GMAT Math

If x is positive, is x > 3 ?

(1) (x - 1)^2 > 4
(2) (x - 2)^2 > 9

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Answer is D...what is the process for answering this?

Question: Is x > 3?

Information given: x is positive.

Statement (1): (x - 1)² > 4

In order for the square of a number to be greater than 4, that number has to be greater than 2 or less than -2.

So, in order for (x - 1)² > 4, it must be the case that (x - 1) > 2 or (x - 1) < -2.

Since we are told that x is positive, there is no way in which (x - 1) < -2, because there is no positive x such that (x - 1) < -2.

So, the only way in which (x - 1)² > 4, is (x - 1) > 2.

We can add 1 to both sides of the inequality and get x > 3.

Sufficient.

Statement (2): (x - 2)² > 9

In order for the square of a number to be greater than 9, that number has to be greater than 3 or less than -3.

So, in order for (x - 2)² > 9, it must be the case that (x - 2) > 3 or (x - 2) < -3.

Since we are told that x is positive, there is no way in which (x - 2) < -3, because there is no positive x such that (x - 2) < -3.

So, the only way in which (x - 2)² > 9, is (x - 2) > 3.

We can add 2 to both sides of the inequality and get x > 5.

Sufficient.

The correct answer is D.