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What is x?

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What is x? [#permalink]  30 Nov 2012, 04:00
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5% (low)

Question Stats:

52% (01:53) correct 47% (01:14) wrong based on 17 sessions
What is x?

(1) The median of set (x, 1, -1, 3, -x) = 0
(2) The median of set (x, 1, -1, 3, -x) = x/2

[Reveal] Spoiler:
1). there are five elements so the median has to be the middle number, therefore the middle number would have to be zero, so x would have to be zero, however zero is not positive or negative.

Dont think im understanding the question quite right??

Thanks
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Nov 2012, 04:05, edited 1 time in total.
Edited the question.
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Re: What is x? [#permalink]  30 Nov 2012, 04:07
Expert's post
sje12 wrote:
What is x?

(1) The median of set (x, 1, -1, 3, -x) = 0
(2) The median of set (x, 1, -1, 3, -x) = x/2

[Reveal] Spoiler:
1). there are five elements so the median has to be the middle number, therefore the middle number would have to be zero, so x would have to be zero, however zero is not positive or negative.

Dont think im understanding the question quite right??

Thanks

The question asks to find the value of x not to determine whether it's positive or negative.

What is the value of x?

Note that the median of a set with odd number of elements is just the middle element, when arranged in ascending/descending order.

(1) The median of set \{x, -1, 1, 3, -x\} is 0. The median of this set of 5 (odd) elements must be the middle term, hence x=0. Sufficient.

(2) The median of set \{x, -1, 1, 3, -x\} is \frac{x}{2}. It could be that x=0 (in this case the set is {-1, 0, 0, 1, 3}) as well as it could be that x=2 (in this case the set is {-2, -1, 1, 2, 3}). Not sufficient.

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Re: What is x? [#permalink]  30 Nov 2012, 04:22
But they label that x is negative and positive, and zero is not negative or positive, thats just what confuses me, why have they done that, or why is it irrelevant
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Re: What is x? [#permalink]  30 Nov 2012, 04:25
Expert's post
sje12 wrote:
But they label that x is negative and positive, and zero is not negative or positive, thats just what confuses me, why have they done that, or why is it irrelevant

You can write 0 as -0, there is nothing wrong with it (if it's what you are talking about).
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Re: What is x?   [#permalink] 30 Nov 2012, 04:25
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