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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 even integer and q is an odd integer tagged by: Brent@GMATPrepNow ##### This topic has 3 expert replies and 0 member replies ### Top Member ## If p is an even integer and q is an odd integer If p is an even integer and q is an odd integer, which of the following must be an odd integer? A. p/q B. pq C. 2p+q D. 2(p+q) E. 3p/q Can some experts show me the easiest solution in this problem? OA C ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 1778 messages Followed by: 14 members Upvotes: 43 Top Reply lheiannie07 wrote: If p is an even integer and q is an odd integer, which of the following must be an odd integer? A. p/q B. pq C. 2p+q D. 2(p+q) E. 3p/q Letâ€™s examine our answer choices to determine which must produce an odd integer. A) p/q Since p is even and q is odd, p/q will never be an odd integer. (For example, 6/3 = 2.) B) pq Again, since p is even and q is odd, pq will never be an odd integer. (For example, 2 x 3 = 6.) C) 2p+q Since 2p is even and q is odd, 2p + q = even + odd = odd. Thus, 2p + q MUST BE an odd integer. Answer: C _________________ Scott Woodbury-Stewart Founder and CEO ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12442 messages Followed by: 1244 members Upvotes: 5254 GMAT Score: 770 Top Reply lheiannie07 wrote: If p is an even integer and q is an odd integer, which of the following must be an odd integer? A. p/q B. pq C. 2p+q D. 2(p+q) E. 3p/q Another approach is to take each answer choice and plug in an even number for p and an odd number for q, and see which answer choices yield an ODD value. The easiest numbers to test are p = 0 (which is EVEN) and q = 1 (which is ODD) We get: A. p/q = 0/1 = 0, which is EVEN. ELIMINATE A B. pq = (0)(1) = 0, which is EVEN. ELIMINATE B C. 2p+q = 2(0) + 1 = 1, which is ODD. KEEP C D. 2(p+q) = 2(0 + 1) = 2, which is EVEN. ELIMINATE D E. 3p/q = (3)(0)/1 = 0, which is EVEN. ELIMINATE E Answer: C Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our 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 Legendary Member Joined 20 Jul 2017 Posted: 503 messages Followed by: 10 members Upvotes: 86 GMAT Score: 770 To solve this problem, we need to know our even/odd number properties: even+even=even even+odd=odd odd+odd=even even*even=even even*odd=even odd*odd=odd Looking over the answer choices, we see that C is the only option that will work: 2p + q = even*even + odd = even + odd = odd. _________________ Erika John - Content Manager/Lead Instructor https://gmat.prepscholar.com/gmat/s/ Get tutoring from me or another PrepScholar GMAT expert: https://gmat.prepscholar.com/gmat/s/tutoring/ Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial Check out our PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE 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 • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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