A range of a set of numbers is always positive - it's the positive difference between the largest and smallest terms. In this question, we want to compare the range to the mean.

In both of these statements, we're told that the set contains negative numbers. From statement (1), we know that there are no positive numbers in the set, and therefore the mean cannot be positive. Since the range will always be positive, we know that the range is larger than the mean. From statement (2), we're told that the median is negative. This doesn't necessarily imply that the mean is negative (we could have the set [-3, -1, 100] for example), but any negative numbers in the set will pull the mean down. Since the range would be the positive distance between the largest and the smallest number in the set, and the smallest number will have to be negative, the range will be greater than the mean.

srcc25anu wrote:Can Range = ZERO? what if for the first condition: Set S = {0,0,0} then range = 0 and median = 0 and range is not greater than median.
I attempted this question and marked only B was sufficient
please advice

You're exactly right.
Here's the full solution.

Target question: Is the range of the set S greater than its mean?

Statement 1: Set S does not contain positive elements
There are several sets of numbers that meet this condition. Here are two:
Case a: Set S = {-1, -2}, in which case the range (1) is greater than the mean (-1.5)
Case b: Set S = {0, 0}, in which case the range (0) is not greater than the mean (0)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The median of set S is negative
If the median is negative, then there are two possible scenarios, both of which lead us to the same conclusion.
Scenario 1: all of the values are negative. In this scenario, the mean must be negative. Since the range is always greater than or equal to zero, we can be certain that the range is greater than the mean.
Scenario 2: some values are negative, and some are positive. In this scenario, the mean will be greater then the smallest value and less than the biggest value. Since the range equals the biggest value (a positive value) minus the smallest value (a negative value), the range will greater than the biggest value in the set. So, we can be certain that the range is greater than the mean.
In both possible scenarios, we come to the same conclusion: the range is greater than the mean.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent