Question

The numbers 44997 and 43080, leave the same remainder when divided by x. Given that $100\le x\le 999$, how many solutions are possible for x?

• A. 1
• B. 3
• C. 2
• D. 4
• E. >4

Answer 1

The correct option is C 2

option (c)

This is based on constant remainder theorem.

Take the difference of 44997 and 43080= 1917.

Number of 3 digit factors $=2(\frac{1917}{3}=639$ and $\frac{1917}{9}=213)$