As long as one of these terms is divisible by 3 the whole mess will be divisible by 3 once it's multiplied out. Since n is an integer, anything that covers 3 consecutive integers MUST be divisible by 3. This means that these terms will work:
Of course the GMAT wouldn't make it so easy that one of these options is actually an answer, but that's OK. Since we're dealing with multiples of 3, if we add 3 or subtract 3 from any of these terms the answer will still work.
Let's say n = 7
n(n+1)(n+2) = 7(8)(9
BUT, adding or subtracting 3 to any of these terms will get the same answer
n(n+4)(n-1) = 7(11)(6
so we're looking for one of these options that's just had 3 added or subtracted from it
Right off the bat A works.
n(n+1)(n-4) = n(n+1)(n-1-3)Answer A