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.