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Set S = If the mean is a+b, what is the median

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CEO
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Set S = If the mean is a+b, what is the median [#permalink] New post 31 Jan 2008, 12:21
Set S = [a-b, b-a, a+b]
If the mean is a+b, what is the median?
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Re: median [#permalink] New post 31 Jan 2008, 12:26
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bmwhype2 wrote:
Set S = [a-b, b-a, a+b]
If the mean is a+b, what is the median?


mean = (a-b+b-a+a+b)/3 = (a+b)/3 = (a+b) -> a+b = 0 -> b = -a

assume a> 0 -> b-a < 0 and a-b > 0 -> a+b = 0 is the median
assume a < 0 -> a-b < 0, b-a > 0 -> a+b = 0 is the median

a+b is the median and a + b = 0, so I guess 0 is the median
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Re: median [#permalink] New post 31 Jan 2008, 12:31
thanks.

my initial concern was whether we can infer that a+b is the median but i overlooked the fact that we needed a number, not the expression (because a+b, where a and b are both zero, implies all the 3 terms, a-b, a+b, a-b are also zero.)
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Re: median [#permalink] New post 31 Jan 2008, 12:35
bmwhype2 wrote:
thanks.

my initial concern was whether we can infer that a+b is the median but i overlooked the fact that we needed a number, not the expression (because a+b, where a and b are both zero, implies all the 3 terms, a-b, a+b, a-b are also zero.)


just to clarify: a and b don't have to be equal to zero, b = -a satisfies the condition of a+b being the mean of the set. However, for each (a,b) such that b = -a, a+b = 0 and it is going to be the median of the set.
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Re: median [#permalink] New post 31 Jan 2008, 12:51
maratikus wrote:
bmwhype2 wrote:
thanks.

my initial concern was whether we can infer that a+b is the median but i overlooked the fact that we needed a number, not the expression (because a+b, where a and b are both zero, implies all the 3 terms, a-b, a+b, a-b are also zero.)


just to clarify: a and b don't have to be equal to zero, b = -a satisfies the condition of a+b being the mean of the set. However, for each (a,b) such that b = -a, a+b = 0 and it is going to be the median of the set.

yea, understood. b-a and a-b are "polar opposites" where they eventually net out to zero.
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Re: median   [#permalink] 31 Jan 2008, 12:51
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Set S = If the mean is a+b, what is the median

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