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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 ## Is quadrilateral PQRS a parallelogram? tagged by: AbeNeedsAnswers ##### This topic has 3 expert replies and 0 member replies ## Is quadrilateral PQRS a parallelogram? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Is quadrilateral PQRS a parallelogram? (1) Adjacent sides PQ and QR have the same length. (2) Adjacent sides RS and SP have the same length. E Source: Official Guide 2020 ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1979 messages Followed by: 30 members Upvotes: 470 AbeNeedsAnswers wrote: Is quadrilateral PQRS a parallelogram? (1) Adjacent sides PQ and QR have the same length. (2) Adjacent sides RS and SP have the same length. E Source: Official Guide 2020 For the quadrilateral PQRS to be a parallelogram, the opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. Let's take each statement one by one. (1) Adjacent sides PQ and QR have the same length. The opposite sides may or may not be equal. Insufficient. (2) Adjacent sides RS and SP have the same length. The opposite sides may or may not be equal. Insufficient. (1) and (2) together Still, the opposite sides may or may not be equal. Insufficient. The correct answer: E Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: GRE Manhattan | ACT Tutoring San Antonio | GRE Prep Courses Boston | Houston IELTS Tutoring | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12985 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 AbeNeedsAnswers wrote: Is quadrilateral PQRS a parallelogram? (1) Adjacent sides PQ and QR have the same length. (2) Adjacent sides RS and SP have the same length. E Source: Official Guide 2020 Target question: Is quadrilateral PQRS a parallelogram? If you recognize that each statement on its own is not sufficient, we can jump straight to . . . Statements 1 and 2 combined There are infinitely-many quadrilaterals that satisfy BOTH statements. Here are two: Case a: PQRS could be a square. Since a square is a type of parallelogram, the answer to the target question is YES, quadrilateral PQRS IS a parallelogram Case b: PQRS could be kite-shaped. In this case, the answer to the target question is NO, quadrilateral PQRS is NOT a parallelogram Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT Answer: E Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 496 members Upvotes: 2867 GMAT Score: 800 Hi All, We're asked if quadrilateral PQRS is a parallelogram? This is a YES/NO question can be answered with a bit of logic (and a couple of drawings). By definition, a parallelogram must have 4 sides and each pair of 'opposite' sides must be parallel. 1) Adjacent sides PQ and QR have the same length. 'Adjacent' sides refer to two sides that are next to one another (and meet at a point): -A Square fits this description - and is a parallelogram, so the answer to the question is YES. -Any other 4-sided shape with 2 equal sides that touch and 2 others sides that are NOT the same length as the first 2 - that's NOT a parallelogram, so the answer to the question is NO. Brent's explanation provides a nice example of the second shape. Fact 1 is INSUFFICIENT 2) Adjacent sides RS and SP have the same length. Fact 2 essentially provides the same information that Fact 1 provides (but about the other 2 sides). The examples that fit Fact 1 also fit Fact 2 - and lead us to two different answers (one "YES" and one "NO"). Fact 2 is INSUFFICIENT Combined, we know... 1) Adjacent sides PQ and QR have the same length. 2) Adjacent sides RS and SP have the same length. Even with both Facts, we can end up with shapes that are parallelograms or not, so the answer to the question is inconsistent. Combined, INSUFFICIENT Final Answer: E GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • FREE GMAT Exam Know how you'd score today for$0

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