Bunuel wrote:

If 0 < a < b < c, does the median of a, b, and c equal the mean of a, b, and c?

(1) The range of a, b, and c equals 2(c - b).

(2) The sum of a, b, and c is three times one of the numbers a, b, or c.

Here a, b, c are unequal positive numbers such that a < b < c. So their median is definitely 'b'. We need to know whether their mean is also equal to 'b' or not.

(1) Range of a, b, c = c - a. This is given as 2(c-b). So c - a = 2c - 2b or c = 2b - a or c + a = 2b.

Their mean = (a+b+c)/3 = (2b+b)/3 = b. So the mean is same as median. Sufficient.

(2) Sum = a+b+c. Since the numbers are unequal and sum is three times one of these, it could only be equal to three times b (since b is the middle number).

So a+b+c = 3b or a+c = 2b. Same as in first statement, so mean = b, same as median. Sufficient.

Hence

D answer