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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 GMATPrep Question 28 This topic has 1 expert reply and 2 member replies If m and n are integers, Is m odd? 1. n+m is odd. 2. n+m=n^2+5 Please help me on the above question, as i am not able to get the logic behind this!! Senior | Next Rank: 100 Posts Joined 11 Mar 2008 Posted: 50 messages Upvotes: 6 You can solve this by picking some numbers. Choice 1: n + m is odd Sum of two integers is odd only if one of the numbers is odd and the other is even. So you can see that is the case n is even m has to be odd and in the case where n is odd m has to be even. So 1 is not sufficient to answer if m is odd. You can just pick numbers: pick an odd value for n (say 3) and then m has to be even(say 4) to make the sum odd (7) Similarly you can interchange values and see that if n is even (4) then m has to be odd (3) to make the sum odd (7) Choice 2: n + m = n^2 + 5 Pick an odd value for n in one example and an even value in the other. See what happens to m. Let's say n is 4(even) then 4 + m = 16 + 5, m = 17 (odd) Now pick a odd value for n (say 5) then 5 + m = 25 + 5, m = 25 (odd) So 2 is sufficient condition to say that m is odd. The answer is B GMAT/MBA Expert GMAT Instructor Joined 08 Jan 2008 Posted: 3225 messages Followed by: 611 members Upvotes: 1710 GMAT Score: 800 gurudev wrote: If m and n are integers, Is m odd? 1. n+m is odd. 2. n+m=n^2+5 Please help me on the above question, as i am not able to get the logic behind this!! (1) we know that to get an odd sum, one is odd and one is even, but we have no clue which is which: insufficient. (2) More complicated, pick numbers! if n = 2, then we get: 2 + m = 4 + 5 m = 7. So "yes", m is odd. if n = 3, then we get: 3 + m = 9 + 5 m = 11. So "yes", m is odd. So, regardless of whether n is even or odd, m is always odd. (2) is sufficient alone, choose (B). Using number properties instead of picking numbers: n+m=n^2+5 m = n^2 - n + 5 m = n(n-1) + 5 well, since n is an integer, n and (n-1) are consecutive integers, which means one term is even and the other is odd. Therefore, regardless of the value of n, the product of n and (n-1) will always be even (since even*odd=even). So: m = even - 5 Since (even - odd) is always odd, m MUST be odd: sufficient. _________________ Stuart Kovinsky | Kaplan GMAT Faculty | Toronto Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount Free GMAT Practice Test under Proctored Conditions! - Find a practice test near you or live and online in Kaplan's Classroom Anywhere environment. Register today! Junior | Next Rank: 30 Posts Joined 20 Jul 2008 Posted: 29 messages Upvotes: 1 Yeah Got it now!!!! Thanks a ton.. • 5 Day FREE Trial Study Smarter, Not Harder 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 • 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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