Author 
Message 
TAGS:

Hide Tags

EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16746
Location: United States (CA)

Re: E is a collection of four ODD integers and the greatest
[#permalink]
Show Tags
15 Aug 2018, 19:51
Hi zs2, IF you want to use the numbers +1 and 3 as two of your four odd numbers, then that's absolutely fine; by extension though, since those two values differ by 4, each of the OTHER two ODD numbers in the set would have to be +1, 1 or 3. Thus, your possible Standard Deviations would be... 3, 1, 1, 1.... which has the SAME S.D. as 3, 3, 3, 1, so we only count this option ONCE. 3, 3, 1, 1 3, 3, 1, 1... which has the SAME S.D as 3, 1, 1, 1, so we only count this option ONCE. 3, 1, 1, 1 You still end up with 4 DIFFERENT possible S.D.s This same pattern will occur if you use the numbers 13 and 17 too. GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Manager
Joined: 15 Nov 2017
Posts: 50

Re: E is a collection of four ODD integers and the greatest
[#permalink]
Show Tags
05 Feb 2019, 06:13
Hi Bunuel, Is there a simple algebraic approach to solve this within 2 minutes? I am really getting stuck on this one. Thank you!! KHow Bunuel wrote: I know this question, I've posted it in my topic: http://gmatclub.com/forum/psquestions ... 85897.html But there is a typo, it should be: E is a collection of four ODD integers and the greatest difference between any two integers in E is 4. The standard deviation of E must be one of how many numbers?(A) 3 (B) 4 (C) 5 (D) 6 (E) 7 Let the smallest odd integer be 1, thus the largest one will be 5. We can have following 6 types of sets: 1. {1, 1, 1, 5} > mean=2 > meanx=(1, 1, 1, 3); 2. {1, 1, 3, 5} > mean=2.5 > meanx=(1.5, 1.5, 0.5, 2.5); 3. {1, 1, 5, 5} > mean=3 > meanx=(2, 2, 2, 2); 4. {1, 3, 3, 5} > mean=3 > meanx=(2, 0, 0, 2); 5. {1, 3, 5, 5} > mean=3.5 > meanx=(2.5, 0.5, 1.5, 1.5); 6. {1, 5, 5, 5} > mean=4 > meanx=(3, 1, 1, 1). CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:1. Find the mean, \(m\), of the values. 2. For each value \(x_i\) calculate its deviation (\(mx_i\)) from the mean. 3. Calculate the squares of these deviations. 4. Find the mean of the squared deviations. This quantity is the variance. 5. Take the square root of the variance. The quantity is th SD. Expressed by formula: \(standard \ deviation= \sqrt{variance} = \sqrt{\frac{\sum(mx_i)^2}{N}}\). You can see that deviation from the mean for 2 pairs of the set is the same, which means that SD of 1 and 6 will be the same and SD of 2 and 5 also will be the same. So SD of such set can take only 4 values. Answer: B. Hope it's clear.



Intern
Joined: 02 Aug 2013
Posts: 3
Concentration: Technology, Leadership
GMAT Date: 11302013

Re: E is a collection of four ODD integers and the greatest
[#permalink]
Show Tags
17 Feb 2019, 02:21
why are we not using negative integers such as (3,1,1,1)



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16746
Location: United States (CA)

Re: E is a collection of four ODD integers and the greatest
[#permalink]
Show Tags
17 Feb 2019, 13:40
Hi shivmsp, IF you want to use the numbers +1 and 3 as two of your four odd numbers, then that's absolutely fine; by extension though, since those two values differ by 4, each of the OTHER two ODD numbers in the set would have to be +1, 1 or 3. Thus, your possible Standard Deviations would be... 3, 1, 1, 1.... which has the SAME S.D. as 3, 3, 3, 1, so we only count this option ONCE. 3, 3, 1, 1 3, 3, 1, 1... which has the SAME S.D as 3, 1, 1, 1, so we only count this option ONCE. 3, 1, 1, 1 You still end up with 4 DIFFERENT possible S.D.s GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Senior Manager
Joined: 10 Apr 2018
Posts: 268
Location: United States (NC)

