Data Sufficiency

if X^4-Y^4 is odd, Which of the following are odd


I X^2-Y^2



II X^2+Y^2



III X^2-2XY+Y^2

X^4-Y^4 is odd

Possible scenarios

1. X-Odd, Y-Even
2. X-Even, Y-odd


Condition 1: X^2+Y^2

when X-Odd and Y-Even

X^2 is odd and Y^2 is even

When X-even and Y-odd

X^2 is even and Y^2 is odd

Hence X^2+Y^2 is odd

Same logic applies for X^2-Y^2 also.

Hence X^2+Y^2 is odd

Condition 3: X^2-2XY+Y^2

X^2+Y^2 is always odd and 2XY is always even

Hence X^2-2XY+Y^2 is also odd