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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 ## A rectangle has sides x and y and diagonal z. What is the ##### This topic has 3 expert replies and 0 member replies ### Top Member ## A rectangle has sides x and y and diagonal z. What is the ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult A rectangle has sides x and y and diagonal z. What is the perimeter of the rectangle? (1) x - y = 7. (2) z = 13. OA C Source: Princeton Review ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2653 messages Followed by: 18 members Upvotes: 43 Top Reply BTGmoderatorDC wrote: A rectangle has sides x and y and diagonal z. What is the perimeter of the rectangle? (1) x - y = 7. (2) z = 13. We are given that a rectangle has sides x and y and diagonal z, thus: x^2 + y^2 = z^2 We need to determine the perimeter of the rectangle, which is 2x + 2y. Statement One Alone: x - y = 7 Since x - y = 7, (x - y)^2 = 7^2 or x^2 + y^2 - 2xy = 49. However, this does not allow us to determine a unique value for x or y. Statement one alone is not sufficient. Statement Two Alone: z = 13 Knowing the value of z does not allow us to determine a unique value for x or y. Statement two alone is not sufficient. Statements One and Two Together: From both statements, we have x^2 + y^2 - 2xy = 49 and z = 13. From the stem analysis, we have x^2 + y^2 = z^2. So x^2 + y^2 = 13^2 or x^2 + y^2 = 169. Substitute 169 for x^2 + y^2 in x^2 + y^2 - 2xy = 49, we have: 169 - 2xy = 49 120 = 2xy 60 = xy y = 60/x Substitute this in x - y = 7, and we have: x - 60/x = 7 Multiplying the equation by x, we have: x^2 - 60 = 7x x^2 - 7x - 60 = 0 (x - 12)(x + 5) = 0 x = 12 or x = -5 Since x canâ€™t be negative, x = 12, and, hence, y = 60/x = 5. So the perimeter of the rectangle is 2(12) + 2(5) = 34. Answer: C _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1952 messages Followed by: 30 members Upvotes: 470 Top Reply BTGmoderatorDC wrote: A rectangle has sides x and y and diagonal z. What is the perimeter of the rectangle? (1) x - y = 7. (2) z = 13. OA C Source: Princeton Review Needless to state that none of the statements alone can work; there are many possibilities when we consider that x, y, and z can be real numbers (not necessarily integers). (1) and (2) together You must remember a few Pythagorean triplets: {3, 4, 5}; {5, 12, 13}; {7, 24, 25}. We see that in the Pythagorean triplet {5, 12, 13}, the diagonal is 13, which is also the value of diagonal in the given problem. The given values of the other two sides are 5 and 12; we see that 12 and 5 differ by 7 (= x - y). Thus, x = 12, and y = 5. Thus, perimeter = 2(x + y) = 2(12 + 5) = 34. Sufficient. The correct answer: C Alternatively, you can apply a traditional approach. Since z is diagonal, we have z^2 = x^2 + y^2 ---(1) From x - y = 7, we have x = y + 7 Thus, 13^2 = (y + 7)^2 + y^2 Upon solving, we get y = 12 and x = 5. Sufficient. Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: Manhattan Review India | Manhattan Review Hyderabad | Madhapur GMAT Courses | Dilsukhnagar GRE Prep | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 BTGmoderatorDC wrote: A rectangle has sides x and y and diagonal z. What is the perimeter of the rectangle? (1) x - y = 7. (2) z = 13. Source: Princeton Review $? = 2\left( {x + y} \right)\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\boxed{\,\,? = x + y\,\,}$ $$\left( 1 \right)\,\,\,x - y = 7\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {8,1} \right)\,\,\,\,\, \Rightarrow \,\,\,? = 9\,\, \hfill \cr \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {9,2} \right)\,\,\,\,\, \Rightarrow \,\,\,? = 11\,\, \hfill \cr} \right.$$ $$\left( 2 \right)\,\,{x^2} + {y^2} = {z^2} = {13^2}\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x;y} \right) = \left( {5\,\,;\,\,12} \right)\,\,\,\,\, \Rightarrow \,\,\,? = 17\,\, \hfill \cr \,{\rm{Take}}\,\,\left( {x;y} \right) = \left( {{{13} \over {\sqrt 2 }}\,\,;\,\,{{13} \over {\sqrt 2 }}} \right)\,\,\,\,\, \Rightarrow \,\,\,? = {{2 \cdot 13} \over {\sqrt 2 }} \ne 17\, \hfill \cr} \right.$$ $$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{ \,x - y = 7 \hfill \cr \,{x^2} + {y^2} = {13^2} \hfill \cr} \right.\,\,\,\,\,\,\mathop \Rightarrow \limits^{x+y\,\, > \,\,0} \,\,\,\,\,x + y = 17\,\,\,\,\,\left[ {\,5,12,13\,\,{\rm{shortcut}}\,} \right]\,\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.\,\,$$ $${\rm{POST - MORTEM}}\,\,:\,\,\,\left\{ \matrix{ \,x - y = 7\,\,\,\mathop \Rightarrow \limits^{{\rm{squaring}}} \,\,\,{x^2} + {y^2} - 2xy = {7^2} \hfill \cr \,{x^2} + {y^2} = {13^2} \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,2xy = {13^2} - {7^2} = \left( {13 + 7} \right)\left( {13 - 7} \right)\,\,\,\,\, \Rightarrow \,\,\,\,2xy = 120\,$$ $${x^2} + {y^2} + \underline {2xy} = {13^2} + \underline {2xy} = {13^2} + 120\,\,\,\,\, \Rightarrow \,\,\,\,\,{\left( {x + y} \right)^2} = 289 = {17^2}\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{x + y\,\, > \,\,0} \,\,\,\,\,\,\,x + y = 17\,\,\,\,$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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