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GMAT Instructor
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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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Intern
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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..
Please waiting your reply
is it valid to consider that when range is zero maybe numbers are identical or maybe there's one number ??
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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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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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Manager
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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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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 ! Posted from my mobile device 
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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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since 1st term is 3. sd= 0 and range = 0 both means that all the terms are same. hence D
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1. Sufficient .
as it tells us all the numbers are same.
2. Sufficient.
as it tells us all the numbers are same.
Answer is D.
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first of all i also thought the answer should be D but i chose B finally...
the question said the first number is 3
statement 1 says that the range= highest-lowest
there would be 2 cases: every number in the set is 3 3 3 or the highest number is 3 and the second and the third are both 0
becuase the question doesnt say that the numbers in the set must be in order, we cant conclude anything about this statement.
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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 Doesn't matter 1st, 2nd or nth term is 3. If one of the elements is "3" and the range of the set is 0; then all elements must be 3 irrespective of the order you write those elements. Range 0- All elements identical. Std Dev 0- All elements identical. Ans: "D" ****************************
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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 From both the statement same thing can be concluded that each element is equal to 3 only hence D is the answer 
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