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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 \(\frac{x}{2}\)
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Re M2035 [#permalink]
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16 Sep 2014, 00:09
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. Answer: A
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Re: M2035 [#permalink]
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28 Jul 2015, 09:05
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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.
Answer: A 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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Re: M2035 [#permalink]
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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.
Answer: A 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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Re: M2035 [#permalink]
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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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Re: M2035 [#permalink]
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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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Re: M2035 [#permalink]
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31 Oct 2017, 04:28
+1 for A
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Re: M2035 [#permalink]
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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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Re: M2035 [#permalink]
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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.
Answer: A Hi Bunuel, Are we missing x=2 as a probable option? Still statement A is correct but just for clarity..



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Re: M2035 [#permalink]
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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.
Answer: A 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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Re: M2035 [#permalink]
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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.
Answer: A 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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Re: M2035 [#permalink]
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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?
Thanks in advance,
Regards,



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Re: M2035 [#permalink]
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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?
Thanks in advance,
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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