Is N^2 - N divisible by 12? N/11 is an integer N/19 is an : Quant Question Archive [LOCKED]
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 20 Jan 2017, 08:16

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

Author Message
CEO
Joined: 21 Jan 2007
Posts: 2756
Location: New York City
Followers: 11

Kudos [?]: 854 [0], given: 4

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

### Show Tags

20 Dec 2007, 12:30
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Is N^2 - N divisible by 12?

N/11 is an integer
N/19 is an integer
CEO
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 548

Kudos [?]: 3559 [0], given: 360

### Show Tags

20 Dec 2007, 12:41
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: 2756
Location: New York City
Followers: 11

Kudos [?]: 854 [0], given: 4

### Show Tags

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: 879
Followers: 6

Kudos [?]: 772 [0], given: 33

### Show Tags

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.

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

Re: divisibility n^2-n   [#permalink] 21 Dec 2007, 20:37
Display posts from previous: Sort by