If n is the product of 3 consecutive integers, which of the following

There's a nice rule says: The product of k consecutive integers is divisible by k, k-1, k-2,...,2, and 1
So, for example, the product of any 5 consecutive integers will be divisible by 5, 4, 3, 2 and 1
NOTE: the product may be divisible by other numbers as well, but these divisors are guaranteed.

In this question, n is the product of 3 consecutive integers.
So, according to the rule, n must be divisible by 3, 2 and 1
So, we already know that statements I and II must be true.

Do we need to check statement III? No.
Notice that NONE of the answer choices include all 3 statements. Since we've already concluded that statements I and II are true, the correct answer is D.

HOWEVER, if you want to check statement III, notice that the product of 1, 2 and 3 (3 consecutive integers) is 6, and 6 is not divisible by 4