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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 pe ##### This topic has 2 expert replies and 1 member reply ### Top Member ## A rectangle has sides x and y and diagonal z. What is the pe ## 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 ### Top Member Legendary Member Joined 02 Mar 2018 Posted: 1121 messages Followed by: 2 members Top Reply For a rectangle, 2 sides are equal, and with diagonal z, we will b having a right angled triangle. By Pythagoras, $$z^2=x^2+y^2$$ We are looking for the perimeter of the rectangle, Let the perimeter = P $$P=2\left(x+y\right)\ find\ P$$ Statement 1 $$x-y=7$$ This means that x and y can be 1 and 6, 2 and 5, 3 and 4, 0 and 7 respectively and alternatively since there is no definite conclusion, statement 1 is INSUFFICIENT. Statement 2 z = 13 ; with pythagoras theorem $$z^2=x^2+y^2$$ $$13^2=x^2+y^2$$ $$169=x^2+y^2$$ Lots of value can also satisfy the equation, hence statement 2 is INSUFFICIENT. Combining statement 1 and 2 together Statement 1 : x+y =7 y = 7 - x and z = 13 From pythagoras $$z^2=x^2+y^2$$ where y = 7- x and z = 13 $$13^2=x^2+\left(7-x\right)^2$$ $$13^2=x^2+\left(7-x\right)\left(7-x\right)$$ $$13^2=x^2+49-7x-7x+x^2$$ $$169=x^2+49-14x+x^2$$ $$169=2x^2-14x+49$$ $$2x^2-14x+49-169=0$$ $$2x^2-14x-120=0\left(Quadratic\ equation\ \right)$$ $$2x^2-24x+10x-120=0$$ $$\left(2x^2-24x\right)+\left(10x-120\right)=0$$ $$2x\left(x-12\right)+10\left(x-12\right)=0$$ $$2x+10=0\ or\ x-12=0$$ $$x=-5\ OR\ x=12$$ (x cannot be a negative integer) from x + y = 7 where x = 12 12 + y =7 y = 5, the P = 2 (x+y) = 2 (17) = 34 Both statements together are SUFFICIENT. $$Answer\ is\ Option\ C$$ ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15362 messages Followed by: 1866 members Upvotes: 13060 GMAT Score: 790 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 Always look for special triangles such as 3-4-5 and 5-12-13. Statement 2: Case 1: Case 2: Since each case will yield a different perimeter, INSUFFICIENT. Statement 1: Case 1: Case 3: Since each case will yield a different perimeter, INSUFFICIENT. Statements combined: Since only a 5-12-13 triangle has both legs with a difference of 7 and a hypotenuse of 13, only Case 1 is viable: Thus, the perimeter of the rectangle can be determined. SUFFICIENT. The correct answer is C. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 02 Jun 2008 Posted: 2475 messages Followed by: 351 members Upvotes: 1090 GMAT Score: 780 Statement 1 is not sufficient, since the sides could be anything. Statement 2 also isn't sufficient, because you'll have different perimeters when, say, the quadrilateral is a square and when it isn't. Using both statements, squaring the equation in statement 1, we learn x^2 + y^2 - 2xy = 49 and because of Pythagoras, we know from Statement 2 that x^2 + y^2 = 13^2 = 169. Plugging "169" in above for "x^2 + y^2" we learn 169 - 2xy = 49 2xy = 120 xy = 60 Since x = y +7, we can now substitute for x: (y+7)(y) = 60 If y is positive, as you make y bigger, the left side of the equation above gets bigger, so there can only be one value of y that makes (y+7)(y) exactly equal to 60, and the information is sufficient, since with the value of y we can find x and thus find the perimeter. Of course if we want to find that solution, we can either do so by inspection (we just want two numbers that differ by 7 and multiply to 60, so those numbers are 5 and 12) or we can factor the quadratic we get by expanding the left side. There's also a negative solution that we ignore since y is a length. So the answer is C. _________________ 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 • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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