M14-18

Official Solution:


If list S contains more than one element, how many elements are in list S?

(1) The positive difference between any two elements of list S is 2.

Given that the difference between ANY two elements is 2, the list cannot contain more than two elements. Otherwise, we could find a pair of elements with a difference other than 2. To illustrate, consider a list with two elements, 1 and 3. If we add a third element, say 1, then the difference between the two 1s is 0, not 2. Similarly, if the third element is 3, the difference between the two 3s is 0, not 2. This confirms the list can't have more than two elements and since the list contains more than one element, it contains exactly two elements. Sufficient.

(2) The range of list S is 2.

This is clearly insufficient. For instance, consider \(S=\{0, 2\}\) and \(S=\{0, 0, 2\}\).


Answer: A