IMO E

(1) x^3 > 0

This tells us X is positive = X could be 0 or 1.

X^2 = X^3 ------- INSUFFICIENT

(2) x≠1

X could be 0 or -1. --------- INSUFFICIENT

Joining both Statements

X^3 > 0 and X ≠ 1

Still cant get a definite value ------ INSFUFFIENT

Joining 1 + 2

Still INSUFFICIENT

(1) \(x^3\) > 0
means that x is +ve.
If x is greater than 1 than we get no.
If x is less than 1 than we get yes; x=\(\frac{1}{2}\), \(x^2\)=\(\frac{1}{4}\) and \(x^3\)=\(\frac{1}{8}\); \(x^2\)>\(x^3\)

Insufficient.

(2) x≠1
Clearly insufficient as we do not know the polarity of x.

1+2
Statement 1 still stands
Insufficient.

Option E

Question stem asks if x^2>x^3
Let's simplify the expression

x^2 - x^3 >0
x^2(1-x)>0
For this expression to be greater than 0 we should have both the terms x^2 and 1-x positive or negative. As x^2 is always nonnegative so 1-x needs to be positive as well for the expression to be greater than 0
So 1-x>0
1>x
So basically we have to find if x<1

Statement 1:
x^3>0
This tells us that x>0
The answer will be yes for range 0<x<1 but will be no for x>1
Hence Insufficient
Statement 2
x≠1
This only tells us that x can be any value other than 1. Not sufficient

Combining 2 statements also does not give us a definite answer. The answer will be yes for range 0<x<1 but will be no for x>1

Hence the answer is E