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

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Senior Manager
Joined: 02 Feb 2004
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If set S consists of even number of integers, is the median [#permalink]

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21 Feb 2005, 05:53
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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
[Reveal] Spoiler: OA
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13 Oct 2009, 22:21
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Expert's post
rlevochkin wrote:
mirhaque wrote:
SEE ATTACHED

E.

St. (1) insufficient as we should not forget "0", which is neither positive nor negative. sets can be

{-1, -1, 0, 2}, the mean is -.5, which is negative, or {-1,0,2,4} the mean is 1 which is positive.

St. (2) is also, insufficient, since the set can look like {-1, 0}, the median is the middle number between -1 and 0, which is -.5, so negative, ot it can be {-1,0, 4,4} with median 2, which is positive

putting statements (1) and (2) together does not provide any additional information that can be considered, so Ans. is E.

Not so.

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

Set consists of even number of integers --> median=sum of two middle integers/2

(1) Exactly half of all elements of set S are positive --> either all other are negative or all but one, which at this case must be 0. Not sufficient.

(2) The largest negative element of set S is -1 --> not sufficient

(1)+(2) half positive, biggest negative -1 --> median is either (0 + positive)/2=positive (so not negative) or (-1 + at least smallest positive integer, which is 1)/2=0 (min value of median in this case) also not negative. Q was is the median negative answer NO. SUFFICIENT

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21 Feb 2005, 07:57
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mirhaque wrote:
SEE ATTACHED

Just got hit by a lightening and clearly see why OA is C:

Stem: the set has even number of integers.
stmt 1: half of them are positive
stmt2: -1 is the largest negative.

taking stmt 1 & 2 there can be only two numbers in the set since largest negative is -1 & numbers in the set is even & half of all no in the set is positivr. If zero is not a positive integers, the other integer has to be 1 or greater than 1.

Possible set:
-1,1
-1, 1+

Therefore median, under such circumstances, will always be non-negative.

Last edited by mirhaque on 21 Feb 2005, 08:01, edited 1 time in total.
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04 Aug 2009, 01:31
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arvs212 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.

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

IMO C should be the answer..
take statement 1, it means that half are positive and other half may include all negative numbers or negative numbers and a zero.. not suff..
take 2.. from this we cannot say anything about the median.. all nos. can be negative or some may be negative..
we don't know.. insuff.
take both: half are positive.. other half would be negative. the largest negative is -1 and all are integers.. so minimum positive would be 1. so median will be (-1 + 1)/2 = 0..
hence median is not negative.. median in this case could me 0 or more than 0 but will never be negative..
hence suff..
thus C..

NOTE: 0 is neither positive nor negative..
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Re: If set S consists of even number of integers, is the median [#permalink]

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02 Mar 2013, 12:36
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I am confused with the second statement:- The largest negative element in the set is -1. Shouldn't it be smallest negative integer?

When the largest negative integer is mentioned, does is it not mean that the set can't have a larger (than -1) integer, but have a smaller(-2,-100 etc) negative integer?
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Posts: 39595
Re: If set S consists of even number of integers, is the median [#permalink]

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11 Oct 2014, 04:06
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ApoorvaRed9 wrote:
Bunuel,

Set 1: -1, -4, 1, 1 Median= -3/2 (exactly half positive integers, and -1 is the highest -ve integer)

Set 2: -1, 0, 2, 3 Median = 1 (+ve)

Shouldn't the solution be E?

The median of a set with even terms is the average of two middle terms when arranged in ascending/descending order. So, the median of {-4, -1, 1, 1} is (-1 + 1)/2 = 0, not -3/2.
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21 Feb 2005, 07:44
Antmavel wrote:
For me OA is E

0 is the key but I don't see how C could be the answer. For me it's E.

Statement 1 : insuff
Statement 2: insuff

Statement 1 +2 insuff :

exemple 1 :
-1,2 -> median is positive : 0.5

exemple 2 :
-1,0 -> median is negative : -0.5

0 is not a positive integer => http://mathworld.wolfram.com/Zero.html and you should only use integers as it is stated
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21 Feb 2005, 07:48
yes....OA says rite...its C.

1 and 2 can lead to a YES and a NO.

1... -100,-50,0,1,2,3---yes, -2,-1,0,1,50,100----no....insuff...BCE

2... -100,-50,0,1,2,3---yes, -1,0,1,5,7,80---no...insuff...CE

1and2...suff.....C
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21 Feb 2005, 07:53
Antmavel wrote:
and I dont see why it is not E...

exemple 1 :
-1,5 -> median is positive : 2

exemple 2 :
-1,0.1 -> median is negative : -0.55

Median can be - or +

in you example 2, 0.1 is not an integer ! the set only consists of integers !
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21 Feb 2005, 08:05
mirhaque wrote:
mirhaque wrote:
SEE ATTACHED

Just got hit by a lightening and clearly see why OA is C:

Stem: the set has even number of integers.
stmt 1: half of them are positive
stmt2: -1 is the largest negative.

taking stmt 1 & 2 there can be only two numbers in the set since largest negative is -1 & numbers in the set is even & half of all no in the set is positivr. If zero is not a positive integers, the other integer has to be 1 or greater than 1.

Possible set:
-1,1
-1, 1+

Therefore median, under such circumstances, will always be non-negative.

But you guys are ignoring one case:-

set ={ 12, 3, 1, -1, -5, -7}
Here the median is 0, which is niether +ve nor -ve.
So I think it shud be E.
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21 Feb 2005, 08:11
Vijo wrote:
mirhaque wrote:
mirhaque wrote:
SEE ATTACHED

Just got hit by a lightening and clearly see why OA is C:

Stem: the set has even number of integers.
stmt 1: half of them are positive
stmt2: -1 is the largest negative.

taking stmt 1 & 2 there can be only two numbers in the set since largest negative is -1 & numbers in the set is even & half of all no in the set is positivr. If zero is not a positive integers, the other integer has to be 1 or greater than 1.

