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

##### This topic has expert replies
Elite Legendary Member
Posts: 3906
Joined: 24 Jul 2015
Location: Las Vegas, USA
Thanked: 19 times
Followed by:36 members

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

by [email protected] Revolution » Thu May 13, 2021 9:32 pm

00:00

A

B

C

D

E

## Global Stats

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

I. $$\frac{n^2-1}{2}$$

II. $$\frac{n-1}{2}$$

III. $$\frac{n}{2}$$

A. I only
B. II only
C. III only
D. I & II only
E. I, II, & III 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. Email to : [email protected] Elite Legendary Member Posts: 3906 Joined: 24 Jul 2015 Location: Las Vegas, USA Thanked: 19 times Followed by:36 members ### Re: Que: If n is an odd integer, which of the following MUST BE an integer? by [email protected] Revolution » Sat May 15, 2021 9:27 pm 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 odd integer, Always an integer => n = odd = 2m+1 (m is always an integer) I. $$\frac{n^2-1}{2}=\frac{\left[\left(2m+1\right)^2-1\right]}{2}=\frac{\left[4m^2+4m+1-1\right]}{2}=2m^2+m$$ => AN INTEGER ∴ Option is TRUE II. $$\frac{n-1}{2}=\frac{\left[\left(2m+1\right)-1\right]}{2}=m$$ => AN INTEGER ∴ Option is TRUE III. $$\frac{n}{2}=\frac{\left(2m+1\right)}{2}=m+0.5$$ => NOT AN INTEGER ∴ Option is NOT TRUE Only options I and II are TRUE. Therefore, D is the correct answer. Answer D 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.
Email to : [email protected]

• Page 1 of 1