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In the figure above, triangle PQR has angle measures as

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Source: — Data Sufficiency |

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by Ian Stewart » Sat May 04, 2019 4:14 pm

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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.
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by [email protected] » Mon May 13, 2019 11:56 am

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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

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