## Que : If n is an even integer, which of the following MUST BE an integer?

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### Que : If n is an even integer, which of the following MUST BE an integer?

by [email protected] Revolution » Wed Apr 07, 2021 9:29 pm

00:00

A

B

C

D

E

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Que : If n is an even integer, which of the following MUST BE an integer?

I. $$\frac{\left(n^2-1\right)}{2}$$ II. $$\frac{\left(n-1\right)}{2}$$ III. $$\frac{n}{2}$$

A. I only
B. II only
C. III only
D. I & III only
E. I, II, & III Math Revolution

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[Course] Starting $79 for on-demand and$60 for tutoring per hour and $390 only for Live Online. Email to : [email protected] Elite Legendary Member Posts: 3834 Joined: 24 Jul 2015 Location: Las Vegas, USA Thanked: 19 times Followed by:36 members ### Re: Que : If n is an even integer, which of the following MUST BE an integer? by [email protected] Revolution » Tue Apr 13, 2021 12:18 am Solution: Multi-Choice questions: ‘Must be’ VS ‘Could be’ We have to find the options that must be true ‘MUST BE’: Choose only the options that are absolutely true in ALL cases => ‘n’ is an even integer, Always an integer => n=even=2m (m is always an integer) Option I: $$\frac{n^2-1}{2}=\frac{\left(\left(2m\right)^2-1\right)}{2}=\frac{\left(4m^2-1\right)}{2}=2m^2-0.5$$ => NOT AN INTEGER ∴ Option is not TRUE Option II: $$\frac{n-1}{2}=\frac{2m-1}{2}=m-0.5$$ => NOT AN INTEGER ∴ Option is not TRUE Option III: $$\frac{n}{2}=\frac{2m}{2}=m$$ => INTEGER ∴ Option is always TRUE Only option III is TRUE. Therefore, C is the correct answer. Answer C Math Revolution The World's Most "Complete" GMAT Math Course! Score an excellent Q49-51 just like 70% of our students. [Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions. [Course] Starting$79 for on-demand and $60 for tutoring per hour and$390 only for Live Online.
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