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# What is the value of x?

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CEO
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What is the value of x? [#permalink]  19 Nov 2007, 15:30
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Question Stats:

57% (02:11) correct 43% (01:09) wrong based on 45 sessions
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

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-value-of-x-143334.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Feb 2014, 23:13, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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SVP
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Kudos [?]: 584 [0], given: 19

Re: median [#permalink]  19 Nov 2007, 17:03
bmwhype2 wrote:
What is 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

hu ... is there any typo?

What is 1-1? is it 1.1 or (1 - 1) = 0?
Director
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Assuming that 1 and -1 are two different numbers

1. Median of (-x,1,-1,3,x) = 0 only value of X which will satisfy this equation is 0. as in that case 0 will be the median.... satisfied

2. Median of (-x,1,-1,3,0) = x/2, in this case X can be either 2 or 0, in both the case it will satisfy the median... insufficient.

Now lets assure 1-1=0 is one number, then in that case

1. Median of (-x,0,3,x) = 0, only value of X, whicn can satisfy this equation is 0.... satisfied

2. Median of (-x,0,3,x) = x/2 In this case X can be both 0 and 1 hence insufficient.

In both the cases answer is A

Amar
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Amardeep Sharma wrote:

2. Median of (-x,1,-1,3,0) = x/2, in this case X can be either 2 or 0, in both the case it will satisfy the median... insufficient.

Amar

In the Q we have the digit = x, notably (x,1-1,3,-x)
Where is the typo then?

Btw, agree with 1) - Sufficient, but I lost with 2)
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Re: median [#permalink]  19 Nov 2007, 22:29
bmwhype2 wrote:
What is 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

Stat 1:
There are 5 elements which means the 3rd element has to be 0. -x and -1 have to be the 1st 2 elements. 1 and 3 have to be last 2 elements which leaves x = 0. Suff.

Stat 2:
Same reasoning as 1 but x can = 0 or 1; insuff.

A
Director
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Whatever wrote:
Amardeep Sharma wrote:

2. Median of (-x,1,-1,3,0) = x/2, in this case X can be either 2 or 0, in both the case it will satisfy the median... insufficient.

Amar

In the Q we have the digit = x, notably (x,1-1,3,-x)
Where is the typo then?

Btw, agree with 1) - Sufficient, but I lost with 2)

Typo is in the question, where the comma is not used between 1 and -1

Amar
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Kudos [?]: 24 [0], given: 63

Re: What is x? 1. The median of set (x,1-1,3,-x) is 0 2. The [#permalink]  17 Feb 2014, 15:14
I'm sorry.. I think I'm missing something?

How can the median of set {−1,0,1,3} be 0? Shouldn't it be .5?
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Re: What is x? 1. The median of set (x,1-1,3,-x) is 0 2. The [#permalink]  17 Feb 2014, 19:47
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Expert's post
bmwhype2 wrote:
What is 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

I think the only problem with this question is that it is missing a comma.

What is 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

Solution:

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.

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Kudos [?]: 24 [0], given: 63

Re: What is x? 1. The median of set (x,1-1,3,-x) is 0 2. The [#permalink]  17 Feb 2014, 23:59
VeritasPrepKarishma wrote:
bmwhype2 wrote:
What is 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

I think the only problem with this question is that it is missing a comma.

What is 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

Solution:

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.

Thanks Karishma
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Re: What is the value of x? [#permalink]  18 Feb 2014, 23:14
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Expert's post
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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-value-of-x-143334.html
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Re: What is the value of x?   [#permalink] 18 Feb 2014, 23:14
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