Mo2men wrote:Is x^2 > 1/x?

(1) x^2>x

(2) 1>1/x

CRITICAL POINTS occur where an inequality is UNDEFINED and where the two sides are EQUAL.
To determine the valid range for an inequality, test one value to the left and right of each critical point.

Question stem: x² > 1/x ?
Here, the critical points are x=0 (in which case 1/x is undefined) and x=1 (in which case the two sides are equal).
If we test x=-1 (a value to the left of 0), x=1/2 (a value between 0 and 1) and x=2 (a value to the right of 1), only x=-1 and x=2 satisfy x² > 1/x.
Implication:
The valid ranges for x² > 1/x are x<0 and x>1.
Question stem, rephrased:
Is x<0 or x>1?

Statement 1: x² > x
Here, the critical points are x=0 and x=1, since each of these values makes the two sides of the inequality equal.
If we test x=-1 (a value to the left of 0), x=1/2 (a value between 0 and 1) and x=2 (a value to the right of 1), only x=-1 and x=2 satisfy x² > x.
Implication:
The valid ranges for x² > x are x<0 and x>1.
Thus, the answer to the question stem is YES.
SUFFICIENT.

Statement 2: 1 > 1/x
Here, the critical points are x=0 (in which case 1/x is undefined) and x=1 (in which case the two sides are equal).
If we test x=-1 (a value to the left of 0), x=1/2 (a value between 0 and 1) and x=2 (a value to the right of 1), only x=-1 and x=2 satisfy 1 > 1/x.
Implication:
The valid ranges for 1 > 1/x are x<0 and x>1.
Thus, the answer to the question stem is YES.
SUFFICIENT.

The correct answer is D.