Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
Rephrase the question by expanding the left side of the inequality:
Is x2 – 4x + 4 > x2?
Is -4x + 4 > 0?
Is 4 > 4x?
Is 1 > x?
Statement 1: INSUFFICIENT. The values of x for which x2 > x are either negative or greater than 1. (Test numbers to prove this.) However, we do not know whether x is less than or greater than 1.
Statement 2: INSUFFICIENT. The expression 1/x is positive when x itself is positive. However, again we do not know whether x is less than or greater than 1.
Statements 1 & 2 together: SUFFICIENT. Combining the two conditions, we see that x must be greater than 1. This provides a definitive “No” answer to the given question, and thus we have sufficiency.
The correct answer is C.