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# M20-35

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:09
Expert's post
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Difficulty:

55% (hard)

Question Stats:

60% (01:02) correct 40% (01:15) wrong based on 128 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 $$\frac{x}{2}$$
[Reveal] Spoiler: OA

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16 Sep 2014, 00:09
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Official Solution:

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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28 Jul 2015, 09:05
Bunuel wrote:
Official Solution:

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.

Hi Bunuel,
At first i correctly thought that x must be 0 as {$$-1, 0, 0, 1, 3$$} is possible but than I eliminated stmt 1 as 0 can not be written as -0 ( as mentioned -x)
is there a typo in the Q or can we assume both -x and x to be 0
thanks.
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29 Jul 2015, 00:18
Ankur9 wrote:
Bunuel wrote:
Official Solution:

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.

Hi Bunuel,
At first i correctly thought that x must be 0 as {$$-1, 0, 0, 1, 3$$} is possible but than I eliminated stmt 1 as 0 can not be written as -0 ( as mentioned -x)
is there a typo in the Q or can we assume both -x and x to be 0
thanks.

-0 = 0, so nothing wrong with it.
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12 Oct 2017, 23:58
Hi,

what if x is negative eg ( -4,-1,1,3,4) median here is 0. isnt st1 insufficient?

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13 Oct 2017, 00:06
shweta.aarya@gmail.com wrote:
Hi,

what if x is negative eg ( -4,-1,1,3,4) median here is 0. isnt st1 insufficient?

The median of a set with odd number of elements is the middle term, when arranged in ascending/descending order. The media of {-4, -1, 1, 3, 4} is 1, not 0.
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31 Oct 2017, 04:28
+1 for A
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31 Oct 2017, 05:45
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 $$\frac{x}{2}$$

we need a single value of X

condition 1 : 0 is the median then zero is a part of the set mentioned :so x and -x =0 hence an unique answer :sufficient
condition 2: x/2 is median :X can be any any number 0 or 2 itself : so not sufficient

A is correct option

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07 Nov 2017, 23:13
Bunuel wrote:
Official Solution:

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.

Hi Bunuel,
Are we missing x=-2 as a probable option? Still statement A is correct but just for clarity..

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07 Nov 2017, 23:26
ManishKM1 wrote:
Bunuel wrote:
Official Solution:

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.

Hi Bunuel,
Are we missing x=-2 as a probable option? Still statement A is correct but just for clarity..

Are you talking about (2)? If x = -2, then the set is $$\{-2, -1, 1, 2, 3\}$$. The median = 1, but we are told that it should be x/2 = -1.
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07 Nov 2017, 23:31
Bunuel wrote:
ManishKM1 wrote:
Bunuel wrote:
Official Solution:

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.

Hi Bunuel,
Are we missing x=-2 as a probable option? Still statement A is correct but just for clarity..

Are you talking about (2)? If x = -2, then the set is $$\{-2, -1, 1, 2, 3\}$$. The median = 1, but we are told that it should be x/2 = -1.

Got it..Thanks a lot..

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13 Nov 2017, 06:32
Good afternoon Bunuel,

I was wondering when a set is written, it is all the time written in an ascending order.

In our case: (X<-1<1<3<-X) and thus I understood that -X>3 which mean X=O for (2).

Shall I understood that in a set when a variable is present it is not always presented in ascending order?

Regards,

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13 Nov 2017, 06:35
Tpral wrote:
Good afternoon Bunuel,

I was wondering when a set is written, it is all the time written in an ascending order.

In our case: (X<-1<1<3<-X) and thus I understood that -X>3 which mean X=O for (2).

Shall I understood that in a set when a variable is present it is not always presented in ascending order?

Regards,

A set, by definition, is a collection of elements without any order. While, a sequence, by definition, is an ordered list of terms.
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