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Set S consists of even number of integers. Is the median of [#permalink]
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14 Aug 2007, 22:52
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Set S consists of even number of integers. Is the median of set S negative ?
1 . Exactly half of all the elements of set S are positive.
2. The biggest negative element of set S is 1.



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Joined: 04 Jun 2007
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empty_spaces wrote: Set S consists of even number of integers. Is the median of set S negative ?
1 . Exactly half of all the elements of set S are positive.
2. The biggest negative element of set S is 1.
This should be E.
Stmt 1: insufficient.
S={1,0,1,2}; Median=0.5
S={2,1,1,2}; Median=0
Stmt 2: insufficient.
We don't know how many elements are there in the set.
Both together, I am confused. What does "biggest negative element" mean? 1 > all other negative integers, so there can be any other negative element in the set. Or is the definition of biggest in terms of the absolute value. However, in either case it will be insufficient.
S={1,4}; S={1,1} Different medians.



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Joined: 06 Aug 2007
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sumande wrote: empty_spaces wrote: Set S consists of even number of integers. Is the median of set S negative ?
1 . Exactly half of all the elements of set S are positive.
2. The biggest negative element of set S is 1. This should be E. Stmt 1: insufficient. S={1,0,1,2}; Median=0.5 S={2,1,1,2}; Median=0 Stmt 2: insufficient. We don't know how many elements are there in the set. Both together, I am confused. What does "biggest negative element" mean? 1 > all other negative integers, so there can be any other negative element in the set. Or is the definition of biggest in terms of the absolute value. However, in either case it will be insufficient. S={1,4}; S={1,1} Different medians.
if you combine both statements medial will always be greater than or equal to 0. C.



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Joined: 04 Jun 2007
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racha24 wrote: sumande wrote: empty_spaces wrote: Set S consists of even number of integers. Is the median of set S negative ?
1 . Exactly half of all the elements of set S are positive.
2. The biggest negative element of set S is 1. This should be E. Stmt 1: insufficient. S={1,0,1,2}; Median=0.5 S={2,1,1,2}; Median=0 Stmt 2: insufficient. We don't know how many elements are there in the set. Both together, I am confused. What does "biggest negative element" mean? 1 > all other negative integers, so there can be any other negative element in the set. Or is the definition of biggest in terms of the absolute value. However, in either case it will be insufficient. S={1,4}; S={1,1} Different medians. if you combine both statements medial will always be greater than or equal to 0. C.
That depends on the definition of "biggest number". 1 is bigger than 4, so we can have a 4 in the set. But considering absolute values, we cannot. Then the answer will be C. (I shouldn't solve these too early in the morning. ) But otherwise the answer should be E.
Am I making any sense? (I have a feeling, I am not.)



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Joined: 10 Jun 2007
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empty_spaces wrote: Set S consists of even number of integers. Is the median of set S negative ?
1 . Exactly half of all the elements of set S are positive.
2. The biggest negative element of set S is 1.
I'll go with C
It would be C if we consider half elements positive and half negative
Say S={1,1} or S={6,1,1,1} will give you a median of either 0 or positive number; thus, can never be negative.
If we consider half positive, some zeros, some negative, you get the same result that median can never be negative.



Director
Joined: 12 Jul 2007
Posts: 858

good question. I'll go with C. That largest negative number being 1 is the key.



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My question still is "how do you define the largest negative number?"



Director
Joined: 12 Jul 2007
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sumande wrote: My question still is "how do you define the largest negative number?"
Absolute values have nothing to do with this.
The median is the average of the middle two numbers. Since half the numbers are positive we know that we are averaging some number with a number >= 1. If the biggest negative number of set S is 1 that means you would average 1 (or more) and 1 and you'd get >= 0. if you averaged 1 and 0 you'd get > 0. there's no way to average them and get less than 0. so it's C.
im sorry if this isn't what you're asking. I'm rather confused on what exactly your question is



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eschn3am wrote: sumande wrote: My question still is "how do you define the largest negative number?" Absolute values have nothing to do with this. The median is the average of the middle two numbers. Since half the numbers are positive we know that we are averaging some number with a number >= 1. If the biggest negative number of set S is 1 that means you would average 1 (or more) and 1 and you'd get >= 0. if you averaged 1 and 0 you'd get > 0. there's no way to average them and get less than 0. so it's C. im sorry if this isn't what you're asking. I'm rather confused on what exactly your question is
Thanks for attempting to understand my vague question.
My confusion is simple. The question says the biggest negative value is 1. So does that mean that 4 or 5 or 99 cannot be part of the set ?? For me they are lesser than 1. So, the biggest value being 1 does not tell us anything.
Forget about the absolute value thing, it was too early in the morning.



Director
Joined: 12 Jul 2007
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Quote: The question says the biggest negative value is 1. So does that mean that 4 or 5 or 99 cannot be part of the set ?? For me they are lesser than 1. So, the biggest value being 1 does not tell us anything.
No, you're right here. The biggest negative value is 1 so the other one can be 100, 50, 23523523 or 0. It doesn't matter. They are asking for the MEDIAN of the set, not the average. The median is the middle term of a set (when there are an odd number of elements) or the average of the middle two elements if a set has an even number of elements (like this one). That means the sets can look like any of these
{235, 1, 1, 23}
{2, 1, 1, 2}
{1, 0, 1, 2}
all we know is that two integers (the two on the right if you list them by size) must be positive. The smallest number can be anything it wants, but the largest negative number is for sure 1. so you could have 0, 1 or 25, 1.
but the average of the two center terms will ALWAYS be a positive number (or at the lowest, 0). The median of the set will never be negative. so you get C.



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eschn3am wrote: Quote: The question says the biggest negative value is 1. So does that mean that 4 or 5 or 99 cannot be part of the set ?? For me they are lesser than 1. So, the biggest value being 1 does not tell us anything. No, you're right here. The biggest negative value is 1 so the other one can be 100, 50, 23523523 or 0. It doesn't matter. They are asking for the MEDIAN of the set, not the average. The median is the middle term of a set (when there are an odd number of elements) or the average of the middle two elements if a set has an even number of elements (like this one). That means the sets can look like any of these {235, 1, 1, 23} {2, 1, 1, 2} {1, 0, 1, 2} all we know is that two integers (the two on the right if you list them by size) must be positive. The smallest number can be anything it wants, but the largest negative number is for sure 1. so you could have 0, 1 or 25, 1. but the average of the two center terms will ALWAYS be a positive number (or at the lowest, 0). The median of the set will never be negative. so you get C.
Stupid me...I was imagining the set without 1 !!



Director
Joined: 12 Jul 2007
Posts: 858

That would do it! lol
If exactly half the numbers are positive that means the other ones must be 0 or negative. either way it works out to be a positive median



Director
Joined: 03 May 2007
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Schools: University of Chicago, Wharton School

empty_spaces wrote: Set S consists of even number of integers. Is the median of set S negative ?
1 . Exactly half of all the elements of set S are positive.
2. The biggest negative element of set S is 1.
using 1 and 2: the lowest median could be 0, which is not ve.
so its C.










