Explanation

In this geometry question, as in all geometry questions on the GMAT, there is a limited set of possible geometric facts that we are expected to know and apply. We are asked for the area of the triangle, so we know the area formula is one of them. If we can get base and a height for the triangle, we'll have sufficient data to calculate the area. Let's turn to the statements, separately first.

Statement (1) has a few important pieces of information. First, it tells us that PS bisects QR. We know this because if QR=10, as the question tells us, and SR=5, then QS=5 and they are of equal measure. Moreover, since PS bisects QR, PS is perpendicular to QR, even though it's not marked as a right angle. That means that QR can be a base of the triangle and PS can be its height. If that's not clear, imagine rotating the triangle so that the line QR is at the bottom, and then it should be clear. So we have a base and a height and we know the value of both. We can calculate the area (it's 25). Statement (1) is sufficient.

Statement (2) tells us that PQ = PR. This might seem insufficient after all the numbers that the previous statement threw at us, but, in fact, since PQR is a right triangle, with this new piece of information we now know it's a 45-45-90 triangle. The ratios of lengths of such a triangle are , so We'll be able to solve for x (it's ), and that's the value of PR and PQ, which are a valid base-height pair, so we can calculate the area (again, it's 25). Statement (2) is sufficient.

The correct answer is (D).