Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 29 Jul 2012
Posts: 14

List M (not shown) consists of 8 different integers, each [#permalink]
Show Tags
Updated on: 16 Oct 2012, 05:20
Question Stats:
55% (01:37) correct 45% (01:33) wrong based on 1732 sessions
HideShow timer Statistics
4, 6, 8, 10, 12, 14, 16, 18, 20, 22 List M (not shown) consists of 8 different integers, each of which is in the list shown. What is the standard deviation of the numbers in list M ? (1) The average (arithmetic mean) of the numbers in list M is equal to the average of the numbers in the list shown. (2) List M does not contain 22. Stuck on this question and taking a lot of time to solve it any good solutions for this question?
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by pnf619 on 15 Oct 2012, 19:17.
Last edited by Bunuel on 16 Oct 2012, 05:20, edited 1 time in total.
Edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 47037

Re: List M (not shown) consists of 8 different integers, each [#permalink]
Show Tags
16 Oct 2012, 05:35
4, 6, 8, 10, 12, 14, 16, 18, 20, 22
List M (not shown) consists of 8 different integers, each of which is in the list shown. What is the standard deviation of the numbers in list M ?Given list consists of 10 evenly spaced integers. Mean=(First+Last)/2=13 and Sum=(Mean)*(# of terms)=130. Given that list M is obtained by removing 2 integers from the list shown. To determine the standard deviation of list M we must know which 2 integers were removed. (1) The average (arithmetic mean) of the numbers in list M is equal to the average of the numbers in the list shown > the mean of list M is also 13. Thus the sum of the integers in list M is 13*8=104, which means that the sum of the 2 integers removed is 130104=26. The 2 integers removed could be: (4, 22), (6, 20), ..., (12, 14). Not sufficient. (2) List M does not contain 22. We know only one of the numbers removed. Not sufficient. (1)+(2) From (1) we know that the the sum of the 2 integers removed is 26 and from (2) we know that one of the integers removed is 22. Therefore the second integer removed is 2622=4. List M consists of the following 8 integers: {6, 8, 10, 12, 14, 16, 18, 20}. So, we can determine its standard deviation. Sufficient. Answer: C. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Manager
Joined: 21 Sep 2012
Posts: 229

Re: Data sufficiency OG 13  Statistics [#permalink]
Show Tags
16 Oct 2012, 03:07
The question states that List M has 8 numbers to be picked from 10. 12+14/2 = 13 since 10 numbers the sum would be 130. since statement 1 says that we need to have an equal average of 13. now the sum needs to be 13*8=104.
so we have to reduce the sum by 26 which can be done in many different ways but just pointing out 2 cases 6,8,10,12,14,16,18,20 4,8,10,12,14,16,18,22
both sets have different SD so insufficient
statement 2 says that you can't pick 22 4,6,8,10,12,14,16,18 4,6,8,10,12,14,16,20
again insufficient
now when we combine 1 and 2 we can't pick 22 so our list is 4,6,8,10,12,14,16,18,20
but in our list M we need the sum to add up to 104 this can only be done by eliminating 4 6,8,10,12,14,16,18,20
so the only list available is the one mentioned above so the answer is C
hope its clear.




Manager
Joined: 29 Apr 2012
Posts: 92
Location: United States
Concentration: International Business, Real Estate
GMAT Date: 10222012

Re: Data sufficiency OG 13  Statistics [#permalink]
Show Tags
15 Oct 2012, 20:22
pnf619 wrote: 4,6,8,10,12,14,16,18,20,22
List M (not shown) consists of 8 different integers, each of which is in the list shown. what is the standard deviation of the numbers in the list M?
1) The average ( arithmetic mean) of the numbers in the list M is equal to the average of the numbers in the list shown. 2) list M is does not contain 22.
Stuck on this question and taking a lot of time to solve it any good solutions for this question? Let us name this list as N, which contains 4,6,8,10,12,14,16,18,20,22. AMean is = 13 Now we need to prepare a list M. statememnt 1> avg of M = avg of L M could be anything but has an avg of 13...so > not sufficient stmt 2 > M does not has 22 . >not sufficient using both 1 and 2 > avg=13 and no 22 in the list. we have only one list left: 6,8,10,12,14,16,18,20 which has avg of 13. Thus C



Intern
Joined: 22 Mar 2011
Posts: 2

Re: List M (not shown) consists of 8 different integers, each [#permalink]
Show Tags
31 Oct 2012, 22:18
Great explanation, Bunuel! Thank you.



