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

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Senior Manager
Joined: 20 Dec 2004
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Set S consists of even number of integers. Is the median of [#permalink]

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24 Dec 2007, 20:42
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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

Kudos [?]: 110 [0], given: 0

CEO
Joined: 17 Nov 2007
Posts: 3585

Kudos [?]: 4478 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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24 Dec 2007, 22:26
E

S1={{-1,-1,-1....,-1}, {2,2,2,2...,2}} ==> S1 consists with n "-1" and n "2"
S2={{-1,-1,-1....,-1}, {0.5,0.5,0.5,0.5...,0.5}} ==> S2 consists with n "-1" and n "0.5"

S1 and S2 satisfied 1 and 2 conditions both individually and in combination.

median (S1) = (-1+2)/2 = 0.5 positive
median (S2) = (-1+0.5)/2 = -0.25 negative

INSUFF.

Last edited by walker on 25 Dec 2007, 00:43, edited 1 time in total.

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Director
Joined: 03 Sep 2006
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24 Dec 2007, 23:41
walker wrote:
E

S1={{-1,-1,-1....,-1}, {2,2,2,2...,2}} ==> S1 consists with n "-1" and n "2"
S2={{-1,-1,-1....,-1}, {0.5,0.5,0.5,0.5...,0.5}} ==> S2 consists with n "-1" and n "0.5"

S1 and S2 satisfied 1 and 2 conditions both individually and in combination.

median (S1) = (-1+2)/2 = 0.5 positive
median (S1) = (-1+0.5)/2 = -0.25 negative

INSUFF.

Wow! What I liked in your explanation is that you created S1 and S2, which satisfy both 1 and 2 individually as well as the combination of the 1 and 2.

It took me more than 2 minutes and answer was still wrong!

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Senior Manager
Joined: 20 Dec 2004
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25 Dec 2007, 11:12
OA is C.

So can we give it another shot...

Also it said integers so I am not sure how is S2 a valid set with 0.5 in there...

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Intern
Joined: 14 Dec 2007
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25 Dec 2007, 13:32
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

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CEO
Joined: 17 Nov 2007
Posts: 3585

Kudos [?]: 4478 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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26 Dec 2007, 00:45
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

ahhhhhhh.....

Kudos [?]: 4478 [0], given: 360

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26 Dec 2007, 18:16
wow .... what a silly mistake ... i wasnt considering 0 to satisfy 'non-negative', and picked E.

aaaaaaah !

ok stat 1 isnt sufficient because we could have lets say 6 and -2, which gives a median of 2. Or, we can have -7 and 6, which gives median of -1

statement 2 says -1 is largest negative in set. so again, we could have -1 and 6, median is 2.5, or -1 and 1, median is 0. not sufficient.

together, we have -1, and element right after that is positive. So, we can have -1 and 1 to give median zero, or -1 and 2 to give median 0.5 .... choose any positive number , and median is always going to be positive. So , sufficient to answer that, NO, Median will not be negative

Kudos [?]: 173 [0], given: 2

26 Dec 2007, 18:16
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