• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
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 ## (n - 1) (n + 1) is divided by 24 ##### This topic has 1 expert reply and 4 member replies ### GMAT/MBA Expert ## (n - 1) (n + 1) is divided by 24 If n is a positive integer and r is the remainder when (n - 1) (n + 1) is divided by 24, what is the value of r? (1) n is not divisible by 2. (2) n is not divisible by 3. OA C _________________ The mind is everything. What you think you become. â€“Lord Buddha Sanjeev K Saxena Quantitative Instructor The Princeton Review - Manya Abroad Lucknow-226001 www.manyagroup.com Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. Senior | Next Rank: 100 Posts Joined 21 Feb 2009 Posted: 91 messages Upvotes: 2 Test Date: 15 April 2009 Target GMAT Score: 700+ Try picking numbers 1) n is not divisible by 2 n=3 (3-1)(3+1)=8 8:24=0+8 r=8 n=5 (5-1)(5+1)=24 24:24=1+0 r=0 Two different values of r, this means that the condition is insufficient 2) n is not divisible by 3 n=2 (2-1)(2+1)=3 3:24=0+3 r=3 n=5, as we know already r=0 Two different values, means condition is insufficient 1 and 2) n is not divisible by 2 and 3 n=5 r=0 n=7 (7-1)(7+1)=48 48:24=2 r=0 n=11 (11-1)(11+1)= 120 120:24=5 r=0 We can try other numbers and the result will yield to r=0, therefore answer is C. Legendary Member Joined 22 Jul 2008 Posted: 683 messages Followed by: 2 members Upvotes: 73 (n-1), n, (n+1) are consecutive numbers. 24 = 3*(2^3) St 1: n is odd That means (n-1) and (n+1) are even 48*50 when divided by 24 the remainder is 0 26*28 when divided by 24 the remainder is not 0 Insuff St 2: n is not divisible by 3 which means either (n-1) or (n+1) is divisible by 3, because if there are 3 consecutive numbers then one of the numbers is divisible by 3. 25*27 when divided by 24 the remainder is not 0 24*26 when divided by 24 the remainder is 0 Insuff Combining 1 and 2 We know (n-1) and (n+1) are even and one of them is divisible by 3. 36*38 when divided by 24 remainder is 0 72*74 when divided by 24 remainder is 0 Suff Answer is C. ### GMAT/MBA Expert GMAT Instructor Joined 21 Jan 2009 Posted: 3650 messages Followed by: 81 members Upvotes: 267 GMAT Score: 760 Nailya's nice; mals24's marvelous!! _________________ The mind is everything. What you think you become. â€“Lord Buddha Sanjeev K Saxena Quantitative Instructor The Princeton Review - Manya Abroad Lucknow-226001 www.manyagroup.com Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. Senior | Next Rank: 100 Posts Joined 12 Mar 2013 Posted: 44 messages Upvotes: 3 what is the remainder when 0/24 ? i thought it would be 0/24= quiotent 0 dividend 24 remainder 24 if n=1 (not a multiple of 2 or 3 ) (n-1)(n+1)=0 0/24 = 0 R 24 Master | Next Rank: 500 Posts Joined 01 May 2013 Posted: 149 messages Followed by: 9 members Upvotes: 54 J N wrote: what is the remainder when 0/24 ? i thought it would be 0/24= quiotent 0 dividend 24 remainder 24 0 is divisible by every number. So, when 0 is divided by any number, the remainder is 0. Apart from that, when an integer M is divided by some integer N, then the resulting operation will be of the form M = qN + r, where q and r are also integers and M = dividend, N = divisor, q = quotient, and r = remainder. And r < q < M. In this case, 0 = 0*24 + 0 As we are dividing 0 by 24, the resulting remainder cannot be greater than 0 - this should have been your clue that remainder cannot be 24. • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for \$0

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

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

### Top First Responders*

1 Brent@GMATPrepNow 43 first replies
2 Ian Stewart 35 first replies
3 Jay@ManhattanReview 32 first replies
4 GMATGuruNY 27 first replies
5 Scott@TargetTestPrep 13 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

189 posts
2 Max@Math Revolution

Math Revolution

90 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

75 posts
4 GMATGuruNY

The Princeton Review Teacher

44 posts
5 Ian Stewart

GMATiX Teacher

42 posts
See More Top Beat The GMAT Experts