Senior Manager
Joined: 15 Aug 2013
Posts: 271

Re: List M (not shown) consists of 8 different integers, each [#permalink]
Show Tags
04 May 2014, 14:47
Bunuel wrote: Bumping for review and further discussion. Hi Bunuel, I have a general question on Standard Deviation. I realize that SD is the spread from the mean, but what I have a hard time understanding is if "weight averages" come into play. Let's assume the list is [10,10,14,18,18]  the spread is from 10 to 18 so the deviation is 4 to the right and 4 to the left. Correct? Now if we assume that the list is [10,13,14,15,25]  without calculating(since the gmat won't ask us to calculate SD if i'm not mistaken, which one has the higher SD? The second list obviously has a wider range(10 to 25) but the numbers are bunched up closer. I guess, what i'm asking is, what carries more weight? Have a wider range or have multiple numbers on the edges(albeit a smaller range). Hope my question makes sense. Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 47037

Re: List M (not shown) consists of 8 different integers, each [#permalink]
Show Tags
05 May 2014, 01:08
russ9 wrote: Bunuel wrote: Bumping for review and further discussion. Hi Bunuel, I have a general question on Standard Deviation. I realize that SD is the spread from the mean, but what I have a hard time understanding is if "weight averages" come into play. Let's assume the list is [10,10,14,18,18]  the spread is from 10 to 18 so the deviation is 4 to the right and 4 to the left. Correct? Now if we assume that the list is [10,13,14,15,25]  without calculating(since the gmat won't ask us to calculate SD if i'm not mistaken, which one has the higher SD? The second list obviously has a wider range(10 to 25) but the numbers are bunched up closer. I guess, what i'm asking is, what carries more weight? Have a wider range or have multiple numbers on the edges(albeit a smaller range). Hope my question makes sense. Thanks Neither alone. For example, {1, 8} has larger stander deviation than {1, 3, 5, 7, 9} (notice that the first set has smaller range and less terms then the second one). The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.For, {10, 10, 14, 18, 18}: mean=14, and the deviations from the mean are 4, 4, 0, 4, 4. For, {10, 13, 14, 15, 25}: mean=15.4, and the deviations from the mean are 5.4, 2.4, 1.4, 9.6, 49.6. Since the second set is a bit more widespread then the first one, then it must have larger standard deviation.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 11 Sep 2013
Posts: 149
Concentration: Finance, Finance

Re: List M (not shown) consists of 8 different integers, each [#permalink]
Show Tags
09 Oct 2014, 14:06
Can you give more question like this to practice



GMAT Club Legend
Joined: 16 Oct 2010
Posts: 8124
Location: Pune, India

Re: List M (not shown) consists of 8 different integers, each [#permalink]
Show Tags
09 Oct 2014, 21:13
pnf619 wrote: 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
List M (not shown) consists of 8 different integers, each of which is in the list shown. What is the standard deviation of the numbers in list M ?
(1) The average (arithmetic mean) of the numbers in list M is equal to the average of the numbers in the list shown. (2) List M does not contain 22.
Stuck on this question and taking a lot of time to solve it any good solutions for this question? It's a good question and can be easily solved using your understanding of mean of AP. The list shown has 10 equally spaced numbers. Their mean will be the average of middle two numbers i.e. average of 12 and 14 which is 13. List M has 8 of these 10 numbers. We need the SD of list M. (1) The average (arithmetic mean) of the numbers in list M is equal to the average of the numbers in the list shown. The mean of list M is 13. But we don't know how the numbers of list M deviate from the mean. We can select 8 numbers in different ways to get mean of 13. (2) List M does not contain 22. We are left with 9 numbers from which we select 8. The SD will be different depending on the numbers we select. Using both, we have 9 numbers whose mean must be 13. One easy way we know in which we can select the numbers is drop 4 to get 8 equally spaced numbers whose mean will be 13. List M  (6, 8, 10, 12, 14, 16, 18, 20) Can you get the same mean by dropping some other number and keeping 4? Think about it  it is not possible. The number of numbers must stay 8. If you replace any other number by 4, the total sum will change which will change the mean. Hence, the only way to select list M is this one. We can easily find the SD here so both statements together are sufficient. Answer (C)
_________________
Karishma Private Tutor for GMAT Contact: bansal.karishma@gmail.com



