If set S consists of even number of integers, is the median

Bunuel,

Set 1: -1, -4, 1, 1 Median= -3/2 (exactly half positive integers, and -1 is the highest -ve integer)

Set 2: -1, 0, 2, 3 Median = 1 (+ve)

Shouldn't the solution be E?

I too agree with this interpretation. Statement 2 should mention that -1 is the smallest negative integer in the Set. If it were the largest, it leaves open the possibility of having other negative integers in the set.

Hi,

can statement 1 also mean that all of the other integers are 0? As in, half of the integers are positive (as given in the statement) and half are 0.

1) Half of the set is positive
Consider the set: 0022 (median is>0)
and the set: -10,-10,2,2 (median is <0)
Clearly ins.

2) Largest negative integer is -1
This is not sufficient since we don't know anything else
ex: -1,-1,-1,-1 is possible as is -1,400,400,400 etc

3)
Combing the two statements:
If half are positive, then the rest are either 0 or negative.
Lets say the rest are negative:
no matter how big the set it will always take this form:
a,b,c,d,...,-1,(positive values)
Where -1 will be one of the two values used to compute the median (since in an even number, the median is the average of the two middle terms)
So if we find the smallest median possible, it would be the case where the first positive value is 1. So that would lead to a median of 0. All other terms would lead to a positive median.
The other case is where there is a zero term, in which case the median is always positive.

Either way, there is no chance for the median to be a negative value - so we can always say NO to the question

C

Yes - saying that half is positive implies that the other half is non-positive which means less than or equal to 0. So you could have a mix of 0 and negatives, or all negative or all 0.