Confusing set of numbers

[yourshail123]

For a certain set of numbers, if x is in the set, then (x-3) is also in the set. If the number 1 is in the set, which of the following must also be in the set?
I. 4
II. -1
III. -5

A) I only
B) II only
C) III only
D) I and II
E) II and III

#GMAT Prep Question Bank.

Correct answer choice [spoiler]C)[/spoiler] says only -5 must be in the set.
However, if we consider 1 is in the set, then 1 could be equal to either x or (x-3). Therefore, when 1=(x-3), we get x=4 and yes x is in the set.
Can someone please clarify? Am I missing something here??

[eaakbari]

For every value x in the set, x-3 is present

We are given 1 is present
Hence x-3 i.e. 1-3 = - 2 is present

If -2 is present, then x-3 = -2 -3 = -5 is present

For choices 1 & 2, 7 and 2 have to be in the set, which we aren't given.

Hence IMO C

The reason 4 cannot be an answer choice is because we do not know the upper and lower limits of the set and we cannot take a converse of the statement
The set could be
{ 1,-2,-5,-8....}
which could never contain 4.