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Is median of set S negative?

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by vittalgmat » Thu Jan 08, 2009 1:00 am
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

[spoiler]OA: C
However I chose B.
Wow!!!. as I am typing I realize my mistake. Stmt said that "biggest negative element" is -1 NOT "biggest element".
Damn!!!. I fell in the trap. Cant click the "back" button :(.
[/spoiler]
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by rajataga » Thu Jan 08, 2009 1:58 am
I still don't get the problem....

IMO it should be E....

Just for clarification, when there an even number of elements, the median is the mean of the middle 2 elements right??
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by rajataga » Thu Jan 08, 2009 2:12 am
actually now i understand,

if both the statements are taken together, the median will always be non-negative.

Hence, C
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by coffee5251 » Thu Jan 08, 2009 10:34 am
rajataga wrote: if both the statements are taken together, the median will always be non-negative.
can you explain this?

Also, how would statement 2 be rephrased? I took it to mean "-1 is the smallest number in the set"... since -1 is the biggest negative number so the value of any bigger negative number would be less than -1. Is that wrong?
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by coffee5251 » Thu Jan 08, 2009 10:35 am
rajataga wrote: if both the statements are taken together, the median will always be non-negative.
can you explain this?

Also, how would statement 2 be rephrased? I took it to mean "-1 is the smallest number in the set"... since -1 is the biggest negative number so the value of any bigger negative number would be less than -1. Is that wrong?
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by amitabhprasad » Thu Jan 08, 2009 11:15 am
I am still confused
lest say set consist of 2 umbers and taking both statement 1 and 2

S = {-1,1}
in this case median = (-1+1)/2 = 0

case 2:
S={-1,-2,4,5}
median = (-2+4)/2 = 1

am I missing any thing ??
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by cramya » Thu Jan 08, 2009 11:44 am
S = {-1,1}
in this case median = (-1+1)/2 = 0

case 2:
S={-1,-2,4,5}
median = (-2+4)/2 = 1
Amit,

Good question.

In both cases its not negative. 0 is non positive and non negative.

We can surely answer the question "Is the median of set S negative" with a NO.

If the question was Is the median of the set positive then the answer would have been E IMO since 0 is non positive ; anything else would be positive. The difference in wording is subtle but there in lies the beauty of these testmakers...

Hope this helps!

Regards,
Cramya
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by amitabhprasad » Thu Jan 08, 2009 11:50 am
Thanks again buddy...
All the time I was thinking "0" is non negative. But not sure why I picked "E"
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by pandeyvineet24 » Thu Jan 08, 2009 9:59 pm
What if the set is
S = {-2,-1,0,1}

Would not the median be -1 ?.
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by thirst » Thu Jan 08, 2009 10:04 pm
for both, 0 cannot be one of the numbers because case i) half of the numbers are positive integer. 0 is not positive nor negative...

therefore it must be {-2,-1,1,2} or some number larger than 1, in which case it is still a sufficient no.
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