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VyshnaviV
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If set S consists of even number of integers, is the median 25 May 2013, 07:45
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sudiptak
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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.


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


plzzz give answers with explanations...thnx

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.

Please post OA also.

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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If we take a set as S: {-3,-2,-1,0,1,2,3,4}.,this contains exactly half +ve integers and the greatest -ve integer in -1 ., the median is positive..i.e., (0+1)/2=1/2
And if we consider the set S: {-3,-2,-1,1,2,3}.,this contains exactly half +ve integers and the greatest -ve integer is -1.,the median is neither negative nor positive..i.e.,(-1+1)/2=0
HEnce the answer should be E..as both answers when combined also didnt provide the solution..
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If set S consists of even number of integers, is the median 25 May 2013, 07:56
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VyshnaviV
If we take a set as S: {-3,-2,-1,0,1,2,3,4}.,this contains exactly half +ve integers and the greatest -ve integer in -1 ., the median is positive..i.e., (0+1)/2=1/2
And if we consider the set S: {-3,-2,-1,1,2,3}.,this contains exactly half +ve integers and the greatest -ve integer is -1.,the median is neither negative nor positive..i.e.,(-1+1)/2=0
HEnce the answer should be E..as both answers when combined also didnt provide the solution..
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The question asks whether the median is negative. In both cases you got that the median is NOT negative. Hence when taken together the statements are sufficient to give a definite NO answer to the question. The correct answer is C, not E.

Complete solution: if-set-s-consists-of-even-number-of-integers-is-the-median-14343-20.html#p1097147

Hope it helps.
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If set S consists of even number of integers, is the median 10 Oct 2014, 23:24
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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?


Bunuel
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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

Answer C
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If set S consists of even number of integers, is the median 11 Oct 2014, 04:06
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ApoorvaRed9
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?
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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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If set S consists of even number of integers, is the median 15 Aug 2020, 04:52
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dave785
I'm getting hung up on the phrase "Largest Negative number"

Interpretation of that phrase is why people are arguing either E or C.

Does that mean that the possible negative numbers are less than -1? That's how I translate it. In other words, if -1 is the largest negative number, then we could also have -2, -3, -4 etc.. in the set. In essence, it's a meaningless statement since the number has to be an integer anyway and there is no negative integer "larger" than -1. Treating it this way would lead to answer E.

If, however, you are interpretting it as the largest integer that is then made negative (IE the the rest of the numbers in the set must be >-1), then that would lead to answer C.

The literal meaning, as i take it, leads to answer E... but I misread the question the first time around and answered C, and only noticed the difference in the different poster's responses.
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I too agree with this interpretation. Statement 2 should mention that -1 is the smallest negative integer in the Set. If it were the largest, it leaves open the possibility of having other negative integers in the set.
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If set S consists of even number of integers, is the median 14 Feb 2021, 10:13
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Hi,

can statement 1 also mean that all of the other integers are 0? As in, half of the integers are positive (as given in the statement) and half are 0.
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If set S consists of even number of integers, is the median 25 Jun 2023, 00:55
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1) Half of the set is positive
Consider the set: 0022 (median is>0)
and the set: -10,-10,2,2 (median is <0)
Clearly ins.

2) Largest negative integer is -1
This is not sufficient since we don't know anything else
ex: -1,-1,-1,-1 is possible as is -1,400,400,400 etc

3)
Combing the two statements:
If half are positive, then the rest are either 0 or negative.
Lets say the rest are negative:
no matter how big the set it will always take this form:
a,b,c,d,...,-1,(positive values)
Where -1 will be one of the two values used to compute the median (since in an even number, the median is the average of the two middle terms)
So if we find the smallest median possible, it would be the case where the first positive value is 1. So that would lead to a median of 0. All other terms would lead to a positive median.
The other case is where there is a zero term, in which case the median is always positive.

Either way, there is no chance for the median to be a negative value - so we can always say NO to the question

C
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If set S consists of even number of integers, is the median 25 Jun 2023, 00:56
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sidship21
Hi,

can statement 1 also mean that all of the other integers are 0? As in, half of the integers are positive (as given in the statement) and half are 0.
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Yes - saying that half is positive implies that the other half is non-positive which means less than or equal to 0. So you could have a mix of 0 and negatives, or all negative or all 0.
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If set S consists of even number of integers, is the median 23 Sep 2025, 23:03
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