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# What is the value of x?

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Joined: 29 Nov 2012
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What is the value of x? [#permalink]

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30 Nov 2012, 05:00
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46% (01:19) correct 54% (01:48) wrong based on 96 sessions

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What is the value of x?

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

M20-35
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Feb 2014, 01:20, edited 3 times in total.
Edited the question.

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30 Nov 2012, 05:07
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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30 Nov 2012, 05:22
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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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30 Nov 2012, 05:25
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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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What is the value of x? [#permalink]

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17 Feb 2014, 16:18
What is the value of x?

(1) The median of set {x,−1,1,3,−x} is 0

(2) The median of set {x,−1,1,3,−x} is x2
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Re: What is the value of x? [#permalink]

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17 Feb 2014, 22:07
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anindame wrote:
What is the value of x?

(1) The median of set {x,−1,1,3,−x} is 0

(2) The median of set {x,−1,1,3,−x} is x2

Median of a set is the middle value when the numbers are arranged in increasing order. When there are odd number of numbers e.g. 5 here, the median is simply the 3rd number.

Arranging the set in increasing order: (-1, 1, 3) Now there are two numbers x and -x too in this set which we don't know where to place right now.

1. The median of set (x, 1, -1, 3, -x) is 0
We are given that the median here is 0 which means the third number must be 0. Since we don't have any 0 yet in the set, x (and hence -x too) must be 0.
The set must be (-1, 0, 0, 1, 3).
There is no other way to get a median of 0. Hence x = 0. Sufficient.

2. The median of set (x, 1, -1, 3, -x) is x/2
We saw above that x could be 0 in which case median will be x/2 = 0/2 = 0. So the value x = 0 satisfies this condition.
The median could also be the middle number right now i.e. 1. If x = 2, we get the set (-2, -1, 1, 2, 3) and the median here is 1 which is x/2. Hence x = 2 also satisfies this condition. This means we have two values for x (0 and 2) and not a unique value so this statement alone is not sufficient.

For a discussion on this question, check: what-is-x-1-the-median-of-set-x-1-1-3-x-is-0-2-the-55865.html#p398159
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Re: What is the value of x? [#permalink]

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18 Feb 2014, 01:23
anindame wrote:
What is the value of x?

(1) The median of set {x,−1,1,3,−x} is 0

(2) The median of set {x,−1,1,3,−x} is x2

Merging similar topics. Please refer to the solutions above.
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Re: What is the value of x? [#permalink]

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09 Jun 2017, 15:49
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Re: What is the value of x?   [#permalink] 09 Jun 2017, 15:49
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