1. X^2-2y>0. if x=2 and y =1 then X>Y. However if x=-2 and y=1, X<Y, but satifies the equation 1 - and cant say x > y or not. Hence Insufficient.
2. X^3-Y^4 >0. Y^4 is always +ve. X^3 can be +ve or -ve. It has to be larger than Y^4 to satisfy the equation. So X>Y always. Sufficient.
I would take a C.
statement 2 : what about x = 0.4 y = 0.5
x^3 > y^4 but is x > y ..No
The 3 cases to be considered are negativity, (0,1) range and > 1 range
x^5 >2y^5 hence x>y.