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

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

N/11 is an integer
N/19 is an integer
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 [#permalink] New post 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
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 [#permalink] New post 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.
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Re: divisibility n^2-n [#permalink] New post 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
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Is N^2 - N divisible by 12? N/11 is an integer N/19 is an

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