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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 ## If P is an odd integer and (P^2 + Q * R) is an even integer, tagged by: Gmat_mission ##### This topic has 2 expert replies and 0 member replies ## If P is an odd integer and (P^2 + Q * R) is an even integer, ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If P is an odd integer and (P^2 + Q * R) is an even integer, then which of the following must be true? A. either Q or R is an odd integer B. either Q or R is an even integer C. both Q and R are odd integers D. both Q and R are even integers E. nothing can be concluded OA=E. I need help here. I've got confused. Help, please. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15105 messages Followed by: 1859 members Upvotes: 13060 GMAT Score: 790 Gmat_mission wrote: If P is an odd integer and (P^2 + Q * R) is an even integer, then which of the following must be true? A. either Q or R is an odd integer B. either Q or R is an even integer C. both Q and R are odd integers D. both Q and R are even integers E. nothing can be concluded Let P=1. Case 1: (P² + QR) = 2 Plugging P=1 into the equation above, we get: 1² + QR = 2 QR = 1. If Q=1 and R=1, then B and D are not true. Eliminate B and D. If Q=2 and R=1/2, then A and C is not true. Eliminate A and C. The correct answer is E. _________________ 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 25 Apr 2015 Posted: 2012 messages Followed by: 15 members Upvotes: 43 Gmat_mission wrote: If P is an odd integer and (P^2 + Q * R) is an even integer, then which of the following must be true? A. either Q or R is an odd integer B. either Q or R is an even integer C. both Q and R are odd integers D. both Q and R are even integers E. nothing can be concluded Since P is odd, P^2 is also odd.In order for P^2 + Q * R to be even, Q * R must be odd, since odd + odd = even. If we knew that both Q and R were integers, then necessarily both Q and R would have to be odd. However, Q could be 2 and R could be 1/2, in which case the product Q * R = 2 x 1/2 = 1 is still an odd integer. Therefore, we cannot conclude anything about the parity of Q and R. Thus, the answer is E. Answer: E _________________ Scott Woodbury-Stewart Founder and CEO • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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