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

It is currently 16 Sep 2014, 22:13

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

If N is a positive integer, is 9 a factor of N?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 24 May 2010
Posts: 85
Followers: 3

Kudos [?]: 7 [0], given: 1

GMAT ToolKit User
If N is a positive integer, is 9 a factor of N? [#permalink] New post 24 May 2010, 21:58
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

53% (02:11) correct 47% (00:38) wrong based on 61 sessions
If N is a positive integer, is 9 a factor of N?

(1) 18 is a factor of N2
(2) 27 is a factor of N3
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Nov 2013, 11:00, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29655
Followers: 3493

Kudos [?]: 26248 [1] , given: 2707

Re: Prime numbers [#permalink] New post 25 May 2010, 02:43
1
This post received
KUDOS
Expert's post
Jinglander wrote:
can someone show me how to answer this without having to find actual number

If N is a positive integer, is 9 a factor of N?

1. 18 is a factor of N^2
2. 27 is a factor of N^3


Algebraic approach:

Given n=integer>0. Q: is n=9k (where k is a positive integer)?

(1) 18 is a factor of n^2 --> n^2=18p, where p is a positive integer --> n=3\sqrt{2p} --> as n is an integer \sqrt{2p} must be an integer too, taking the even integer values --> so basically n=3\sqrt{2p} would be a multiple of 3*2=6, taking the following values: 6, 12, 18, ... So n may or may not be a multiple of 9. Not sufficient.

(2) 27 is a factor of n^3 --> n^3=27q, where q is a positive integer --> n=3\sqrt[3]{q} --> as n is an integer \sqrt[3]{q} must be an integer too --> so basically n=3\sqrt[3]{q} would be just a multiple of 3: 3, 6, 9, 12, ... So n may or may not be a multiple of 9. Not sufficient.

(1)+(2) From (1) n is a positive multiple of 6 and from (2) n is a positive multiple of 3 --> n is a positive multiple of 6, so n could be 6, 12, 18, ... Thus n may or may not be a multiple of 9. Not sufficient.

Answer: E.

Also:

!
Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/
Please post DS questions in the DS subforum: gmat-data-sufficiency-ds-141/

No posting of PS/DS questions is allowed in the main Math forum.

_________________

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

PLEASE READ AND FOLLOW: 11 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 NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 24 May 2010
Posts: 85
Followers: 3

Kudos [?]: 7 [0], given: 1

GMAT ToolKit User
Re: Prime numbers [#permalink] New post 25 May 2010, 06:11
I will post in the right place from now on. Also in part 1 why only take the even integers to realize is was a multiple of 6

Posted from my mobile device Image
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29655
Followers: 3493

Kudos [?]: 26248 [2] , given: 2707

Re: Prime numbers [#permalink] New post 25 May 2010, 06:20
2
This post received
KUDOS
Expert's post
Jinglander wrote:
I will post in the right place from now on. Also in part 1 why only take the even integers to realize is was a multiple of 6

Posted from my mobile device Image


n=3\sqrt{2p}=integer --> \sqrt{2p}=integer, which basically means that 2p is a even perfect square: 4, 16, 36, 64 --> so \sqrt{2p} can be \sqrt{4}=2, \sqrt{16}=4, \sqrt{36}=6, \sqrt{64}=8, ... even numbers --> n=3*even, so n is multiple of 6 for sure.

Hope it's clear.
_________________

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

PLEASE READ AND FOLLOW: 11 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 NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 24 May 2010
Posts: 85
Followers: 3

Kudos [?]: 7 [0], given: 1

GMAT ToolKit User
Re: Prime numbers [#permalink] New post 25 May 2010, 07:27
Thanks

Posted from my mobile device Image
Manager
Manager
avatar
Joined: 19 May 2010
Posts: 58
Followers: 1

Kudos [?]: 2 [0], given: 1

Re: Prime numbers [#permalink] New post 27 May 2010, 09:10
I feel stupid for asking, but why are prime numbers only positive? Can't negative numbers be prime numbers, i.e. -2 or -3? Is this something I just have to know and not worry too much about?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29655
Followers: 3493

Kudos [?]: 26248 [0], given: 2707

Re: Prime numbers [#permalink] New post 27 May 2010, 10:13
Expert's post
hcb wrote:
I feel stupid for asking, but why are prime numbers only positive? Can't negative numbers be prime numbers, i.e. -2 or -3? Is this something I just have to know and not worry too much about?


By definition a prime number is a positive integer that has no positive integer divisors other than 1 and itself.

So just remember it and don't worry about it.

(The main reason we have this restrictions in definition is that if we remove them there will be some problems with fundamental theorem of arithmetic (unique prime factorization theorem), so removing them would require many other adjustment).
_________________

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

PLEASE READ AND FOLLOW: 11 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 NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 19 May 2010
Posts: 58
Followers: 1

Kudos [?]: 2 [0], given: 1

Re: Prime numbers [#permalink] New post 27 May 2010, 10:15
OK - thanks Bunuel :)
SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 2406
Followers: 196

Kudos [?]: 38 [0], given: 0

Premium Member
Re: If N is a positive integer, is 9 a factor of N? [#permalink] New post 10 Apr 2014, 01:43
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: If N is a positive integer, is 9 a factor of N?   [#permalink] 10 Apr 2014, 01:43
    Similar topics Author Replies Last post
Similar
Topics:
1 N is a positive integer. Is 9 a factor of N? 1. 18 is the gmatcraze 2 25 Aug 2008, 07:42
N is a positive integer. Is 9 the factor of N ? a. 18 is the sondenso 2 26 May 2008, 03:04
Experts publish their posts in the topic N is a positive integer. Is 9 the factor of N? 1. 18 is the bmwhype2 10 18 Dec 2007, 13:57
N is a positive integer. Is 9 a factor of N? 1. 18 is the bmwhype2 2 07 Nov 2007, 09:52
Q9: If n and t are positive integers, is n a factor of t? saurya_s 12 23 Sep 2004, 06:29
Display posts from previous: Sort by

If N is a positive integer, is 9 a factor of N?

  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®.