Data Sufficiency

If set S consists of even number of integers, is the median of set negative?
1.Exactly half of all elements of set S are positive.
2.The largest negative element of set S is -1.

Anurag,

I am unable to understand your explanation, you have quoted the below examples to depict the various scenarios:


1. {-1, 0, 1, 2} --> Median = (-1 + 0 + 1 + 2)/2 = 1 > 0
2. {-1, 1} --> Median = (-1 + 1)/2 = 0
3. {-3, -1, 1, 2} --> Median = (-3 -2 + 1 + 2)/2 = -1 < 0


But I don't understand the above calculations of median...

Shouldn't {-1, 0, 1, 2}'s median be (0+1)/2??

Not sure if I am missing something here..

khandelwal.ab:

Anurag made a mistake while he might have been trying to do it quickly. I am sure this is what he wanted to write:

1. {-1, 0, 1, 2} --> Median = (0 + 1)/2 = 1/2 > 0
2. {-1, 1} --> Median = (-1 + 1)/2 = 0
3. {-3, -1, 1, 2} --> Median = (-2 + 1)/2 = -1/2 < 0

The median value is the value smack in the middle of numbers arranged in an increasing or decreasing order. For even number of elements, you average the middle two; for odd number of elements, you take the middle value. I am sure you knew this already, but I wanted to clear any confusion.

Anurag, could you please edit your post?

Let me know if this helps

ankita1709 wrote:If set S consists of even number of integers, is the median of set negative?
1.Exactly half of all elements of set S are positive.
2.The largest negative element of set S is -1.

St1) Insufficient because we do not the value of the middle two terms (we just know that one is positive and one is negative) which is required for the calculation of median when even number of integers are there in a set

St2) Insufficient: Same reason as above

Combine st1 and st2: Now we know that one of the middle terms is -1 and the other middle term has to be > or = 1 (because half are positive integers) and therefore, the median will be > or = 0.

Hence, C

Note that, -1 is the largest negative integer. Hence, statement 2 is a redundant information. Therefore, the answer is either A or E.

I didnt quite get why -1 is redundant..

I am also not sure why -1 is redundant..

According me answer should be B

If set S consists of even number of integers, is the median of set negative?
1.Exactly half of all elements of set S are positive.
2.The largest negative element of set S is -1.

1) obviously insufficient, don't have any numbers to work with
2) the largest NEGATIVE element of the set is -1, that means it could be {-1,3,4,5} or {-3,-2,-1,1}, obviously insufficient, because the statement never said anything about how many positive or negative integers are there

if we combine both, the set could be {-1,0,0,1,3,4}, in this case, the median is 0.5
the set could also be {-3,-2,-1,1,3,4}, in this case the median is 0
so the median has to be >0, therefore, we can conclude that the median of the set will not be negative, that's why I think it should be C