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Math Expert V
Joined: 02 Sep 2009
Posts: 57244
D01-18  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 55% (00:41) correct 45% (00:48) wrong based on 214 sessions

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Set $$S$$ consists of $$N$$ elements. If $$N \gt 2$$, what is the standard deviation of $$S$$?

(1) The mean and median of the set are positive

(2) The difference between any two elements of the set is equal

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Math Expert V
Joined: 02 Sep 2009
Posts: 57244
Re D01-18  [#permalink]

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Official Solution:

Statement 1: If the mean and median of the set are positive, the standard deviation could be any. The set could have elements {1, 1, 1} or {1, 2, 3} or {10, 20, 30, 40, 50}. In each case, the standard deviation is not the same. So not sufficient..

Statement 2: If difference between any elements of the set is equal, then the set has to have same elements because the number of elements is greater than 2. So standard deviation is 0. Sufficient.

Answer: B
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Intern  B
Joined: 20 Jun 2013
Posts: 8
Concentration: Finance
GMAT Date: 12-20-2014
GPA: 3.71
Re: D01-18  [#permalink]

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Bunuel wrote:
Official Solution:

Statement 1: If the mean and median of the set is positive, the standard deviation could be any. The set could have elements {1, 1, 1} or {1, 2, 3} or {10, 20, 30, 40, 50}. In each case, the standard deviation isn’t the same. So NSF.

Statement 2: If difference between any elements of the set is equal, then the set has to have same elements because the number of elements is greater than 2. So standard deviation is 0. Sufficient.

Answer: B

Statement 2: If difference between any elements of the set is equal, then the set has to have same elements because the number of elements is greater than 2. So standard deviation is 0. Sufficient.

I'm confused why they have to be the same elements because the number of elements is greater than 2.. If the difference is equal, can't it just be {1,3,5..} or {1,5,9..} which means SD can be anything..

Also, can you explain difference between elements and numbers in this case? This may be adding to my confusion.
Math Expert V
Joined: 02 Sep 2009
Posts: 57244
Re: D01-18  [#permalink]

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3
1
codeblue wrote:
Bunuel wrote:
Official Solution:

Statement 1: If the mean and median of the set is positive, the standard deviation could be any. The set could have elements {1, 1, 1} or {1, 2, 3} or {10, 20, 30, 40, 50}. In each case, the standard deviation isn’t the same. So NSF.

Statement 2: If difference between any elements of the set is equal, then the set has to have same elements because the number of elements is greater than 2. So standard deviation is 0. Sufficient.

Answer: B

Statement 2: If difference between any elements of the set is equal, then the set has to have same elements because the number of elements is greater than 2. So standard deviation is 0. Sufficient.

I'm confused why they have to be the same elements because the number of elements is greater than 2.. If the difference is equal, can't it just be {1,3,5..} or {1,5,9..} which means SD can be anything..

Also, can you explain difference between elements and numbers in this case? This may be adding to my confusion.

Second statement says that the difference between ANY two elements of the set is equal. If the set does not have all the elements equal, for example, if the set is {1, 3, 5}, then the difference between ANY two elements of the set won't be equal: 3-1=2 but 5-1=4. Hence the set must have same elements.

As for your other question: element of a set and number of a set are the same thing - member of a set.
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Joined: 16 Apr 2013
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GMAT 1: 760 Q49 V45 Re: D01-18  [#permalink]

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Given statement 1, can we conclude Set S is evenly spaced?
Current Student Joined: 04 Mar 2015
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Re: D01-18  [#permalink]

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Statement mentions that mean and median are equal not positive as mentioned in the answer explanation.
Current Student Joined: 04 Mar 2015
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GMAT 1: 670 Q45 V37 GPA: 3.5
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Re: D01-18  [#permalink]

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1
Statement mentions that mean and median are equal not positive as mentioned in the answer explanation.
Intern  Joined: 06 Nov 2014
Posts: 29
Re: D01-18  [#permalink]

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Bunuel wrote:
Official Solution:

Statement 1: If the mean and median of the set is positive, the standard deviation could be any. The set could have elements {1, 1, 1} or {1, 2, 3} or {10, 20, 30, 40, 50}. In each case, the standard deviation is not the same. So NSF.

Statement 2: If difference between any elements of the set is equal, then the set has to have same elements because the number of elements is greater than 2. So standard deviation is 0. Sufficient.

