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
Que : If n is an even integer, which of the following MUST BE an integer?
This topic has expert replies
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
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]
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
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
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.
Email to : [email protected]