Data Sufficiency

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 biggest negative element of set S is -1

[spoiler]OA: C
However I chose B.
Wow!!!. as I am typing I realize my mistake. Stmt said that "biggest negative element" is -1 NOT "biggest element".
Damn!!!. I fell in the trap. Cant click the "back" button .
[/spoiler]

I still don't get the problem....

IMO it should be E....

Just for clarification, when there an even number of elements, the median is the mean of the middle 2 elements right??

actually now i understand,

if both the statements are taken together, the median will always be non-negative.

Hence, C

rajataga wrote: if both the statements are taken together, the median will always be non-negative.

can you explain this?

Also, how would statement 2 be rephrased? I took it to mean "-1 is the smallest number in the set"... since -1 is the biggest negative number so the value of any bigger negative number would be less than -1. Is that wrong?

rajataga wrote: if both the statements are taken together, the median will always be non-negative.

can you explain this?

Also, how would statement 2 be rephrased? I took it to mean "-1 is the smallest number in the set"... since -1 is the biggest negative number so the value of any bigger negative number would be less than -1. Is that wrong?

I am still confused
lest say set consist of 2 umbers and taking both statement 1 and 2

S = {-1,1}
in this case median = (-1+1)/2 = 0

case 2:
S={-1,-2,4,5}
median = (-2+4)/2 = 1

am I missing any thing ??

S = {-1,1}
in this case median = (-1+1)/2 = 0

case 2:
S={-1,-2,4,5}
median = (-2+4)/2 = 1

Amit,

Good question.

In both cases its not negative. 0 is non positive and non negative.

We can surely answer the question "Is the median of set S negative" with a NO.

If the question was Is the median of the set positive then the answer would have been E IMO since 0 is non positive ; anything else would be positive. The difference in wording is subtle but there in lies the beauty of these testmakers...

Hope this helps!

Regards,
Cramya

Thanks again buddy...
All the time I was thinking "0" is non negative. But not sure why I picked "E"

What if the set is
S = {-2,-1,0,1}

Would not the median be -1 ?.

for both, 0 cannot be one of the numbers because case i) half of the numbers are positive integer. 0 is not positive nor negative...

therefore it must be {-2,-1,1,2} or some number larger than 1, in which case it is still a sufficient no.