number properties

[sud21]

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

[ArunangsuSahu]

THIS IS A YES/NO Question

Rule for Remainder:

a/b gives remainder c
d/b gives remainder e

(a+d)/b will give remainder (c+e) unless (c+e) becomes a multiple of b

Same for multiplication

Statement 1:
(x-y) divided by 5 gives remainder 1
So,(x-y)^2 will also give remainder 1 when divided by 5

but No Conclusion...INSUFFICIENT

Statement 2:
(x+y) divided by 5 gives remainder 3
So,(x+y)^2 will also give remainder 3 when divided by 5

but No Conclusion...INSUFFICIENT

Combining,
(x+y)^2+(x-y)^2=2(x^2+y^2) will give remainder of (1+3)=4 when divided by 5
So,(x^2+y^2) is not divisible by 5

(C) is the choice