Question

On dividing $2272$ as well as $875$ by a 3-digit number $N$, we get the same remainder in each case. The sum of the digits of $N$ is

• A. $10$
• B. $11$
• C. $12$
• D. $13$

Answer 1

The correct option is A $10$

$N_1=2272;N_2=875$
When $N_1$ and $N_2$ divide by $N$ give remainder $r$
Then $N_1-r,N_2-r$ is also divisible by $N$

$\frac{(2272-r)-(875-r)}{N}$

$\frac{1397}{N\to 11,127}$

$\therefore N=127$
Sum of digit $=1+2+7=10$