Is positive integer N divisible by 3? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 22 Feb 2017, 03:08

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is positive integer N divisible by 3?

Author Message
TAGS:

Hide Tags

Intern
Joined: 19 Dec 2009
Posts: 4
Followers: 0

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

Is positive integer N divisible by 3? [#permalink]

Show Tags

05 Apr 2010, 08:26
2
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

63% (01:53) correct 37% (01:10) wrong based on 160 sessions

HideShow timer Statistics

Is positive integer N divisible by 3?

(1) N^2/36 is an integer

(2) 144/N^2 is an integer
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Aug 2014, 02:10, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Manager
Joined: 26 May 2005
Posts: 208
Followers: 2

Kudos [?]: 119 [0], given: 1

Re: Is positive integer N divisible by 3? [#permalink]

Show Tags

05 Apr 2010, 10:49
1
This post was
BOOKMARKED
silver870 wrote:
I don't understand why the answer is A, and not D. Can someone please explain?

Is positive integer N divisible by 3?

1.) N^2 / 36 is an integer

2.) 144 / N^2 is an integer

st 1) N^2 / 36 is an integer
36 = 2^2 * 3^3
For N^2 to be evenly divided by 36, N should have factors at a minimum, one 2 and one 3. Sufficient
st 2) 144 / N^2 is an integer
144 = 2^4 * 3^2
N could be either 2, 4, or 3. Not sufficient

A
Manager
Joined: 04 Apr 2010
Posts: 89
Schools: UCLA Anderson
Followers: 2

Kudos [?]: 47 [0], given: 17

Re: Is positive integer N divisible by 3? [#permalink]

Show Tags

05 Apr 2010, 18:37
I agree with Chix47, with a little more detail...

S1. The prime factorization of 36 is
2^2 * 3^2
therefore to be divisible by 36, both N^2 and N must have 3 as a factor
S

S2. this statement is written differently from the first. notice that N^2 is in the denominator. Possible values for N^2 are 16, 9, 4. Therefore possible values for N are 4, 3, 2.

4/3 = not an integer
3/3 = an integer

therefore for S2 you get "sometimes yes, sometimes no" and it is insufficient.
_________________

Intern
Joined: 19 Dec 2009
Posts: 4
Followers: 0

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

Re: Is positive integer N divisible by 3? [#permalink]

Show Tags

06 Apr 2010, 09:35
Now I get it.

Thanks for info.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13910
Followers: 589

Kudos [?]: 167 [0], given: 0

Re: Is positive integer N divisible by 3? [#permalink]

Show Tags

04 Aug 2014, 20:37
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.
_________________
Manager
Joined: 03 Jun 2015
Posts: 55
Followers: 1

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

Is positive integer N divisible by 3? [#permalink]

Show Tags

13 Jan 2016, 09:44
silver870 wrote:
Is positive integer N divisible by 3?

(1) N^2/36 is an integer

(2) 144/N^2 is an integer

From (1) $$n^2/36$$= INT
Therefore the values for $$n^2$$ that fit the condition = 36, 144 and so on
n= 6, 12 (bcoz $$n$$ is positive int) and so on. Fact (1) SUFF
From (2) $$144/n^2$$= INT
Therefore $$n^2$$ could be 1, 4, 9....
and when n= 1 (No), 2 (No), 3 (Yes). Fact 2 INSUFF
Hence A
_________________

Sortem sternit fortem!

Last edited by Sash143 on 07 Feb 2017, 08:35, edited 1 time in total.
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 1926
Followers: 59

Kudos [?]: 421 [0], given: 476

Re: Is positive integer N divisible by 3? [#permalink]

Show Tags

14 Jan 2017, 22:26
A very useful property -> X and X^n always have the exact same prime factors.
For N to be divisible by 3 => 3 must be the prime factors of N.

Statement 1=>
N^2/36 is an integer.
N^2 has both 2 and 3 as it prime.
Thus N must have 3 as its prime too.
Hence Sufficient.
Statement 2=>
Lets use test Cases here.
N=1 => 144/1^2 =Integer => 1 is not divisible by 3.
N=3 => 144/N^2 =integer => 3 is divisible by 3.
Hence not sufficient.

Hence A

_________________

Give me a hell yeah ...!!!!!

Senior Manager
Joined: 26 Oct 2016
Posts: 274
Location: United States
Schools: HBS '19
GPA: 4
WE: Education (Education)
Followers: 12

Kudos [?]: 24 [0], given: 703

Re: Is positive integer N divisible by 3? [#permalink]

Show Tags

06 Feb 2017, 06:14
I did this problem with difference approach. Can some one please evaluate is my approach towards this problem correct?
Attachments

problem.jpg [ 1.41 MiB | Viewed 94 times ]

_________________

Thanks & Regards,
Anaira Mitch

Re: Is positive integer N divisible by 3?   [#permalink] 06 Feb 2017, 06:14
Similar topics Replies Last post
Similar
Topics:
If n is positive integer, is 3^n+n^(2+1) not divisible by 3? 17 19 Mar 2016, 22:09
5 If n is a positive integer, is n – 1 divisible by 3? 8 19 Jun 2015, 01:12
8 If n is a positive integer is n-1 divisible by 3 ? 6 24 Sep 2012, 22:09
If n is a positive integer, is n^3 - n divisible by 4? (1) n 2 18 Jun 2011, 21:09
5 If n is a positive integer, is n3 n divisible by 4? 1. n = 6 24 Feb 2008, 17:59
Display posts from previous: Sort by