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# m14 q5

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Intern
Joined: 29 Nov 2009
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06 Dec 2009, 06:36
I seldom doubt the correctness of any question, however, this one forced me to :-

If set S consists of even number of integers, is the median of set negative?
1. Exactly half of all elements of set S are positive.
2. The largest negative element of set S is -1.

IMO : E

My explanation :
My approach.. testing for C and E options
0 cannot be the 3rd element as question is Postive=Negative and 0 doesnot fit the criteria...

{ -8 , -1 ,2, 1 } = -0.5 = is negative ... ( note : the question doesnot say "IS MEDIAN a NEGATIVE INTEGER.. implies, it is a
negative number )
therefore for above set meeting st1 and st2 Answer is YES

consider,
{-3,-1,1,2} = 0 = Neither +ve nor -ve

therfoer for above set meeting st1 and st 2... Answer is NO

The OA must be "E"

What am I missing here ??
Manager
Joined: 29 Oct 2009
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GMAT 1: 750 Q50 V42
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06 Dec 2009, 08:32
I believe you have misunderstood St. (2).

'The largest negative element of set S is -1' implies that there can be no integer in set S which has a greater negative value than -1.

Also, we know that -1 is the first negative integer and thereby also the smallest negative integer.

Thus, combing these two facts, we can conclude that -1 must be the only possible value that any negative integer in set S can hold.

This is what St.(2) tells us.

Now clearly, by itself it is not sufficient. (Nor is St.(1) for that matter). However, combing the two statements, we can see that the value of the median can never be negative. Consider the following case :

Set S = {-1, -1, 1, 1}

From St.(1) we know that number of negative values must be equal to number of positive values.

Also, since -1 is the only possible negative value that any element in set S can hold and 1 is the smallest possible positive value in that any element in set S can hold. The smallest possible median for set S will be 0.

Any other positive integer value in set S will result in a median greater than 0.

Thus we can conclude that with both statements taken into consideration, it is possible to answer the question stem.

Hope this clears things up a bit.

Cheers.
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Joined: 04 Nov 2009
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06 Dec 2009, 20:46
Agree that it is C.

But
Quote:
I believe you have misunderstood St. (2).

'The largest negative element of set S is -1' implies that there can be no integer in set S which has a greater negative value than -1.

Also, we know that -1 is the first negative integer and thereby also the smallest negative integer.

I think the wording may be a little unclear in srihari's reply.
-1 is not the smallest negative integer- it is the highest of all negative integers as -1>-2>-3>-4>....
So the set can contain -8, -189 etc but it definitely contains -1. So i

So if the set has half positive integers (St 1) and has -1, it will look like (assuming 4 elements)
{-8,-1,1,2} - median is 0 - not negative
{-1,0,2,1} - median is 1 - not negative

The median will be the average of a positive integer and zero, or the average of a positive integer and a negative integer. Since -1 is the largest negative integer in the set, the median is either the average of a positive integer and zero, or the average of a positive integer and -1 - in both cases it can't be negative.
Intern
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07 Dec 2009, 10:12
4test1 wrote:
Agree that it is C.

But
Quote:
I believe you have misunderstood St. (2).

'The largest negative element of set S is -1' implies that there can be no integer in set S which has a greater negative value than -1.

Also, we know that -1 is the first negative integer and thereby also the smallest negative integer.

I think the wording may be a little unclear in srihari's reply.
-1 is not the smallest negative integer- it is the highest of all negative integers as -1>-2>-3>-4>....
So the set can contain -8, -189 etc but it definitely contains -1. So i

So if the set has half positive integers (St 1) and has -1, it will look like (assuming 4 elements)
{-8,-1,1,2} - median is 0 - not negative
{-1,0,2,1} - median is 1 - not negative

The median will be the average of a positive integer and zero, or the average of a positive integer and a negative integer. Since -1 is the largest negative integer in the set, the median is either the average of a positive integer and zero, or the average of a positive integer and -1 - in both cases it can't be negative.

I dont think we can assum the set to be { -1,0,2,1} reason : the statement says exactly Half Positive !! right ?
therfore other half will be exactly neagtive??

hey... I believe, I found it, it says Exactly Half Postive, does it imply that other half may have exact neagtive or few negative ???
Re: m14 q5   [#permalink] 07 Dec 2009, 10:12
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# m14 q5

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