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

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Director
Joined: 01 Apr 2008
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If set S consists of even number of integers, is the median [#permalink]  18 Sep 2009, 22:08
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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.
Manager
Joined: 29 Jul 2009
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Location: France
GPA: 3.95
WE: Information Technology (Computer Software)
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Kudos [?]: 97 [0], given: 15

Re: Largest -ve element !! [#permalink]  18 Sep 2009, 23:27
Economist 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.

1=> consider numbers { -10, -2 , 0 , 0 , 1 , 3 } Or {-10, -5 , 1 , 2 }
not suff.

2==> doesn't tells you anything about all the elements.
not suff.

Together => {- 3 , -2, -1, 0, 0, 1 , 2 , 3 }
or {- 3 , -2, -1, 1,2 ,3}
not suff.

So E .
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Joined: 19 Jul 2009
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Schools: McIntire, Fuqua, Villanova, Vandy, WashingtonU
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Kudos [?]: 10 [0], given: 4

Re: Largest -ve element !! [#permalink]  18 Sep 2009, 23:35
Spoilt wrote:
Together => {- 3 , -2, -1, 0, 0, 1 , 2 , 3 }

{- 3 , -2, -1, 0, 0, 1 , 2 , 3} 0 is not positive, half of numbers should be positive

Median = (the smallest positive number + next smallest number)/2
Worst case scenariot, the smallest positive number is 1 and next smallest number is -1 (no zeros inbetween), median is non-negative.
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Manager
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Kudos [?]: 94 [0], given: 60

Re: Largest -ve element !! [#permalink]  19 Sep 2009, 03:53
This question has already been discussed here
ds-set-14343.html

The answer is C, as set consists of only 2 elements(because stmt1 states hals of the elements are positive and stmt2 gives the info that the largest -ve element is -1). The point is that question asks whether set has a negative median or not. In case(-1;1) median is 0, thus it is not negative nor positive. suff. in set (-1;2) median is always positive. suff.
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Re: Largest -ve element !!   [#permalink] 19 Sep 2009, 03:53
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