GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 13 Oct 2019, 21:32

### 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

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

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 24 May 2010
Posts: 73
If N is a positive integer, is 9 a factor of N?  [#permalink]

### Show Tags

Updated on: 01 Sep 2017, 09:30
11
00:00

Difficulty:

65% (hard)

Question Stats:

55% (01:43) correct 45% (01:29) wrong based on 288 sessions

### HideShow timer Statistics

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

Originally posted by Jinglander on 24 May 2010, 22:58.
Last edited by Bunuel on 01 Sep 2017, 09:30, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 58335
Re: If N is a positive integer, is 9 a factor of N?  [#permalink]

### Show Tags

25 May 2010, 03:43
5
2
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.

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.

_________________
##### General Discussion
Manager
Joined: 24 May 2010
Posts: 73
Re: If N is a positive integer, is 9 a factor of N?  [#permalink]

### Show Tags

25 May 2010, 07:11
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
Math Expert
Joined: 02 Sep 2009
Posts: 58335
Re: If N is a positive integer, is 9 a factor of N?  [#permalink]

### Show Tags

25 May 2010, 07:20
2
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

$$n=3\sqrt{2p}=integer$$ --> $$\sqrt{2p}=integer$$, 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.
_________________
Manager
Joined: 19 May 2010
Posts: 53
Re: If N is a positive integer, is 9 a factor of N?  [#permalink]

### Show Tags

27 May 2010, 10:10
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?
Math Expert
Joined: 02 Sep 2009
Posts: 58335
Re: If N is a positive integer, is 9 a factor of N?  [#permalink]

### Show Tags

27 May 2010, 11:13
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).
_________________
Current Student
Joined: 12 Aug 2015
Posts: 2574
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If N is a positive integer, is 9 a factor of N?  [#permalink]

### Show Tags

20 Aug 2016, 09:11
what on earth are N2 and N3

Regards
Stonecold
_________________
Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3584
Re: If N is a positive integer, is 9 a factor of N?  [#permalink]

### Show Tags

20 Aug 2016, 10:33
2
stonecold wrote:
what on earth are N2 and N3

Regards
Stonecold

Lol.. Try to understand the emotions

N2 and N3 means N^2 and N^3.
_________________
My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.
Current Student
Joined: 12 Aug 2015
Posts: 2574
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If N is a positive integer, is 9 a factor of N?  [#permalink]

### Show Tags

20 Aug 2016, 11:49
abhimahna wrote:
stonecold wrote:
what on earth are N2 and N3

Regards
Stonecold

Lol.. Try to understand the emotions

N2 and N3 means N^2 and N^3.

Then E is the answer i guess
Logic used => N and N^p has same prime factor.
A better way => Take N =6 and Smash that E
_________________
Intern
Joined: 28 Aug 2017
Posts: 6
Re: If N is a positive integer, is 9 a factor of N?  [#permalink]

### Show Tags

01 Sep 2017, 09:26
I really don't understand why it is writen as N2 instead of N^2
Intern
Joined: 26 Aug 2017
Posts: 6
Re: If N is a positive integer, is 9 a factor of N?  [#permalink]

### Show Tags

01 Sep 2017, 09:49
Condition of N is not clear so E will be ans

Sent from my Redmi 4A using GMAT Club Forum mobile app
SVP
Joined: 26 Mar 2013
Posts: 2341
Re: If N is a positive integer, is 9 a factor of N?  [#permalink]

### Show Tags

01 Sep 2017, 09:51
Jinglander wrote:
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

(1) 18 is a factor of N^2

Let N = 6.............. 18 factor of (6)^2................Answer is No

Let N =18.............. 18 factor of (18)^2..............Answer is Yes

Insufficient

(2) 27 is a factor of N^3

Let N = 6.............. 27 factor of (6)^3................Answer is No

Let N =18.............. 27 factor of (18)^3..............Answer is Yes

Insufficient

Combine 1 & 2

Use same examples above.....No clear answer

Non-Human User
Joined: 09 Sep 2013
Posts: 13081
Re: If N is a positive integer, is 9 a factor of N?  [#permalink]

### Show Tags

04 Feb 2019, 06:23
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.
_________________
Re: If N is a positive integer, is 9 a factor of N?   [#permalink] 04 Feb 2019, 06:23
Display posts from previous: Sort by