netigen wrote:Whats the rule between median, mean and Range?

OA is B

Range = the distance between the largest and smallest term in the set (and since it's a distance, it's always positive).

Mean = the average

Median = the term in the middle of the set (or, if there's an even number of terms, the average of the two middle terms).

Q: is range > mean.

(1) no positive terms in S.

We know that the set has more than 1 term, but we don't know that the terms are distinct.

So, our set could be {0,0,0}, which has a range of 0 and a mean of 0. Is 0 > 0? NO.

Our set could be (-2, 0), which has a range of 2 and a mean of -1. Is 2 > -1? YES.

Could be yes or no... insufficient.

(2) The median is negative.

If the median is negative, range will ALWAYS be greater than the mean.

We know that the middle term (or the average of the two middle terms) is negative. Therefore, there's at least 1 negative term in the set.

For example:

{-20, 2} has a negative median (with 2 terms, median = mean) and a negative mean. Range is always positive, so range > mean.

{-1, -1, 50} has a negative median (-1) and a postive mean (16). However, since it has a combination of positives and negatives, the range must be greater than any number in the set, so it must be greater than the mean (which will be inside the set).

Whenever a set has a combination of negatives and positives, range will be outside the set (i.e. greater than any term in the set).

Whenever a set is all negatives, range will be outside the set (since range is always positive).

When a set is all positives, range could be inside OR outside the set (but this time range will be SMALLER than any number in the set, never bigger).

For example:

{1, 4, 9} has a range of 8.

{4, 5, 6} has a range of 2.

So, (2) is suff and (1) isn't: choose (B).

Thanks a lot for clarifying on the rules.