I'm pretty confused on the question below...
If set \(S\) consists of distinct numbers such that the difference between any two different elements of set \(S\) is an integer, how many elements does set \(S\) contain?
1 The difference between any two different elements of set \(S\) is 2.
2 The range of set \(S\) is 2.
Statement (1) by itself is sufficient. S1 says that there are only two different elements in the set.
As all elements in the set are distinct, we can conclude that set \(S\) contains 2 elements.
Statement (2) by itself is insufficient. Consider \((-1, 0, 1)\) and \((0, 2)\) .
The correct answer is A.
Am I missing something here? Where on earth does it say in S1 that there are only two elements in the set? To me, it says that the difference between ANY two elements is 2. Which means that the set could be (0,2,4,6,8,12) or just (2,4).
Can anyone please offer an explanation?