If n is a prime number and n ≠ 3, which of the following could be the remainder when 100! + n is divided by 3?
I. 2
II. 1
III. -3 Select
A) II only B) III only C) I and II only D) II and III only E) I, II and III
Notice that we are told that n is a prime number and n ≠ 3. Thus, n cannot be 1.   n also cannot be 6 or any other multiple of 3, thus the remainder cannot be 0.   It can be 1 for n=2 and 2 for n=5.   Answer: I and II only.
<result>C</result>
If n is a prime number and n ≠ 3, which of the following could be the remainder when 100! + n is divided by 3?
I. 2
II. 1
III. -3