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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 ## Which of the following MUST yield an integer when . . . . tagged by: Vincen ##### This topic has 1 expert reply and 0 member replies ### Top Member ## Which of the following MUST yield an integer when . . . . Which of the following MUST yield an integer when divided by 5? A. The sum of five consecutive positive integers. B. The square of a prime number. C. The sum of two odd integers. D. The product of three consecutive odd numbers. E. The difference between a multiple of 8 and a multiple of 3. The OA is the option A. How can I show that the correct answer is option A? Experts, could you give me some help, please? ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Top Reply Hello Vincen. Let's take a look at your question. The sum of five consecutive positive integers is: n + (n+1) + (n+2) + (n+3) + (n+4) = 5n + 10 = 5(n+2). So, it is multiple of 5. Therefore, it MUST yield an integer when divided by 5. Hence, there is no need to try the rest of the options. The correct answer is A. I hope this explanation may help you. Regards. ------------------------------------------------------------------------------------------------------------------------------------------------------ If you want we can prove that the rest of the options are incorrect. Option 2: The square of a prime number is not always divisible by 5. We can choose 3, then 3^2=9. Option 3: The sum of two odd integers is not always divisible by 5. We can choose 3 and 5, then 3+5=8. Option 4: The product of three consecutive odd numbers is not always divisible by 5. We can choose 17, 19 and 21. Option 5: The difference between a multiple of 8 and a multiple of 3 is not always divisible by 5. We can choose 24-3=21. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • 5 Day FREE Trial Study Smarter, Not Harder 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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