Concept: The question tests on the basics of Inequality in a DS format


St (1):- x + y > 0
=>Neither of them are 0 (as x y ≠ 0, and both of them cannot be negative as x + y >0)

So both are positive or one of them is a negative value.

If both are positive then is x^3 + y^3 > 0 ?- Definitive Yes

If one of them is negative it must be smaller in magnitude than the other as their sum, x+ y>0

In that case also the cube of the larger number will be greater than the cube of the smaller number and x^3 + y^3 > 0- Definitive Yes (Sufficient)

St(2):- xy > 0

Either both x and y are of same sign

If both are positive, x3+y3>0

If both are negative, x3+y3<0


(option a)