Re: E is a collection of four ODD integers and the greatest
[#permalink]
Show Tags
07 May 2019, 13:25
Bunuel wrote: I know this question, I've posted it in my topic: http://gmatclub.com/forum/psquestions ... 85897.html But there is a typo, it should be: E is a collection of four ODD integers and the greatest difference between any two integers in E is 4. The standard deviation of E must be one of how many numbers?(A) 3 (B) 4 (C) 5 (D) 6 (E) 7 Let the smallest odd integer be 1, thus the largest one will be 5. We can have following 6 types of sets: 1. {1, 1, 1, 5} > mean=2 > meanx=(1, 1, 1, 3); 2. {1, 1, 3, 5} > mean=2.5 > meanx=(1.5, 1.5, 0.5, 2.5); 3. {1, 1, 5, 5} > mean=3 > meanx=(2, 2, 2, 2); 4. {1, 3, 3, 5} > mean=3 > meanx=(2, 0, 0, 2); 5. {1, 3, 5, 5} > mean=3.5 > meanx=(2.5, 0.5, 1.5, 1.5); 6. {1, 5, 5, 5} > mean=4 > meanx=(3, 1, 1, 1). CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:1. Find the mean, \(m\), of the values. 2. For each value \(x_i\) calculate its deviation (\(mx_i\)) from the mean. 3. Calculate the squares of these deviations. 4. Find the mean of the squared deviations. This quantity is the variance. 5. Take the square root of the variance. The quantity is th SD. Expressed by formula: \(standard \ deviation= \sqrt{variance} = \sqrt{\frac{\sum(mx_i)^2}{N}}\). You can see that deviation from the mean for 2 pairs of the set is the same, which means that SD of 1 and 6 will be the same and SD of 2 and 5 also will be the same. So SD of such set can take only 4 values. Answer: B. Hope it's clear. Hi Bunuel, Just want to clarify, we are told that greatest difference between any two integers is 4. this means that they are odd seines of integers with common difference 4 But in the sets 1. {1, 1, 1, 5} > mean=2 > meanx=(1, 1, 1, 3); 2. {1, 1, 3, 5} > mean=2.5 > meanx=(1.5, 1.5, 0.5, 2.5); 3. {1, 1, 5, 5} > mean=3 > meanx=(2, 2, 2, 2); 4. {1, 3, 3, 5} > mean=3 > meanx=(2, 0, 0, 2); 5. {1, 3, 5, 5} > mean=3.5 > meanx=(2.5, 0.5, 1.5, 1.5); 6. {1, 5, 5, 5} > mean=4 > meanx=(3, 1, 1, 1). if we take difference between any two integers its not 4 Had it been that range is 4 then above set does work . What am i missing?
_________________
Probus
~You Just Can't beat the person who never gives up~ Babe Ruth



Intern
Joined: 03 Jun 2019
Posts: 22

Re: E is a collection of four ODD integers and the greatest
[#permalink]
Show Tags
21 Jun 2019, 04:09
Bunuel wrote: cumulonimbus wrote: Bunuel wrote: I know this question, I've posted it in my topic: http://gmatclub.com/forum/psquestions ... 85897.html But there is a typo, it should be: E is a collection of four ODD integers and the greatest difference between any two integers in E is 4. The standard deviation of E must be one of how many numbers?(A) 3 (B) 4 (C) 5 (D) 6 (E) 7 Let the smallest odd integer be 1, thus the largest one will be 5. We can have following 6 types of sets: 1. {1, 1, 1, 5} > mean=2 > meanx=(1, 1, 1, 3); 2. {1, 1, 3, 5} > mean=2.5 > meanx=(1.5, 1.5, 0.5, 2.5); 3. {1, 1, 5, 5} > mean=3 > meanx=(2, 2, 2, 2); 4. {1, 3, 3, 5} > mean=3 > meanx=(2, 0, 0, 2); 5. {1, 3, 5, 5} > mean=3.5 > meanx=(2.5, 0.5, 1.5, 1.5); 6. {1, 5, 5, 5} > mean=4 > meanx=(3, 1, 1, 1). CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:1. Find the mean, \(m\), of the values. 2. For each value \(x_i\) calculate its deviation (\(mx_i\)) from the mean. 3. Calculate the squares of these deviations. 4. Find the mean of the squared deviations. This quantity is the variance. 5. Take the square root of the variance. The quantity is th SD. Expressed by formula: \(standard \ deviation= \sqrt{variance} = \sqrt{\frac{\sum(mx_i)^2}{N}}\). You can see that deviation from the mean for 2 pairs of the set is the same, which means that SD of 1 and 6 will be the same and SD of 2 and 5 also will be the same. So SD of such set can take only 4 values. Answer: B. Hope it's clear. Hi, in the sets above why aren't sets [3,5,5,5] and [3,3,3,5] considered? Their is no limit on minimum range. This cases are not possible since "the greatest difference between any two integers in E is 4" means that the range of the set is 4. Doesn't The greatest difference between any two integers means the maximum difference of any two integers in this set can have is 4. So why cant we consider sets like {1,1,1,1} and {1,1,3,3} as the difference between any two integers in this set is not exceeding 4. Can you please help to prove how this interpretation is wrong?



