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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, PQRT is a rectangle. What is the length tagged by: AbeNeedsAnswers ##### This topic has 2 expert replies and 0 member replies ## In the figure above, PQRT is a rectangle. What is the length ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult In the figure above, PQRT is a rectangle. What is the length of segment PQ ? (1) The area of region PQRS is 39 and TS = 6. (2) The area of region PQRT is 30 and QR = 10. B Source: Official Guide 2020 ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12982 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 AbeNeedsAnswers wrote: In the figure above, PQRT is a rectangle. What is the length of segment PQ ? (1) The area of region PQRS is 39 and TS = 6. (2) The area of region PQRT is 30 and QR = 10. B Source: Official Guide 2020 Let's assign some variables to some of the lengths... Target question: What is the value of x? Statement 1: The area of region PQRS is 39 and TS = 6. Region PQRS is a TRAPEZOID Area of trapezoid = (height)(base1 + base2)/2 So, we get: (x)(y + z)/2 = 39 Replace z (aka TS) with 6 to get: (x)(y + 6)/2 = 39 Multiply both sides by 2 to get: (x)(y + 6) = 78 At this point, we can see that there's no way to definitively solve this equation for x (aka PQ) Statement 1 is NOT SUFFICIENT Statement 2: The area of region PQRT is 30 and QR = 10 PQRT is a rectangle, so the area = (base)(height) We can write: xy = 30 Replace y (aka QR) with 10 to get: (x)(10) = 30 Solve: x = 3 (i.e., PQ = 3 Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: B 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 told that PQRT is a rectangle. We're asked fo the length of segment PQ. This question can be solved with a mix of Geometry rules and TESTing VALUES. To start, when dealing with complex shapes, it helps to break the shape down into 'pieces': here, we're dealing with a rectangle and a right triangle. (1) The area of region PQRS is 39 and TS = 6. TS is the 'base' of the triangle, but we don't know anything about either the height/width of the triangle/rectangle or the length of the rectangle. Thus, there are lots of possible values for PQ. Here are two examples: IF.... PQ = 1, then the area of the triangle is (1/2)(6)(1) = 3 and the area of the rectangle is 39 - 3 = 36. This makes the length 36 and the answer is 1. PQ = 2, then the area of the triangle is (1/2)(6)(2) = 6 and the area of the rectangle is 39 - 6 = 33. This makes the length 16.5 and the answer is 2. Fact 1 is INSUFFICIENT (2) The area of region PQRT is 30 and QR = 10. The information in Fact 2 gives us the length of the rectangle and the area of the rectangle, so we can solve for the width: Area = (Base)(Height) 30 = (10)(Height) 3 = Height Fact 2 is SUFFICIENT Final Answer: B GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • Award-winning private GMAT tutoring Register now and save up to$200

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