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# Set S consists of even number of integers. Is the median of

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Manager
Joined: 22 May 2007
Posts: 211
Set S consists of even number of integers. Is the median of  [#permalink]

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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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Manager
Joined: 27 May 2008
Posts: 135

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26 Jul 2008, 20:21
1
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.
Director
Joined: 27 May 2008
Posts: 530

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27 Jul 2008, 23:42
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
VP
Joined: 17 Jun 2008
Posts: 1474

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28 Jul 2008, 01:23
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.
Director
Joined: 27 May 2008
Posts: 530

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28 Jul 2008, 01:27
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.
VP
Joined: 17 Jun 2008
Posts: 1474

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28 Jul 2008, 02:34
Oh.....I missed that.....thanks Durgesh79.
Manager
Joined: 27 May 2008
Posts: 135

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28 Jul 2008, 02:48
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
Senior Manager
Joined: 19 Mar 2008
Posts: 344

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28 Jul 2008, 09:16
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
Senior Manager
Joined: 06 Apr 2008
Posts: 390

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28 Jul 2008, 09:20
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

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: DS- Median &nbs [#permalink] 28 Jul 2008, 09:20
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