For a certain set of n numbers, where n>1, is the average (arithmetic mean) equal to the median?

(1) If the n number 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).

For any set of EVENLY SPACED NUMBERS:
Average = Median.

Statement 1:
In other words, the numbers are CONSECUTIVE EVEN or ODD integers, as in the following cases:
{0, 2, 4}
{11, 13, 15, 17}
{-7, -5, -3}
In the sets above, if any pair of successive numbers is chosen -- 0 and 2, 13 and 15, -5 and -3 -- the difference is 2.
Since the numbers are EVENLY SPACED, average = median.
SUFFICIENT.

Statement 2:
If n=3, then the range = 2(3-1) = 4.

Case 1: {0, 2, 4},
Here, the numbers are evenly spaced, so average = median,

Case 2: {0, 0, 4}
Here, the average = (0+0+4)/3 = 4/3, while the median = 0.

Since the average = median in Case 1 but not in Case 2, INSUFFICIENT.

The correct answer is A.