GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Sep 2019, 11:36

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# D01-18

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58098

### Show Tags

16 Sep 2014, 00:12
11
00:00

Difficulty:

55% (hard)

Question Stats:

55% (00:41) correct 45% (00:48) wrong based on 216 sessions

### HideShow timer Statistics

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

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 58098

### Show Tags

03 Dec 2014, 04:06
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.

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.
_________________
Intern
Joined: 06 Nov 2014
Posts: 28

### Show Tags

06 Jul 2015, 02:29
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.

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.
Math Expert
Joined: 02 Sep 2009
Posts: 58098

### Show Tags

16 Sep 2014, 00:12
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.

_________________
Intern
Joined: 20 Jun 2013
Posts: 8
Concentration: Finance
GMAT Date: 12-20-2014
GPA: 3.71

### Show Tags

02 Dec 2014, 12:20
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.

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.
Intern
Joined: 16 Apr 2013
Posts: 8
GMAT 1: 760 Q49 V45

### Show Tags

18 Jan 2015, 14:11
Given statement 1, can we conclude Set S is evenly spaced?
Current Student
Joined: 04 Mar 2015
Posts: 6
Location: Pakistan
Concentration: Marketing, Operations
GMAT 1: 670 Q45 V37
GPA: 3.5
WE: Engineering (Energy and Utilities)

### Show Tags

27 Mar 2015, 11:05
Statement mentions that mean and median are equal not positive as mentioned in the answer explanation.
Current Student
Joined: 04 Mar 2015
Posts: 6
Location: Pakistan
Concentration: Marketing, Operations
GMAT 1: 670 Q45 V37
GPA: 3.5
WE: Engineering (Energy and Utilities)

### Show Tags

27 Mar 2015, 11:05
1
Statement mentions that mean and median are equal not positive as mentioned in the answer explanation.
Intern
Joined: 06 Nov 2014
Posts: 28

### Show Tags

05 Jul 2015, 18:04
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.

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
Joined: 02 Sep 2009
Posts: 58098

### Show Tags

06 Jul 2015, 01:05
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.

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?
_________________
Intern
Joined: 28 Aug 2014
Posts: 3
Location: Brazil

### Show Tags

12 Aug 2015, 19:51
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.

Statement mentions that mean and median are equal not positive as mentioned in the answer explanation.
Intern
Joined: 11 Oct 2016
Posts: 3

### Show Tags

04 Jul 2017, 23:09
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
Joined: 02 Sep 2009
Posts: 58098

### Show Tags

04 Jul 2017, 23:34
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.
_________________
Manager
Joined: 28 Jun 2018
Posts: 154
Location: India
Concentration: Finance, Marketing
Schools: CUHK '21 (II)
GMAT 1: 650 Q49 V30
GPA: 4

### Show Tags

07 Aug 2018, 06:58
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?
_________________
Re: D01-18   [#permalink] 07 Aug 2018, 06:58
Display posts from previous: Sort by

# D01-18

Moderators: chetan2u, Bunuel