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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## In the figure above, triangle PQR has angle measures as tagged by: AbeNeedsAnswers ##### This topic has 2 expert replies and 0 member replies ### Top Member ## In the figure above, triangle PQR has angle measures as ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult In the figure above, triangle PQR has angle measures as shown. Is x < y ? (1) PQ = QR (2) PR > QR D Source: Official Guide 2020 ### GMAT/MBA Expert GMAT Instructor Joined 02 Jun 2008 Posted: 2424 messages Followed by: 349 members Upvotes: 1090 GMAT Score: 780 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. _________________ If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10196 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 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 _________________ Contact Rich at Rich.C@empowergmat.com • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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