Is x^3>x^2?

Rewriting:

Is x^3-x^2>0?

Is x^2(x-1)>0?

This will be true if x>1 and false if x<1.

Statement 1: x>0. From the above analysis, the question will be true if x>1, such as 2, but false if 0<x<=1, such as 1/2, both of which are possible if x>0. INSUFFICIENT.

Statement 2: x^2>x, or x^2-x>0 or x(x-1)>0. This is means that either x>1 or x<0. If x>1, x^3>x^2 is true. If x<0, it is false. INSUFFICIENT.

Statements 1&2: If we know that x>0 (from statement 1), then the only way statement 2 could be true is if x>1. Thus, x is definitely greater than 1. We already demonstrated that x^3>x^2 is always true when x>1. SUFFICIENT.

vinni.k wrote:Is x^3 > X^2 ?

(1) x > 0
(2) x^2 > x

Answer is C

Why not answer is E ?

Thanks & Regards
Vinni

Is x^3 > x^2 ?

Case 1: For all x,where x<0, x^3<x^2.
If x=-1, x^3 = -1, x^2 = 1, x^3 < x^2
If x=0, x^3 = 0, x^2 = 0, x^3 = x^2

Case 2:For all x, where 0<x<1, x^3<x^2
If x=1/2, x^3 = 1/8, x^2 = 1/4, x^3 < x^2
If x=1, x^3 = 1, x^2 = 1, x^3 = x^2

Case 3: For all x, where x>1, x^3>x^2
If x =2, x^3 = 8, x^2 = 4, x^3 > x^2

So the question can be rephrased to :Is x > 1?

(1) x > 0

Insufficient, as the value of x can be less than 1(e.g. 1/2 > 0) or greater than 1(e.g. 2 > 0)

(2) x^2 > x

Insufficient, as the conditions x<0 and x>1 satisfy the equation above.

From statement 1 and 2
Intersection of x>0 AND (x<0 and x>1) is x>1 Hence sufficient

Answer C. We can explain you better if you tell us why you think you cannot answer the question using both the statements!

Pete and neelgandham, thank you very much for clearing my doubt.

Regards
Vinni