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Set S consists of even number of integers. Is the median of [#permalink]
 26 Jul 2008, 19:51
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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
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aaron22197 wrote: 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 From 1) Two cases are possible: a) when 0 is present in SET S. then (3,2,1,0,-5,-7) median = +ve (9,7,3,2,0,-9,-11,-13) median = +ve b) when 0 is not present in SET S. then (3,2,1,-2,-4,-6) median = -ve (9,7,3,2,-1,-5,-7,-9) median = +ve Thus NO Definite answer can be determined from 1) From 2) Two cases are possible: a) when 0 is present in SET S. (3,2,0,-1,-2,-3) median = -ve (3,2,1,0,-2,-3) median = +ve Thus NO Definite answer can be determined from 2) Combining 1) and 2) Two cases are possible: a) when 0 is present in SET S. then (3,2,1,0,-5,-7) median = +ve b) when 0 is not present in SET S. (3,2,1,-1,-4,-6) median = 0 (5,3,2,-1,-5,-7) median = +ve Thus a definite answer NO median of set S cant be negative. Thus C is the answer.
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Director
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aaron22197 wrote: 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 as the total number of elements is even, the condistions should satisfy when the numbers of elements is only two statement 1 (0,1) - median +ve (-1,1) - median 0 (-2,1) - median -ve Not suff statement 2 (-1,0) median -ve (-1,1) median 0 (-1, 2) median +ve Not suff combine (-1,1) median 0 (-1,2) median +ve Suff ... as median is not negative in any case ... option C
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aaron22197 wrote:
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
as the total number of elements is even, the condistions should satisfy when the numbers of elements is only two
statement 1
(0,1) - median +ve
(-1,1) - median 0
(-2,1) - median -ve
Not suff
statement 2
(-1,0) median -ve
(-1,1) median 0
(-1, 2) median +ve
Not suff
combine
(-1,1) median 0
(-1,2) median +ve
Suff ... as median is not negative in any case ... option C
Here, if I take more than 2 elements (say 4), then combining the two can give me a +ve or -ve median. Let us take an example here.
(-2,-1,1,1).
Hence, I will go for E.
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scthakur wrote: Here, if I take more than 2 elements (say 4), then combining the two can give me a +ve or -ve median. Let us take an example here.
(-2,-1,1,1).
Hence, I will go for E. median will be zero in this case (-1+1)/2.
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Oh.....I missed that.....thanks Durgesh79.
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Manager
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Here, if I take more than 2 elements (say 4), then combining the two can give me a +ve or -ve median. Let us take an example here.
(-2,-1,1,1).
Hence, I will go for E.[/quote] For an even number of values, it is the mean of the two middle values. Thus for set (-2,-1,1,1), median is 0. Source: http://www.purplemath.com/modules/meanmode.htm
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aaron22197 wrote: 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 (1) consider Set S: -ve, -ve, -ve, +ve, +ve, +ve Then the median will be equal to the average of the middle two terms. The mediam can be -ve, +ve or zero. Not Suff (2) So, in my case, the 3rd term should be -1 -3, -3, -3, -1, +2, +10 (median = -2) -3, -3, -1, +3, +5, +10 (median = +1) Not Suff (1) & (2) -10, -9, -1, +1, +2, +3 (median = 0) -10, -9, -1, +9, +2, +3 (median = 4) median will NOT be negative. Suff Ans is C
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aaron22197 wrote: 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 Statement 1) is insuff. since mod of smallest positive element can be bigger or smaller then largest -ve element Statement 2) is insuff. since two median element can be 0 and -1 as well Combining both median elements can be 0,1 or -1, 1 so median will be 1/2 or 0 which is non -ve Answer is C)
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