Data Sufficiency

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

1. Exactly half of all elements of set S are positive.
2. The largest negative element of set S is -1.

Is it B?

Largest negative element is weird.

a)Exactly half of all elements of set S are positive.
(-1, 5) median = +ive
(-1, 0 ) median = -ive

insufficient

b)The largest negative element of set S is -1.

(-1, 5) median = +ive
(-1, 0 ) median = -ive
insufficient

combining a & b - > insufficient
Hence E

OA - C Can anyone solve this question?

i also got E...
wats the source of the ques and wats the explanation given???

GMAT Club challenges

Well, if set S has the even number of terms then the median would be = (sum of 2 middle terms)/2.
We must find then if the absolute value of the left one is greater than the abs of right middle number. Only then we can get a negative median.
1) Absolutely insufficient... it still can be (-1 and 10), or (-100, 1).
2) Ok we know that the largest of the negatives is -1.
Insufficient.

Knowing that there are only integers in the set, 1+2 will be sufficient.
The largest of negatives in -1, left half of the set side also might include 0, or might not. The least of the positive must be at least 1 ( from the given and stmt 1). So, the baddest scenario when the middle positive=1, and middle negative=-1. then the median is 0.
If the left middle number is 0, then the median is positive. So, NO, it is not negative.