Find all School-related info fast with the new School-Specific MBA Forum

It is currently 28 Aug 2015, 00:21
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is positive integer n 1 a multiple of 3?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 25 Jul 2010
Posts: 143
Followers: 1

Kudos [?]: 162 [0], given: 29

Is positive integer n 1 a multiple of 3? [#permalink] New post 25 Sep 2010, 10:06
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

47% (02:07) correct 53% (01:40) wrong based on 70 sessions
Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3

(2) n^3 + 2n^2 + n is a multiple of 3

[Reveal] Spoiler:
For 1, for following values of n, \(n^3 - n\) becomes multiple of 3 : 2,3,4,5,6,7,8....

However, by plugging these values in n-1, we have different results. thus, not sufficient

For 2, following values of n gets the equation as a multiple of 3 :
2,3,5,6,7,8....
Its again not sufficient.

Combining 1 & 2, we again can't be conclusive. Thus,answer should be E.

Please write where am I wrong?
[Reveal] Spoiler: OA
1 KUDOS received
Retired Moderator
User avatar
Joined: 02 Sep 2010
Posts: 805
Location: London
Followers: 87

Kudos [?]: 638 [1] , given: 25

GMAT ToolKit User Reviews Badge
Re: Positive integer n-1 multiple of 3? [#permalink] New post 25 Sep 2010, 10:15
1
This post received
KUDOS
Orange08 wrote:
Is positive integer n – 1 a multiple of 3?

(1) \(n^3 – n\) is a multiple of 3

(2) \(n^3 + 2n^2+ n\) is a multiple of 3

For 1, for following values of n, \(n^3 - n\) becomes multiple of 3 : 2,3,4,5,6,7,8....

However, by plugging these values in n-1, we have different results. thus, not sufficient

For 2, following values of n gets the equation as a multiple of 3 :
2,3,5,6,7,8....
Its again not sufficient.

Combining 1 & 2, we again can't be conclusive. Thus,answer should be E.

Please write where am I wrong?


(1) \(n^3-n = n(n^2-1) = n(n+1)(n-1)\)
This number will always be a multiple of three ... so not sufficient to answer our question

(2) \(n^3 + 2n^2+ n = n(n+1)^2\)
If this is a multiple of 3, then either n is a multiple of 3 or (n+1) is a multiple of 3. In either case, n-1 cannot be a multiple of 3.
Hence this is sufficient

Answer should be (b)

In your solution above, notice that for all the n's in case (2) n-1 is not a multiple of 3.
_________________

Math write-ups
1) Algebra-101 2) Sequences 3) Set combinatorics 4) 3-D geometry

My GMAT story

GMAT Club Premium Membership - big benefits and savings

Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29090
Followers: 4720

Kudos [?]: 49596 [2] , given: 7395

Re: Positive integer n-1 multiple of 3? [#permalink] New post 25 Sep 2010, 10:16
2
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
Orange08 wrote:
Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3

(2) \(n^3 + 2n^2+ n\) is a multiple of 3

For 1, for following values of n, \(n^3 - n\) becomes multiple of 3 : 2,3,4,5,6,7,8....

However, by plugging these values in n-1, we have different results. thus, not sufficient

For 2, following values of n gets the equation as a multiple of 3 :
2,3,5,6,7,8....
Its again not sufficient.

Combining 1 & 2, we again can't be conclusive. Thus,answer should be E.

Please write where am I wrong?


Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3 --> \(n^3-n=n(n^2-1)=(n-1)n(n+1)=3q\). Now, \(n-1\), \(n\), and \(n+1\) are 3 consecutive integers and one of them must be multiple of 3, so no wonder that their product is a multiple of 3. However we don't know which one is a multiple of 3. Not sufficient.

(2) \(n^3 + 2n^2+ n\) is a multiple of 3 --> \(n^3 + 2n^2+ n=n(n^2+2n+1)=n(n+1)^2=3p\) --> so either \(n\) or \(n+1\) is a multiple of 3, as out of 3 consecutive integers \(n-1\), \(n\), and \(n+1\) only one is a multiple of 3 then knowing that it's either \(n\) or \(n+1\) tells us that \(n-1\) IS NOT multiple of 3. Sufficient.

Answer: B.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6079
Followers: 340

Kudos [?]: 68 [0], given: 0

Premium Member
Re: Is positive integer n 1 a multiple of 3? [#permalink] New post 27 Jun 2015, 04:19
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: Is positive integer n 1 a multiple of 3?   [#permalink] 27 Jun 2015, 04:19
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic If n is a positive integer, is n – 1 divisible by 3? Bunuel 5 19 Jun 2015, 01:12
5 Experts publish their posts in the topic If n is a positive integer is n-1 divisible by 3 ? harikris 5 24 Sep 2012, 22:09
5 Experts publish their posts in the topic Is positive integer n – 1 a multiple of 3? ShreeCS 5 04 Jun 2012, 10:51
Is the positive integer n multiple of 24? 1) n is multiple Madelaine88 6 28 Feb 2011, 11:29
1 Experts publish their posts in the topic Is positive integer n 1 a multiple of 3? (1) n^3 n is a suntaurian 3 17 Feb 2008, 11:49
Display posts from previous: Sort by

Is positive integer n 1 a multiple of 3?

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.