Answer: B

Suppose n=2
Then what will happen for Statement ii)

Consider a case {1,2}

2-1=1 and 1-2 =-1 .
The difference is not the same correct ??
So in a way I am disproving the given statement and this approach is incorrect.

If Set {1,1}

difference is always 0. Therefore SD is 0.

Are there other possibilities or other insights to this ? I want to understand the n=2 case better.
Math Expert V
Joined: 02 Sep 2009
Posts: 57244
Re: D01-18  [#permalink]

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anurag356 wrote:
Bunuel wrote:
Official Solution:

Statement 1: If the mean and median of the set is positive, the standard deviation could be any. The set could have elements {1, 1, 1} or {1, 2, 3} or {10, 20, 30, 40, 50}. In each case, the standard deviation is not the same. So NSF.

Statement 2: If difference between any elements of the set is equal, then the set has to have same elements because the number of elements is greater than 2. So standard deviation is 0. Sufficient.

Answer: B

Suppose n=2
Then what will happen for Statement ii)

Consider a case {1,2}

2-1=1 and 1-2 =-1 .
The difference is not the same correct ??
So in a way I am disproving the given statement and this approach is incorrect.

If Set {1,1}

difference is always 0. Therefore SD is 0.

Are there other possibilities or other insights to this ? I want to understand the n=2 case better.

Question says that n > 2, why are you considering n = 2 there?
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Re: D01-18  [#permalink]

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1
Bunuel wrote:
anurag356 wrote:
Bunuel wrote:
Official Solution:

Statement 1: If the mean and median of the set is positive, the standard deviation could be any. The set could have elements {1, 1, 1} or {1, 2, 3} or {10, 20, 30, 40, 50}. In each case, the standard deviation is not the same. So NSF.

Statement 2: If difference between any elements of the set is equal, then the set has to have same elements because the number of elements is greater than 2. So standard deviation is 0. Sufficient.

Answer: B

Suppose n=2
Then what will happen for Statement ii)

Consider a case {1,2}

2-1=1 and 1-2 =-1 .
The difference is not the same correct ??
So in a way I am disproving the given statement and this approach is incorrect.

If Set {1,1}

difference is always 0. Therefore SD is 0.

Are there other possibilities or other insights to this ? I want to understand the n=2 case better.

Question says that n > 2, why are you considering n = 2 there?

Its true that N>2 is given.

But if in the exam no such condition was given then I ll have to consider 2 elements in a set as well.In that case what will happen is what Im trying to understand. So that I can be prepared.

To understand things better im asking this case.
Intern  Joined: 28 Aug 2014
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Location: Brazil
Concentration: General Management, Leadership
Re: D01-18  [#permalink]

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1
Official Solution:

Statement 1: If the mean and median of the set is positive, the standard deviation could be any. The set could have elements {1, 1, 1} or {1, 2, 3} or {10, 20, 30, 40, 50}. In each case, the standard deviation is not the same. So NSF.

Statement 2: If difference between any elements of the set is equal, then the set has to have same elements because the number of elements is greater than 2. So standard deviation is 0. Sufficient.

Answer: B
Statement mentions that mean and median are equal not positive as mentioned in the answer explanation.
Intern  Joined: 11 Oct 2016
Posts: 3
D01-18  [#permalink]

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Even if the constraint x>2 was not given, option ii would still be sufficient right?
I am not sure how x>2 helps the second option.
Math Expert V
Joined: 02 Sep 2009
Posts: 57244
Re: D01-18  [#permalink]

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pg1 wrote:
Even if the constraint x>2 was not given, option ii would still be sufficient right?
I am not sure how x>2 helps the second option.

If the number of elements is 0 or 1, the second statement won't make any sense. If the number of elements were 2, the question would be much easier.
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Joined: 28 Jun 2018
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Concentration: Finance, Marketing
Schools: CUHK '21 (II)
GMAT 1: 650 Q49 V30 GPA: 4
Re: D01-18  [#permalink]

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Bunuel , I have one doubt, It might be stupid but still I have it
When we say 'Set' --> doesn't it mean a collection of distinct objects. So how come , we are taking Set as {1,1,1} as per second statement.
Doesn't it violate basic definition of Set?
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Give me kudos if you like it , it's totally harmless  Re: D01-18   [#permalink] 07 Aug 2018, 06:58
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