neelesh wrote:

Set S consists of even number of integers. Is the median of set S negative ?

1) Exactly one half of all elements of set S are positive

2) The biggest negative element of set S is -1

I have the OA but do not have an explanation so pls try to provide an explain for the answer

It should be C .

Question is saying that S is a SET of INTEGERS. hence we cannot consider 0.5 as an element of the SET.

ST 1 : Exactly half of all elements of the SET are positive.

Eg: S= { -3,-2,-1,1,2,3}==> Median = 0 ( Non Negative)

S={-10,-9,-8,1,2,3}==>Median =-7/2 ( Negative)

Hence NOT SUFF

ST 2: -1 Must be the biggest negative element in teh SET.

==> -1 must be an element of SET S

Eg : S={ -1,0,1,2} ==> Median= 1/2 ( +ve)

S= {-100,-2,-1,0} ==> Median=-3/2 ( -ve)

Hence NOT SUFF

ST 1+ST2 : ==> Half of the elements must be positive ==> Half of the elements will be either negative & it may/may not contain 0 as an element.

Eg:-100 ,-3,-1,1,2,3} ==>Median=0 ( Non negative)

-100 ,-1 , 0 , 1,2,3} ==> median=1/2 ( Non Negative)

Infact , Whenever 0 is an element of the set S we will have

n/2 no of positive integers ( in the eg 3) , one 0 & ( n/2-1) no of negative integers( in the eg:2) . Median of the set will always be (0+ Positive integer( In the eg:1) )/2 which is always positive.

when there is no 0 in the set then median of the set will always be (-1+ Positive integer)/2. As the min positive integer is 1, Min value of the Median for the SET S will be 0 ( non poisitve)

ST1& ST2 ==> Implying that median of the SET S is always NON NEGATIVE( Either 0 or more than 0).

Hence it should be C