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.