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).
Statement 1:
Tells us that the numbers in the set are all 2 apart. Whenever all the numbers in a set are equally spaced, then the average = the median. Sufficient.
Statement 2:
Tell us nothing about what sorts of numbers are in the set. Insufficient.
The correct answer is A.
Statement 1 in more depth:
Numbers that are equally spaced can be represented as n, n+x, n+2x, n+3x, etc.
Let's say that the numbers are n, n+x, and n+2x.
Average = (n+n+x+n+2x)/3 = (3n+3x)/3 = n+x, which is the median.
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