It is currently 13 Dec 2017, 16:46

Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1


Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If n is a positive integer, is n^2 - 1 divisible by 24?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 29 Aug 2017
Posts: 5

Kudos [?]: 0 [0], given: 3

Re: If n is a positive integer, is n^2 - 1 divisible by 24? [#permalink]

Show Tags

New post 12 Oct 2017, 20:16
I found my answer in the thread. Got it! Thanks again.

Kudos [?]: 0 [0], given: 3

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42583

Kudos [?]: 135543 [0], given: 12697

Re: If n is a positive integer, is n^2 - 1 divisible by 24? [#permalink]

Show Tags

New post 12 Oct 2017, 20:17
sepehr23 wrote:
Great :)! Thanks for the quick answer.
Consequently, the final result is that "The combined answer is sufficient to say that 'n^2 - 1' is NOT divisible by 24, right?"


Please read carefully: "We have that (n-1)(n+1) is divisible by both 3 and 8 so (n-1)(n+1) IS divisible by 3*8=24. Sufficient."
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135543 [0], given: 12697

Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1802

Kudos [?]: 981 [0], given: 5

Re: If n is a positive integer, is n^2 - 1 divisible by 24? [#permalink]

Show Tags

New post 27 Nov 2017, 18:16
kunalbh19 wrote:
If n is a positive integer, is n^2 - 1 divisible by 24?

(1) n is a prime number.
(2) n is greater than 191


We need to determine whether (n^2 - 1)/24 = integer. Notice that 24 is 2^3 x 3, or 8 x 3.

Since n^2 - 1 = (n + 1)(n - 1), when n is odd and not a multiple of 3, we will have the product of two consecutive even integers, one of which is a multiple of 3, and thus n^2 - 1 is divisible by 24. For instance, when n is 5, we have 4 x 6, which is divisible by 24.

Statement One Alone:

n is a prime number.

When n is 5, we see that 24/24 = integer; however, when n = 2, 3/24 does not equal an integer. Statement one is not sufficient to answer the question.

Statement Two Alone:

n is greater than 191.

If n = 192, then n^2 - 1 will be odd and will not be divisible by 24. If n = 199, then n^2 - 1 = (199 + 1)(199 - 1) = 200 x 198 is divisible by 24, since 200 is divisible by 8 and 198 is divisible by 3. Statement two is not sufficient to answer the question.

Statements One and Two together:

From both statements, we see that n is a prime that is greater than 191, and thus it satisfies the case that n is odd and not a multiple of 3. So, n^2 - 1 will be divisible by 24.

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 981 [0], given: 5

Re: If n is a positive integer, is n^2 - 1 divisible by 24?   [#permalink] 27 Nov 2017, 18:16

Go to page   Previous    1   2   [ 23 posts ] 

Display posts from previous: Sort by

If n is a positive integer, is n^2 - 1 divisible by 24?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.