Problem #WSP-000088

Problem

There is a secret gathering of a group of $n$ aliens in a very dark room. You cannot see anyone in the room, but you hear the following questions.

1. “Is at least one of us a Goop?"

2. “Is the number of Goops amongst us an even number?"

3. “Is the number of Goops amongst us a multiple of 3?"

4. $\dots$

5. “Is the number of Goops amongst us a multiple of $n$?"

What are all the possible values of $n$ such that this gathering can happen? Note that each of the $n$ aliens have asked exactly one question.