If m and n are positive integers and r is the remained when

5*(10^n) + m

eg. of this expression will be
50 + m
500 + m
5000 + m
etc

When you divide 50 or 500 or 5000 etc by 3, the remainder will always be 2 (the remainder will be the same as that obtained when you divide the sum of the digits by the numbers by 3 i.e. Sum of digits of 5000 = 5+0+0+0 = 5. When you divide 5 by 3, the remainder is 2. When you divide 5000 by 3, the remainder will be 2 only)

So the remainder when 5*(10^n) + m is divided by is dependent on the value of m.

Statement 2 tells us that m = 1.
So when 5*(10^n) + m is divided by 3, the remainder will be 0 (Remainder when 51 or 501 or 5001 is divided by 3 will be 0).

Answer (B)