Question

A three-digit number $N$ leaves the same remainder upon dividing $68488$ and $67516$. How many possible values does $N$ have?

• A. $8$
• B. $6$
• C. $5$
• D. $4$

Answer 1

Answer: (B)

$6$

$68488$ and $67516$ on dividing with $N$ leaves same remainder.

$N$ is a three digit number.

$68488-67516=972$. On dividing by $972$, $68488$ and $67516$ leaves the same remainder.

Now, three digit factors of $972$ is $486,324,243,162,108$.

So there are six values of $N$.