(11x+y)$
$\therefore$ The result is always divisible by $3,9$.