In the figure above, triangle PQR has angle measures as

If PQ = QR, the triangle is isosceles, and we have two equal angles opposite PQ and QR. So we have two 58 degree angles (x = 58), and since the sum of the three angles in a triangle is 180, we can find the third angle y and answer the question.

In a triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. So if PR > QR, the angle opposite PR is greater than the angle opposite QR, or in other words, y > x, which is what we wanted to know.

So each Statement is sufficient and the answer is D.

Hi All,

We're told that the triangle PQR has angle measures as shown. We're asked if X is less than Y. This is a YES/NO question and is based around a specific Triangle rule (re: in simple terms, the bigger the angle, the bigger the side that's across from it). Since Angle R is 58 degrees, the sum of Angles X and Y is 122 degrees. If X and Y are EQUAL, then the sides across from them will also be EQUAL.

(1) PQ = QR

With the information in Fact 1, we know that two of the sides are EQUAL, so the angles across from them will also be EQUAL. Thus, Angle X = 58 degrees. By extension, Angle Y = 122 - 58 = 64 degrees and the answer to the question is YES.
Fact 1 is SUFFICIENT

(2) PR > QR

Fact 2 tells us that the side across from Angle Y is GREATER than the side across from Angle X, so Y is greater than X and the answer to the question is YES.
Fact 2 is SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich