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

It is currently 25 Jun 2018, 02:52

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is the standard deviation of a certain set greater than 5,000?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

3 KUDOS received
Jamboree GMAT Instructor
User avatar
Status: GMAT Expert
Affiliations: Jamboree Education Pvt Ltd
Joined: 15 Jul 2015
Posts: 4
Location: India
GMAT 1: 710 Q50 V35
Is the standard deviation of a certain set greater than 5,000? [#permalink]

Show Tags

New post 20 Oct 2015, 05:42
3
2
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

34% (00:46) correct 66% (00:55) wrong based on 149 sessions

HideShow timer Statistics

Is the standard deviation of a certain set greater than 5,000?
(1) The range of the set is greater than 6,000.
(2) The range of the set is less than 8,000.
2 KUDOS received
Current Student
avatar
S
Joined: 20 Mar 2014
Posts: 2643
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Is the standard deviation of a certain set greater than 5,000? [#permalink]

Show Tags

New post 20 Oct 2015, 06:37
2
AmitGoyalJamboree wrote:
Is the standard deviation of a certain set greater than 5,000?
(1) The range of the set is greater than 6,000.
(2) The range of the set is less than 8,000.


The OA should not be B. It should be E.

It is not mentioned that the set has a particular # of elements. So consider the set {0,6500} and {0,7500}. SD of set 1 <5000 and SD of set 2 > 5000 and both these sets have 6000<range<8000 after you combine the 2 statements

Statement 1 is shown to be not sufficient by {0,6500} and {0,7500}. Set 1 has SD <5000 and set 2 has SD > 5000. Not sufficient.

Statement 2 is shown to be not sufficient by the same sets, {0,6500} and {0,7500}. Set 1 has SD <5000 and set 2 has SD > 5000. Not sufficient.

Even after combining, you get a "yes" or "no" answer making E as the correct answer.

Additionally, this is not a good GMAT question as GMAT will never (IMO) ask you to specifically calculate SD. You do need to know how SD of a set changes when you modify certain elements and this does not necessarily need you to know how to calculate SD.
Manager
Manager
User avatar
Status: Build your own dreams,Otherwise some one else will hire you to build there's.
Joined: 30 Apr 2015
Posts: 89
Location: India
Concentration: Finance
Schools: BYU-Marriott'18
GMAT 1: 590 Q45 V26
GMAT 2: 660 Q47 V34
GPA: 3.68
GMAT ToolKit User
Re: Is the standard deviation of a certain set greater than 5,000? [#permalink]

Show Tags

New post 20 Oct 2015, 06:52
Standerd deviation is not dependent on range.....we can sometimes deduce standard deviation through range like if the data set is {45,45,45,45}.The range is zero and S.D will also be Zero.
But if set is
{45,30,10,5}Then range will be 40 while s.d will be around 6.
for dataset{45,0,5}range will be 40 while S.D will be greater than 10.
So,OA should be E

If liked the post then give +1 Kudos :-D :beer

We know we can and we will.......
_________________

"Follow your heart and realize that your dream is a dream for a reason"
-Dori Roberts

2 KUDOS received
Jamboree GMAT Instructor
User avatar
Status: GMAT Expert
Affiliations: Jamboree Education Pvt Ltd
Joined: 15 Jul 2015
Posts: 4
Location: India
GMAT 1: 710 Q50 V35
Re: Is the standard deviation of a certain set greater than 5,000? [#permalink]

Show Tags

New post 20 Oct 2015, 07:36
2
hi Engr2012

thanks for responding to the question .
i would request you to reconsider the calculations you are doing .
in the second set { 0,7500} the Standard deviation is 3750 and not > 5000 as suggested by you .

also there is a relation between range and standard deviation .
i will post my explanation in about next 20 - 25 hours . i want to see the response i get .

also i agree GMAT will not ask you to calculate the Standard deviation .
this question also does not expect you to calculate the exact standard deviation .
GMAT tests you on the reasoning so this this question.
Current Student
avatar
S
Joined: 20 Mar 2014
Posts: 2643
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Is the standard deviation of a certain set greater than 5,000? [#permalink]

Show Tags

New post 20 Oct 2015, 07:43
AmitGoyalJamboree wrote:
hi Engr2012

thanks for responding to the question .
i would request you to reconsider the calculations you are doing .
in the second set { 0,7500} the Standard deviation is 3750 and not > 5000 as suggested by you .

also there is a relation between range and standard deviation .
i will post my explanation in about next 20 - 25 hours . i want to see the response i get .

also i agree GMAT will not ask you to calculate the Standard deviation .
this question also does not expect you to calculate the exact standard deviation .
GMAT tests you on the reasoning so this this question.


I understand what you meant with your question but for SD you have 2 different formulae, one for samples SD and 1 for population SD. Both the formulations give you different results. Population SD gives you 3750, while sample SD gives you 5303. I belive for your question, we are referring to population SD and not the sample SD which will make B the answer.

Thanks for the reply.
Expert Post
1 KUDOS received
Math Revolution GMAT Instructor
User avatar
D
Joined: 16 Aug 2015
Posts: 5610
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: Is the standard deviation of a certain set greater than 5,000? [#permalink]

Show Tags

New post 22 Oct 2015, 13:35
1
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is the standard deviation of a certain set greater than 5,000?
(1) The range of the set is greater than 6,000.
(2) The range of the set is less than 8,000.

If we let standard deviation: d, and range: r, the inequality d<=r/2 can be established.
From the original condition, we can see that we want to know whether d>5,000.
Condition 1 gives that r=20,000, but d<=20,000/2=10,000. This is not a sufficient condition, as the range of the question does not include that of this condition.
For question 2, if we say r=8,000, d<=8,000/2=4,000. The answer to what the question asks is always 'no'; the condition is sufficient, and the answer becomes (B).
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Manager
Manager
avatar
Joined: 10 Apr 2015
Posts: 72
Location: India
Concentration: Healthcare, Strategy
GMAT 1: 680 Q49 V34
GPA: 2.4
WE: Marketing (Health Care)
Reviews Badge
Re: Is the standard deviation of a certain set greater than 5,000? [#permalink]

Show Tags

New post 26 Oct 2015, 07:36
Hi,

Can you please elaborate the explanation using both the conventional and variable method?

Regards
Intern
Intern
avatar
Joined: 09 Mar 2014
Posts: 1
Re: Is the standard deviation of a certain set greater than 5,000? [#permalink]

Show Tags

New post 30 Oct 2015, 10:57
AmitGoyalJamboree wrote:
Is the standard deviation of a certain set greater than 5,000?
(1) The range of the set is greater than 6,000.
(2) The range of the set is less than 8,000.



The Range and Standard Deviation are related by a formula which is :

Standard Deviation = Range/4

Taking the first statement..it gives that Range is > 6000, which takes me to:

Let us take range as 10000(Since it is greater than 6000) so 10000/4 is 2500 which is less than 5000( Hence No).

Again let us take range as 24000( Since it is greater than 6000) so 24000/4 is 6000 which is greater than 5000 (Hence Yes)

So First statement is not sufficient.

Now the second statement is Range is less than 8000 (Take 7999 for example which is the maximum value less than 8000)
Here the Standard Deviation would be 7999/4 which is less than 5000. Hence B is correct.
8 KUDOS received
Jamboree GMAT Instructor
User avatar
Status: GMAT Expert
Affiliations: Jamboree Education Pvt Ltd
Joined: 15 Jul 2015
Posts: 4
Location: India
GMAT 1: 710 Q50 V35
Re: Is the standard deviation of a certain set greater than 5,000? [#permalink]

Show Tags

New post 30 Oct 2015, 20:55
8
3
Explanation

The concept used in this question is that
Standard deviation of a certain list ≤ (1/2) range of that list

Statement 1) we do not have the information either about the terms in the list or about their range. So we cannot answer if the standard deviation of a certain set is greater than 5000.
So this statement is insufficient

Statement 2) we know that range is < 8000

Based on the relation between range and standard deviation i.e.
Standard deviation of a certain list ≤ (1/2) range of that list
We can conclude that

Standard deviation of this list < 4000

Though we do not know the exact standard deviation but still the information in statement is sufficient to conclude that
Standard deviation of this list ≤ 5000

Hence we have a definite NO as an answer for the question asked

Hence the statement (2) is sufficient

Answer is option B

The following is the reasoning behind the concept

Standard deviation of a certain set ≤ (1/2) range of the list

Reasoning

One of the convenient 5-step processes to calculate the numerical value of standard deviation is

1. Take the mean of the given terms
2. Take the difference of the terms from the mean
3. Take the Square of the differences
4. Take the average of the squares
5. Standard deviation = (average of the squares)1/2

Lets consider a list of two numbers (0, 10) and let’s calculate the standard deviation

1. Mean of the terms = (0 + 10)/2 = 5
2. On taking the difference of the terms from the mean we will get: 5, -5
3. On taking the Square of the differences we get: 25, 25
4. On taking the average of the squares we get: (25 + 25) / 2 = 25
5. So Standard deviation = (25)1/2
Standard deviation = 5

Conceptually we know that standard deviation signifies how deviated are the terms.
So more deviated are the terms the more is the standard deviation

So if there are only two terms the list will have maximum standard deviation, as the terms will be the extreme or in others maximum deviated.

So we see that in the above list the

Standard deviation = (1/2) range

So if we add a number between the two numbers in the above list then the terms in general will become closer to the mean and hence the standard deviation will become smaller.

For better clarity lets add another term 5 in the list witch had two numbers (0, 10)

Now the new list will become (0, 5,10) and lets calculate the standard deviation

1. Mean of the terms = (0 + 5 +10)/3 = 5
2. On taking the difference of the terms from the mean we will get: 5,0, -5
3. On taking the Square of the differences we get: 25, 0, 25
4. On taking the average of the squares we get: (25 +0 + 25) / 3 = 50/3
5. So Standard deviation = (50/3) 1/2





Now the key point to notice is that the proportion with which the denominator has increased in the 4 Th step, the numerator has not increased.

As in this case if we add a number between the original numbers then we can say the numerator will never increase with the same proportion as the denominator will increase.
Actually for the numerator to increase with the same proportion the 25 should have been added instead of ZERO, which will never be the case as we are adding a number between the previous range.

We can observe that
Standard deviation of the second list ≤ Standard deviation of the first list

Given: Standard deviation of the first list = (1/2) range of the first list

Hence we can say
Standard deviation of the second list ≤ (1/2) range of the first list

So we can conclude that

Standard deviation of a certain list ≤ (1/2) range of that list


_____________________________________________________

Alternate Reasoning

We can also say that standard deviation signifies the average distance of the terms from the mean.
Please note that this average is not same as Arithmetic Average. Technically, it is called Root-Mean-Squared Value, but for GMAT we believe you should KEEP IT SIMPLE, so let us not go in its details.

If we take two terms (0,10)
The average distance from the mean is 5.

If we add another term within 0 and 10 say 5 or 6 then the average distance of the new list will be LESS than the average distance of the terms in the previous list.

So we can say that

Standard deviation of the second list ≤ Standard deviation of the first list

Given: Standard deviation of the first list = (1/2) range of the first list

So we can conclude that

Standard deviation of a certain list ≤ (1/2) range of that list

____________________________________________
Manager
Manager
avatar
B
Joined: 20 May 2014
Posts: 52
Concentration: Finance, Entrepreneurship
GPA: 3.87
GMAT ToolKit User Premium Member
Re: Is the standard deviation of a certain set greater than 5,000? [#permalink]

Show Tags

New post 04 Nov 2015, 07:06
AmitGoyalJamboree wrote:
Explanation

The concept used in this question is that
Standard deviation of a certain list ≤ (1/2) range of that list


Its not very GMATy to depend on a formula especially in DS. SD questions are usually play with the data consistency and "density" or amplitudes of a set" Is this a new question or one from 2008-9 ?
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7060
Premium Member
Re: Is the standard deviation of a certain set greater than 5,000? [#permalink]

Show Tags

New post 17 Jun 2018, 21:32
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: Is the standard deviation of a certain set greater than 5,000?   [#permalink] 17 Jun 2018, 21:32
Display posts from previous: Sort by

Is the standard deviation of a certain set greater than 5,000?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.