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Set A = , If the median is x/2, what is x

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Set A = , If the median is x/2, what is x [#permalink] New post 29 Jan 2008, 12:17
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Set A = [-x, -1, 1, 3, x],
If the median is x/2, what is x?
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Re: median [#permalink] New post 29 Jan 2008, 12:24
bmwhype2 wrote:
Set A = [-x, -1, 1, 3, x],
If the median is x/2, what is x?



are these in order by value? or is it just random? I don't see how it could be in order by value b/c that would mean x/2=1 and x=2, which wouldnt make any sense at all.

I get 0=x

b/c if we have -1,-x... then x must be less than 1 so---> -1,-x,x,1,3 thus x=x/2 --> 2x=x Only way this can be is if x=0.
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Re: median [#permalink] New post 29 Jan 2008, 12:25
I am assuming x is an integer.

If the median of a set of 5 integers is x/2, then x/2 is the "middle" integer when all integers are arranged in increasing order.

so we have, -1, 1, x/2, 3, x. x must logically be the largest integer in the set if x/2 is the median.

Therefore, x must be 4.

Part of me thinks this was almost too easy, so please correct me if I made a mistake somewhere.
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Re: median [#permalink] New post 29 Jan 2008, 12:32
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Set A = [-x, -1, 1, 3, x]

Set A have 5 numbers, Therefore, median is defined by one number: 1 or x (x<1)

1) x/2=1 ==> x=2
2) x/2=x ==> x=0
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Re: median [#permalink] New post 29 Jan 2008, 12:33
Wait, so Set A is already arranged in increasing order?
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Re: median [#permalink] New post 29 Jan 2008, 12:39
walker wrote:
Set A = [-x, -1, 1, 3, x]

Set A have 5 numbers, Therefore, median is defined by one number: 1 or x (x<1)

1) x/2=1 ==> x=2
2) x/2=x ==> x=0


can you elaborate? if x=0, then 0/2 because median is is x/2
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Re: median [#permalink] New post 29 Jan 2008, 12:40
bmwhype2 wrote:
Set A = [-x, -1, 1, 3, x],
If the median is x/2, what is x?


can you provide the answer choices?

0 and 2 both seem to work..
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Re: median [#permalink] New post 29 Jan 2008, 12:43
incognito1 wrote:
bmwhype2 wrote:
Set A = [-x, -1, 1, 3, x],
If the median is x/2, what is x?


can you provide the answer choices?

0 and 2 both seem to work..

this is part of a DS question. both are correct. i just want to see how the answer came about.
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Re: median [#permalink] New post 29 Jan 2008, 12:45
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I guess choices are like

I. 0
II 1
III 2

A only I
B only II
C I and III
D II and III
E I, II and III

:)
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Re: median [#permalink] New post 29 Jan 2008, 12:47
walker wrote:
Set A = [-x, -1, 1, 3, x]

Set A have 5 numbers, Therefore, median is defined by one number: 1 or x (x<1)

1) x/2=1 ==> x=2
2) x/2=x ==> x=0



Ah yes, 2 can be an answer as well. -2,-1,1,2,3 And thus 2/2=1 is the median.

or -1,0,0,1,3. But in either case the original is not in the correct increasing order.

Haven't done a question quite like this before. whats the source?
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Re: median [#permalink] New post 29 Jan 2008, 13:39
walker wrote:
I guess choices are like

I. 0
II 1
III 2

A only I
B only II
C I and III
D II and III
E I, II and III

:)


lol didn't realize this was a DS question ;)
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Re: median [#permalink] New post 29 Jan 2008, 19:29
i just assumed that set was already in increasing order. since there are an odd number of terms, the median is equal to 1, and if 1=x/2, that leads to x=2 .... am i oversimplifying this q ?
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Re: median [#permalink] New post 05 Feb 2008, 05:17
walker wrote:
Set A = [-x, -1, 1, 3, x]

Set A have 5 numbers, Therefore, median is defined by one number: 1 or x (x<1)

1) x/2=1 ==> x=2
2) x/2=x ==> x=0

thanks. finally figured out the logic... :-D
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Re: median [#permalink] New post 05 Feb 2008, 06:52
bmwhype2 wrote:
Set A = [-x, -1, 1, 3, x],
If the median is x/2, what is x?


x >= 0 because there are at least 3 numbers that are greater or equal than 0 and x/2 is the median.

1) x - median -> x = x/2 -> x = 0
2) 1 - median -> x/2 = 1 -> x = 2

there are no other options because the median is greater or equal than zero and it can't be equal to 3 because there are at least 3 numbers smaller than 3.
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Re: median [#permalink] New post 05 Feb 2008, 14:07
I assumed this set wasn't in order. and the value of x was the same integer. for -x equals -2 and x = 2. so I rearranged..

Set A = ( -2, -1, 1, 2, 3)

Median being 1.
Re: median   [#permalink] 05 Feb 2008, 14:07
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