Possible set:
-1,1
-1, 1+

Therefore median, under such circumstances, will always be non-negative.

But you guys are ignoring one case:-

set ={ 12, 3, 1, -1, -5, -7}
Here the median is 0, which is niether +ve nor -ve.
So I think it shud be E.

read 1) it says that half of all integers are positive => there is only one pos integers because there is only one neg integer
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21 Feb 2005, 09:34
State I.....set can be {-1,0,1,2}.....median > 0.....or {-3,-2,1,2}...median is <0....insuff

State II....set can be {-1,-1,-1,-1}......median < 0.....or {-1,2,3,4}....median > 0....insuff

Combine.....{-1,0,2,3}...median > 0.....{-1,-1,1,3}......median = 0...all cases it is never < 0.....ans is NO.....suff
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21 Feb 2005, 17:42
Vijo wrote:
mirhaque wrote:
mirhaque wrote:
SEE ATTACHED

Just got hit by a lightening and clearly see why OA is C:

Stem: the set has even number of integers.
stmt 1: half of them are positive
stmt2: -1 is the largest negative.

taking stmt 1 & 2 there can be only two numbers in the set since largest negative is -1 & numbers in the set is even & half of all no in the set is positivr. If zero is not a positive integers, the other integer has to be 1 or greater than 1.

Possible set:
-1,1
-1, 1+

Therefore median, under such circumstances, will always be non-negative.

But you guys are ignoring one case:-

set ={ 12, 3, 1, -1, -5, -7}
Here the median is 0, which is niether +ve nor -ve.
So I think it shud be E.

Vijo, the question is to know if the median is negative...we knowthat the median is at least equal to 0 so we can answer to the question : no, it is impossible that the median is negative. Median is O or any positive number so C is ok to answer NO to the question
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04 Aug 2009, 01:35
arvs212 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.

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

IMO E,

1. Is Insuff, as it doesn't tell anything about -ve no. ( I mean the range or values)
2. Is also insuff.

Lets combine 1 & 2. Lets consider an example here.
S = ( -3, -2, -1, 1, 2, 3) ( as we know from st 2. that Largest -ve no. is -1 )
In this case the median is 0
and now consider S= ( -3, -2, -1, 2, 3, 4) In this case Median is 1/2
and when S= ( -3, -2, -1, 0, 3, 4) Median = -1/2
Hence 1 & 2 combined also is insuff.

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04 Aug 2009, 01:50
arvs212 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.

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

I think its C

1) Does not solve it. Good but not insufficient.
2) The next number is not 0 but a +ve one so you can say S is not a negative.

I hope. (Sorry if i am not right, I am new here just joined gmatclub)
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04 Aug 2009, 02:10
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.

median for a set made of even number of intigers is the average of the middle 2

from 1

insuff

from 2

insuff

both
to get the median one has to arrange the set in ascending order then take the average of the middle 2

ie: the largest -ve + the least +ve / 2 , as long as we dont know the least +ve we 9 could be at least 1 or 2

median = (1-1)/2 = 0 or (2-1)/2 = 1/2 so we can say that the median is not -ve...suff

C
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05 Aug 2009, 05:34
nitishmahajan wrote:
arvs212 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.

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

IMO E,

1. Is Insuff, as it doesn't tell anything about -ve no. ( I mean the range or values)
2. Is also insuff.

Lets combine 1 & 2. Lets consider an example here.
S = ( -3, -2, -1, 1, 2, 3) ( as we know from st 2. that Largest -ve no. is -1 )
In this case the median is 0
and now consider S= ( -3, -2, -1, 2, 3, 4) In this case Median is 1/2
and when S= ( -3, -2, -1, 0, 3, 4) Median = -1/2
Hence 1 & 2 combined also is insuff.

and when S= ( -3, -2, -1, 0, 3, 4) Median = -1/2---------- this case will not arse when we are comibining stmnt 1 &2 cos, one says half of the numbers are positive. so we can not have the "0" there.

so, 1&2 gives the ans. hence C.
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05 Aug 2009, 06:16
definition of median:
In probability theory and statistics, a median is described as the number separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one. If there is an even number of observations, the median is not unique, so one often takes the mean of the two middle values.

so in this case, we can have a set of -3 -2 -1 1 2 3, hence going by the rule stated above, the median of the set is (-1+1)/2 = 0, and 0 is neither positive nor negative, how is this one C?
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05 Aug 2009, 06:39
sprtng wrote:
definition of median:
In probability theory and statistics, a median is described as the number separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one. If there is an even number of observations, the median is not unique, so one often takes the mean of the two middle values.

so in this case, we can have a set of -3 -2 -1 1 2 3, hence going by the rule stated above, the median of the set is (-1+1)/2 = 0, and 0 is neither positive nor negative, how is this one C?

combining 1&2 we can get the median is either 0 or positive. for any of these case, median is non negative.
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22 Oct 2009, 00:17
Guys,I am not understanding why you people are saying that the set consists of only 2 elements..the answer stands at C only:
eg.: {-2, -1 ,1 ,2} median=0. Is the median -ive?NO (o is neither positive nor negative)

{-3,-2,-1,2,3,4}Median=1/2.NO
{-3,-1,5,8} Median=2.NO. SUFFICIENT>C.

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Re: DS: SET   [#permalink] 22 Oct 2009, 00:17

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