Math Expert
Joined: 02 Sep 2009
Posts: 47037

Re: List M (not shown) consists of 8 different integers, each [#permalink]
Show Tags
10 Oct 2014, 02:36



Manager
Joined: 15 Mar 2015
Posts: 113

Re: List M (not shown) consists of 8 different integers, each [#permalink]
Show Tags
16 May 2015, 09:18
The list consists of 10 numbers, which means we're taking away two of them. (1) Tells us that the two numbers that have been removed were equally far from the mean, but opposite directions. e.g. 4 and 22, 6 and 20, or 8 and 18 etc. It's not sufficient to answer the question as the removal of higher numbers would yield a smaller spread and thus a smaller SD, than would more centric numbers. (2) Tells us that 22 was one of the numbers erased. This does not help us as we would need to know what the other number is. (1)+(2) In addition to the reasoning above, we can conclude that the second number erased was 4. This is based on the restrictions in regards to the possible and distinct pairs from (1) along with one of the members of the pair from (2).
_________________
I love being wrong. An incorrect answer offers an extraordinary opportunity to improve.



GMAT Club Legend
Joined: 16 Oct 2010
Posts: 8124
Location: Pune, India

Re: List M (not shown) consists of 8 different integers, each [#permalink]
Show Tags
20 Sep 2016, 08:46
pnf619 wrote: 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
List M (not shown) consists of 8 different integers, each of which is in the list shown. What is the standard deviation of the numbers in list M ?
(1) The average (arithmetic mean) of the numbers in list M is equal to the average of the numbers in the list shown. (2) List M does not contain 22.
Stuck on this question and taking a lot of time to solve it any good solutions for this question? Responding to a pm: Quote: I solved this question using mean and median. When the numbers in a set are equally spaced, mean is equal to the median. Therefore in set {4,6,8,10,12,14,16,18,20,22}, (12+14)/2 = 13 is the median and the mean. Therefore I assumed that 12 and 14 would remain in the set and as they form the median they would remain the middle values.
Is it correct to assume this question in the manner I did?
Mean is equal to median in the list shown. What says that mean will be equal to median in list M too? Also, if mean = median, it doesn't mean that the set MUST be equally spaced. Even if 12 and 14 are not there in list M, the median of the rest of the set will still be 13. M = {4,6,8,10,16,18,20,22} Median = (10+16)/2 = 13
_________________
Karishma Private Tutor for GMAT Contact: bansal.karishma@gmail.com



Intern
Joined: 10 Jun 2016
Posts: 49

List M (not shown) consists of 8 different integers, each [#permalink]
Show Tags
21 Jan 2017, 09:06
S1 )Not Sufficient. The key point to understand this question is for Average to remain same the Summation of M = {.......} must be 13026 = 104. So the possible combination of numbers (22,4) (20,6)...are to be eliminated. S2) Not Sufficient ST) Once we know in S1 & S2 that 22 is not in M, we determine other number as 4. So Yes C is the answer. Wow. Thanks, CoolKl
_________________
Thank You Very Much, CoolKl Success is the Journey from Knowing to Doing
A Kudo is a gesture, to express the effort helped. Thanks for your Kudos.



Intern
Joined: 11 Oct 2016
Posts: 14

Re: List M (not shown) consists of 8 different integers, each [#permalink]
Show Tags
01 Oct 2017, 08:52
Why can M be something like 12,12,12,12,14,14,14,14.
I chosed E becasue I though the number could repeat.
THanks



Math Expert
Joined: 02 Sep 2009
Posts: 47037

Re: List M (not shown) consists of 8 different integers, each [#permalink]
Show Tags
01 Oct 2017, 08:54
evillasis wrote: Why can M be something like 12,12,12,12,14,14,14,14.
I chosed E becasue I though the number could repeat.
THanks List M (not shown) consists of 8 different integers, each of which is in the list shown.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Re: List M (not shown) consists of 8 different integers, each
[#permalink]
01 Oct 2017, 08:54






