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Given a set {x, y, z}, if the first term in the data set

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v1rok
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Given a set {x, y, z}, if the first term in the data set [#permalink] New post   Updated on: 08 Aug 2012, 05:04
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Given a set {x, y, z}, if the first term in the data set above is 3, what is the third term?

(1) the range of this data set is 0

(2) the standard deviation of this data set is 0

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D

Originally posted by v1rok on 28 Jun 2006, 21:18.
Last edited by Bunuel on 08 Aug 2012, 05:04, edited 1 time in total.
OA added.
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Re: Given a set {x, y, z}, if the first term in the data set [#permalink] New post   08 Sep 2009, 17:08
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v1rok wrote:
Given a set {x, y, z}, if the first term in the data set above is 3, what is the third term?

(1) the range of this data set is 0

(2) the standard deviation of this data set is 0


This is not a good question. Sets are not ordered; to talk about the 'first term' in a set is meaningless. And to say that the range of a set is zero is equivalent to saying the standard deviation is zero: if you know either of these facts, you can be certain that all of the elements in that set must be equal. If the OA is B, the OA is incorrect - the answer is D.
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Re: Given a set {x, y, z}, if the first term in the data set [#permalink] New post   21 Oct 2010, 08:47
It seems nobody was able to see the fact that range means: Greatest-Least
thus if x=3, then z or y=-3 we cannot determine which is -3 though
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Re: Given a set {x, y, z}, if the first term in the data set [#permalink] New post   21 Oct 2010, 12:52
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furkanbaran wrote:
It seems nobody was able to see the fact that range means: Greatest-Least
thus if x=3, then z or y=-3 we cannot determine which is -3 though


I'm quite sure most of the people posting above do understand that range = greatest - least. If the range is zero, then

greatest - least = 0
greatest = least

so if x=3 is the greatest element, then the least element is also 3 (and definitely not -3; if your largest element is 3 and your smallest element is -3, then your range is 6, not zero). Since every element must be somewhere between the least and the greatest element, then everything in the set must be equal if your range is zero. So in the question above, if one element is 3, and the range is zero, then every element is 3.
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Re: Given a set {x, y, z}, if the first term in the data set [#permalink] New post   28 Oct 2010, 02:23
Statement 1 tells us that the range is 0.
It means you can have following scenarios :
x-y = 0
x-z = 0
y-x = 0
y-z = 0
z-x = 0
z-y = 0

Saying that Statement 1 is sufficient means assuming that all elements of the sets are positives numbers. However there is no clues on that in the question.

So statement 1 is insufficient.

Whereas Statement 2 is sufficient.

So my answer will be B as well !
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Re: Given a set {x, y, z}, if the first term in the data set [#permalink] New post   28 Oct 2010, 03:37
The answer is not B

Saying range is 0 immediately implies all the elements in the set must be equal, it does not matter if all of them are positive or negative. Also as Ian pointed out the bigger problem in the question is asking what the third element is, by definition, sets are unordered collections.
whichscore wrote:
Statement 1 tells us that the range is 0.
It means you can have following scenarios :
x-y = 0
x-z = 0
y-x = 0
y-z = 0
z-x = 0
z-y = 0

Saying that Statement 1 is sufficient means assuming that all elements of the sets are positives numbers. However there is no clues on that in the question.

So statement 1 is insufficient.

Whereas Statement 2 is sufficient.

So my answer will be B as well !


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Re: Given a set {x, y, z}, if the first term in the data set [#permalink]
28 Oct 2010, 03:37
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Bunuel
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