Remainder problem

I got C by using the numbers, but here is what tried.

Is x^2+y^2 divisible by 5?
1). When x-y is divided by 5, the remainder is 1
2). When x+y is divided by 5, the remainder is 3

Stmt 1.
X - Y = 5D + 1
square both sides
X^2 + y^2 = 25D^2 + 10D + (1 + 2XY)..............1
Now we can say that 25D^2 + 10D + (2xy+1) can be divisible by 5 if (2xy + 1) is divisible by 5. But we can not say anything abt. this. So insuff.

Stmt. 2
X + Y = 5D + 3
square both sides
X^2 + Y^2 = 25D^2 + 9 + 15D -2XY....................2
This will be divisible by 5 if (9-2XY) is divisible by 5. We can not say this so insuff.

Now combine both.......eq1 = eq2 (as both equals X^2 + y^2), but i m not able to get any useful information from this.
can someone take this approach further or else let me know in this approach itself is incorrect.