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16746
Location: United States (CA)

Re: E is a collection of four ODD integers and the greatest
[#permalink]
Show Tags
21 Jun 2019, 12:57
Hi Sreeragc, The examples that you noted do not fit the 'restrictions' given by the prompt. We're told that the greatest difference between any two of the four numbers IS 4... meaning that the RANGE of the set is 4. IF the question stated that the difference between any two of the numbers was 'no more than 4', then both of your examples would be permissible (since in that situation we'd want a range of 4 OR LESS). GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Intern
Joined: 17 May 2019
Posts: 17

E is a collection of four ODD integers and the greatest
[#permalink]
Show Tags
18 Jul 2019, 10:38
I assumed the numbers to be 2n1,2n+1,2n+3,2n+5 and ended up with distances from the mean as 1,1,3,3 and their variance was 5 .Where is the mistake ? Thanks a lot Bunuel and VeritasKarishma for clarifying



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16746
Location: United States (CA)

Re: E is a collection of four ODD integers and the greatest
[#permalink]
Show Tags
18 Jul 2019, 10:52
Hi GMATestaker, We're told that the greatest difference between any two of the four numbers IS 4... meaning that the RANGE of the set is 4. In your approach, the range of your four values is 6. GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Manager
Joined: 29 Dec 2018
Posts: 97
Location: India
WE: Marketing (Real Estate)

Re: E is a collection of four ODD integers and the greatest
[#permalink]
Show Tags
22 Jul 2019, 19:20
chetan2u, Gladiator59, VeritasKarishmaWhy can't we have a set like (3,3,3,7) in consideration for this question? The greatest difference between any 2 integers is 73=4
_________________
Keep your eyes on the prize: 750



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16746
Location: United States (CA)

Re: E is a collection of four ODD integers and the greatest
[#permalink]
Show Tags
22 Jul 2019, 19:28
Hi DarkHorse2019, You can certainly have a set of numbers as you've described (with the lowest value as 3 and the highest value as 7). The specific group that you listed would have a specific standard deviation. How many OTHER groups of 4 odd numbers can you list that would also have a lowest value of 3 and a highest value of 7 though? The question is asking for the number of different possible Standard Deviations that would fit a particular group  and you've named just one of the options so far. GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10477
Location: Pune, India

Re: E is a collection of four ODD integers and the greatest
[#permalink]
Show Tags
22 Jul 2019, 21:55
DarkHorse2019 wrote: chetan2u, Gladiator59, VeritasKarishmaWhy can't we have a set like (3,3,3,7) in consideration for this question? The greatest difference between any 2 integers is 73=4 This set is considered. Check: https://gmatclub.com/forum/eisacolle ... ml#p815649{1, 1, 1, 5} is exactly the same as {3,3,3,7} as far as SD is considered. Distance from the mean for each element is the same for both sets. {1, 1, 1, 5} Mean = 2 Distance of 2 from mean = 1 Distance of 5 from mean = 3 {3,3,3,7} Mean = 4 Distance of 3 from mean = 1 Distance of 7 from mean = 3 But this is just one of the 6 possible sets. Check the link above for the detailed solution.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Re: E is a collection of four ODD integers and the greatest
[#permalink]
22 Jul 2019, 21:55



Go to page
Previous
1 2
[ 32 posts ]

