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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 ## For integers x and y, when x is divided by y, the remainder ##### This topic has 2 expert replies and 1 member reply ### Top Member ## For integers x and y, when x is divided by y, the remainder ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult For integers x and y, when x is divided by y, the remainder is odd. Which of the following must be true? A. x is odd B. xy is odd C. x and y share no common factors other than 1 D. The sum x + y is odd E. At least one of x and y is odd OA E Source: Veritas Prep ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 BTGmoderatorDC wrote: For integers x and y, when x is divided by y, the remainder is odd. Which of the following must be true? A. x is odd B. xy is odd C. x and y share no common factors other than 1 D. The sum x + y is odd E. At least one of x and y is odd OA E Source: Veritas Prep If both x and y are even, then the remainder when x is divided by y must be even (including 0). So at least one of x and y is odd. Answer: E ### Top Member Legendary Member Joined 29 Oct 2017 Posted: 1004 messages Followed by: 4 members Let $$x=ny+r$$ ($$n=$$ some quotient, $$r=$$remainder) or $$x=ny+2k+1$$ ($$2k+1=$$odd remainder) Now if $$y$$ is even; $$x=ny+2k+1=$$even$$+$$even$$+1=$$odd and if $$y$$ is odd; $$x=$$(odd or even)$$+$$(even)$$+1$$ $$=$$(odd or even) So, at least $$1$$ of $$x$$ and $$y$$ will always be Odd. Regards! ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13033 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorDC wrote: For integers x and y, when x is divided by y, the remainder is odd. Which of the following must be true? A. x is odd B. xy is odd C. x and y share no common factors other than 1 D. The sum x + y is odd E. At least one of x and y is odd OA E Source: Veritas Prep Since, the question asks "Which of the following must be true?", we can eliminate any answer choice that is not necessarily true. So let's test some values that satisfy the given conditions For integers x and y, when x is divided by y, the remainder is odd. One possible case is that x = 9 and y = 6 (since 9 divided by 6 leaves remainder 3) Check the answer choices . . . ELIMINATE B, since xy = 54, which is EVEN ELIMINATE C, since 9 and 6 have a common factor of 3 Another possible case is that x = 6 and y = 5 (since 6 divided by 5 leaves remainder 1) Check the answer choices . . . ELIMINATE A since x is EVEN Another possible case is that x = 11 and y = 5 (since 11 divided by 5 leaves remainder 1) Check the answer choices . . . ELIMINATE D since x is x + y = 16, which is EVEN By the process of elimination, the correct answer is E Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! • FREE GMAT Exam Know how you'd score today for$0

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