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

 It is currently 25 Apr 2015, 23:31

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is N^2 - N divisible by 12? N/11 is an integer N/19 is an

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
Followers: 9

Kudos [?]: 348 [0], given: 4

Is N^2 - N divisible by 12? N/11 is an integer N/19 is an [#permalink]  20 Dec 2007, 12:30
Is N^2 - N divisible by 12?

N/11 is an integer
N/19 is an integer
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 405

Kudos [?]: 2132 [0], given: 359

[#permalink]  20 Dec 2007, 12:41
Expert's post
I guess E.

two examples that satisfied 1 and 2:

1) N=11*19*12 - (N^2-N)=N*(N-1) is divided by 12
2) N=11*19 - (N^2-N)=N*(N-1)=11*19*208 is not divided by 12
CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
Followers: 9

Kudos [?]: 348 [0], given: 4

[#permalink]  21 Dec 2007, 10:44
walker wrote:
I guess E.

two examples that satisfied 1 and 2:

1) N=11*19*12 - (N^2-N)=N*(N-1) is divided by 12
2) N=11*19 - (N^2-N)=N*(N-1)=11*19*208 is not divided by 12

very nice. each case can be plugged in with 0 and the lowest multiple.

OA is E.
Director
Joined: 03 Sep 2006
Posts: 885
Followers: 6

Kudos [?]: 256 [0], given: 33

Re: divisibility n^2-n [#permalink]  21 Dec 2007, 20:37
bmwhype2 wrote:
Is N^2 - N divisible by 12?

N/11 is an integer
N/19 is an integer

Again a very good question, wonderful contribution to the Forum.

Basically, we have to check whether:

N(N-1)/12; which is possible if and only if either N/12 or (N-1)/12.

from ( i ): N/11. Thus N can be 11,22,33,... 11*10/12 ( NO), 22*21/12 (NO), 33*31/12 (NO), 44*43/12 (NO)
This tempts to conclude that from ( i ) we know that N-2-N is not divisible by 2 and we have answer from ( I ).

but there is also the case, such as: N=121, 121/11 = integer.

121*120/12 = integer. (YES)

Thus from ( i ), it may or may not be divisible by 12. Insufficient.

From ( ii ): N/19 = integer, N = 19,38, 57, 76, 95, 114. ( answer would be NO)

But when N= 133, then 133*131/12 = integer.

Thus the answer can be Yes as well No from statement ( ii ) as well.

Therefore the answer is "E".

Can someone suggest more faster and logical approach, because I used the brute force to solve this questions, which won't help in GMAT.

Suggestions please?
Re: divisibility n^2-n   [#permalink] 21 Dec 2007, 20:37
Similar topics Replies Last post
Similar
Topics:
n is positive integer, is n(n+1)(n+2) divisible by 12? 1) 1 05 May 2006, 23:47
if n is a positive integer and n^2 is divisible by 72, then 1 15 Dec 2005, 06:24
If n is a positive integer and n^2 is divisible by 72, then 1 12 Dec 2005, 22:51
If n is a positive integer and n^2 is divisible by 72, then 11 17 Nov 2005, 13:12
If n is a positive integer and n^2 is divisible by 72, then 3 07 Oct 2005, 02:51
Display posts from previous: Sort by

# Is N^2 - N divisible by 12? N/11 is an integer N/19 is an

 Question banks Downloads My Bookmarks Reviews Important topics

 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®.