BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

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

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times
by Max@Math Revolution » Wed Apr 07, 2021 9:29 pm

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

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
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times

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

by Max@Math 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
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1