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

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Manager
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Given a set {x, y, z}, if the first term in the data set [#permalink]

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28 Jun 2006, 21:18
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Aug 2012, 05:04, edited 1 time in total.

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Manager
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28 Jun 2006, 21:30
That was my answer too! But the book says it is (B). I suspect the book is wrong. Unless somebody can prove me why Range=0 does not imply all elements are equal?

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28 Jun 2006, 22:58
Will go wtith D too.......
Given three numbers with range 0 then highest and lowest number should be equal. The third number has to be equal to the other numbers

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29 Jun 2006, 09:26
D. Both are sufficient.
Given first term is 3.

S1: Range = 0 (High - Low) = 0 => All elements equal.
Sufficient.

S2: Std Devn = 0. All elements equal...
Sufficient.

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29 Jun 2006, 10:36
Agree with D.

If Range or Standard deviation of a list is 0, then the list has to contain
1. All zeros ... {0, 0 , 0}
OR
2. Identical elements {3, 3, 3}

Since one of the elements is 3, the rest should also be 3
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Manager
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29 Jun 2006, 10:55
Thanks, guys. Statistically speaking, I was 99.99% sure that I got it right and the book is wrong, but as I learned from experience, never assume anything on GMAT...

Anyway, the book was by Princeton Review. I actually don't like the way they explain Quant. Almost half of the time, they explain a solution by starting plugging numbers out of the blue. I know there are problems where this approach can save time and energy, but they should not have relied on this approach this heavily, IMO...

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Director
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02 Jul 2006, 09:16
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

range = max - min = 0, first term is 3 but we don't know if its the lowest and if it in ascending or descending order, so (A) is INSUFF

SD = 0 => variance = 0 => square of difference of mean and number is 0 => all numbers are same. So (B) is sufficient (all numbers are 3).

(B)

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Director
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02 Jul 2006, 09:22
Thinking again, I think it should be (D), if range is 0 then max = min and all elements are same. B can't be the answer (I thot so first but now I'm sure it can't be right...), what's OA?

necromonger wrote:
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

range = max - min = 0, first term is 3 but we don't know if its the lowest and if it in ascending or descending order, so (A) is INSUFF

SD = 0 => variance = 0 => square of difference of mean and number is 0 => all numbers are same. So (B) is sufficient (all numbers are 3).

(B)

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02 Jul 2006, 13:10
giddi77 wrote:
If Range or Standard deviation of a list is 0, then the list has to contain
1. All zeros ... {0, 0 , 0}
OR
2. Identical elements {3, 3, 3}

Since one of the elements is 3, the rest should also be 3

how about if we say "if Range or Standard deviation of a list is 0, then the list has to contain all Identical elements". identital means it could be all zeros or 1's or 2's or so on. it is not necessary to have all zeros only.

in this example zeros are not possible so only 3's are required.

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02 Jul 2006, 13:32
MA wrote:
giddi77 wrote:
If Range or Standard deviation of a list is 0, then the list has to contain
1. All zeros ... {0, 0 , 0}
OR
2. Identical elements {3, 3, 3}

Since one of the elements is 3, the rest should also be 3

how about if we say "if Range or Standard deviation of a list is 0, then the list has to contain all Identical elements". identital means it could be all zeros or 1's or 2's or so on. it is not necessary to have all zeros only.

in this example zeros are not possible so only 3's are required.

If Range=0 or SD=0 => List contains IDENTICAL elements.
All elements equal to zero happens to be one of the cases..
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08 Sep 2009, 09:23
IMO B. I picked this answer at first. and I think Princeton is right. We really do not know the order of the integers in 1st statement, thus we can not judge which of the integers in the above mentioned set is 3rd, which is the smallest and which is the biggest.
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08 Sep 2009, 17:08
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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13 Oct 2009, 04:35
Sorry for coming late but had a question regarding statement (1)
it says the range is zero , that means that all are identical since the first one is known, However I have read also that if the set contains one number then the range is zero as well, so does this change anything? and only B is considered. Becuase if that is the case we can't determine whether there's a third integer or no..

is it valid to consider that when range is zero maybe numbers are identical or maybe there's one number ??

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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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21 Oct 2010, 12:52
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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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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28 Oct 2010, 03:37

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 !

Posted from my mobile device
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28 Oct 2010, 10:28
I think statement 1 is sufficient as well.

It has been pointed out in previous replies that range is highest value - lowest value.
Since two numbers take on the role of being either the highest value or the lowest value, the third numbers has to be a value in between the highest and the lowest.

therefore, range can equal

x-y, where x >= z >= y
x-z, where x >= y >= z
y-x, where y >= z >= x
y-z, where y >= x >= z
z-x, where z >= y >= x
z-y, where z >= x >= y

In statement 1 we are given that range = 0.

if range = 0 then highest - lowest = 0. Therefore, highest = lowest. The above possibilities will then become

x=y, where x >= z >= y
x=z, where x >= y >= z
y=x, where y >= z >= x
y=z, where y >= x >= z
z=x, where z >= y >= x
z=y, where z >= x >= y

therefore the highest, lowest, and the middle variables are all equal to 3.

Statement 1 is sufficient.

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05 May 2011, 22:20
since 1st term is 3.

sd= 0 and range = 0 both means that all the terms are same.

hence D
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08 May 2011, 12:42
1. Sufficient .

as it tells us all the numbers are same.

2. Sufficient.

as it tells us all the numbers are same.

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Re: DS - Stat   [#permalink] 08 May 2011, 12:42

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