Bunuel
For a certain set of n numbers, where n > 1, is the average (arithmetic mean) equal to the median?
(1) If the n numbers in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2.
(2) The range of the n numbers in the set is 2(n- 1).
Question Stem Analysis:We are given a set containing more than one numbers. We need to determine whether the mean is equal to the median for this set. Recall that in an evenly spaced set, the mean is equal to the median.
Statement One Alone:\(\Rightarrow\) If the n numbers in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2.
This means that the set is an evenly spaced set. Thus, as we noted above, the mean is equal to the median for this set. Statement one alone is sufficient.
Eliminate answer choices B, C, and E.
Statement Two Alone:\(\Rightarrow\) The range of the n numbers in the set is 2(n- 1).
If our set is {1, 3}, then n = 2. Note that the range of this set is 3 - 1 = 2, which is equal to 2(n - 1) = 2(2 - 1) = 2. In this case, the mean is equal to the median.
If our set is {1, 2, 5}, then n = 3. Note that the range of this set is 5 - 1 = 4, which is equal to 2(n - 1) = 2(3 - 1) = 4. However, the mean of this set (which is 8/3) is not equal to the median (which is 2).
Since there is more than one possible answer to the question, statement two alone is not sufficient.
Answer: A