gmatquant25 wrote: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
Statement 1: Exactly half of all the elements of set S are positive.
Hence, the rest of all the elements are either all negative or some negative and some zeroes or all zeroes. Consider the following cases,
- {-2, -2, 1, 2} --> Median = (-2 + 1)/2 = -0.5 --> Negative
{-2, -1, 1, 2} --> Median = (-1 + 1)/2 = 0 --> Not negative
Not sufficient
Statement 2: This means -1 is a element of the S. But from this we cannot determine whether the median is negative or not.
Not sufficient
1 & 2 Together: As we know that exactly half of the elements of S are positive and S has even number of elements, the median of S will be (smallest positive element + the integer just smaller than the smallest positive element)/2.
Now, smallest positive integer that can be in S is 1.
And, the integer just smaller than the smallest positive element of S is either 0 or -1.
Hence, the smallest value of the median is (1 - 1)/2 = 0
So, the median is always non-negative.
Sufficient
The correct answer is C.
