Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 27 Oct 2013
Posts: 2

Which of the following triples of numbers have the same
[#permalink]
Show Tags
01 Nov 2013, 06:08
Question Stats:
59% (01:03) correct 41% (01:08) wrong based on 614 sessions
HideShow timer Statistics
Which of the following triples of numbers have the same standard deviation as the numbers r, s, and t? I. r2, s2, t2 II. 0, rs, ts III. r4, s+5, t1 A. I only B. II only C. I and II only D. I and III only E. I, II, and III Please help me figure out II & III. Thanks!
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 65062

Re: Which of the following triples of numbers have the same
[#permalink]
Show Tags
01 Nov 2013, 06:16
zbvl wrote: Which of the following triples of numbers have the same standard deviation as the numbers r, s, and t?
I. r2, s2, t2 II. 0, rs, ts III. r4, s+5, t1
A. I only B. II only C. I and II only D. I and III only E. I, II, and III
Please help me figure out II & III. Thanks! If we add or subtract a constant to each term in a set the standard deviation will not change.Set {r2, s2, t2} is obtained by subtracting 2 from each term of {r, s, t}. Set {0, rs, ts} is obtained by subtracting s from each term of {r, s, t}. Set {r4, s+5, t1} is totally different from {r, s, t}. Thus the answer is I and II only. Answer: C.
_________________




Math Expert
Joined: 02 Sep 2009
Posts: 65062

Re: Which of the following triples of numbers have the same
[#permalink]
Show Tags
01 Nov 2013, 06:23
Bunuel wrote: zbvl wrote: Which of the following triples of numbers have the same standard deviation as the numbers r, s, and t?
I. r2, s2, t2 II. 0, rs, ts III. r4, s+5, t1
A. I only B. II only C. I and II only D. I and III only E. I, II, and III
Please help me figure out II & III. Thanks! If we add or subtract a constant to each term in a set the standard deviation will not change.Set {r2, s2, t2} is obtained by subtracting 2 from each term of {r, s, t}. Set {0, rs, ts} is obtained by subtracting s from each term of {r, s, t}. Set {r4, s+5, t1} is totally different from {r, s, t}. Thus the answer is I and II only. Answer: C. Similar questions to practice. PS: ifdisthestandarddeviationxyandzwhatisthestan93979.htmlm1172303.htmlm0571689.html#p1145328m0372087.htmlwhichofthefollowingsetshasthestandarddeviation131485.htmlsetaconsistsofallevenintegersbetween2and110876.htmlsetaconsistsofallprimenumbersbetween10and25setb110874.htmlacertainlistof100datahasanaveragearithmeticmean87743.htmlDS: letsbeafinitesetofconsecutivemultiplesof155075.htmlifqisasetofconsecutiveintegerswhatisthestandard151794.htmlisthestandarddeviationofthenumbersxyandzequalto145906.htmlaresearchercomputedthemeanthemedianandthestandard134893.htmlduringanexperimentsomewaterwasremovedfromeachof94166.htmlwhatissdofgivensetofnumberswhoseaverageis104000.htmlthereisasetofconsecutiveevenintegerswhatisthe98877.htmlHope this helps.
_________________



Manager
Joined: 26 May 2013
Posts: 51

Which of the following triples of numbers have the same
[#permalink]
Show Tags
06 Mar 2015, 00:04
zbvl wrote: Which of the following triples of numbers have the same standard deviation as the numbers r, s, and t?
I. r2, s2, t2 II. 0, rs, ts III. r4, s+5, t1
A. I only B. II only C. I and II only D. I and III only E. I, II, and III
Please help me figure out II & III. Thanks! SD is about finding the squareroot of the sum of difference of Avg of the numbers and the numbers individually. If we can find out the (AvgNumber) set same in given options then we can conclude that the SD is same. In the above problem, the Avg of r,s,t is (r+s+t)/3 and the difference with each of the numbers are (s+t2r)/3, (r+t2s)/3 and (r+s2t)/3. If you try to compute the difference in I & II sets, you will notice that the difference remains same for the sets.



Current Student
Joined: 12 Aug 2015
Posts: 2518

Re: Which of the following triples of numbers have the same
[#permalink]
Show Tags
09 Mar 2016, 03:12
Her the rule is that the standard deviation does not change if we add or subtract same thing from all the numbers Hence C Also never ever make the mistake of choosing numbers here. I used to do that .. as some of them may satisfy the third case too.. Regards
_________________



Director
Joined: 28 Nov 2014
Posts: 806
Concentration: Strategy
GPA: 3.71

Re: Which of the following triples of numbers have the same
[#permalink]
Show Tags
21 Aug 2016, 10:05
Bunuel: Please confirm  When there is a different constant added to a list of numbers, does the standard deviation change? For example: a, b, and c have s.d. 'x' Will a+3, b+7, c+3 have s.d. 'x'?



Board of Directors
Status: Emory Goizueta Alum
Joined: 18 Jul 2015
Posts: 3598

Re: Which of the following triples of numbers have the same
[#permalink]
Show Tags
27 Aug 2016, 10:06
Keats wrote: Bunuel: Please confirm  When there is a different constant added to a list of numbers, does the standard deviation change? For example: a, b, and c have s.d. 'x' Will a+3, b+7, c+3 have s.d. 'x'? Adding or subtracting doesn't change the standard deviation while multiplying or dividing does.
_________________
My LinkedIn abhimahna.  My GMAT Story: From V21 to V40  My MBA Journey: My 10 years long MBA DreamMy Secret Hacks: Best way to use GMATClub  Importance of an Error Log!Verbal Resources: All SC Resources at one place  All CR Resources at one placeGMAT Club Inbuilt Error Log Functionality  View More  Best Reply Functionality on GMAT Club!New Visa Forum  Ask all your Visa Related Questions  here  Have OPT questions?  Post them here. Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for freeCheck our new About Us Page here.  Blog: Subscribe to Question of the Day BlogNew! Executive Assessment (EA) Exam  All you need to know!



Director
Joined: 28 Nov 2014
Posts: 806
Concentration: Strategy
GPA: 3.71

Re: Which of the following triples of numbers have the same
[#permalink]
Show Tags
27 Aug 2016, 11:16
abhimahna wrote: Keats wrote: Bunuel: Please confirm  When there is a different constant added to a list of numbers, does the standard deviation change? For example: a, b, and c have s.d. 'x' Will a+3, b+7, c+3 have s.d. 'x'? Adding or subtracting doesn't change the standard deviation while multiplying or dividing does. Looks like you have not read my question clearly. I understand adding/subtracting doesn't effect s.d. But if I ask you to calculate s.d. for below a) s+1, t + 6, u +4 b) s+1, t+ 1, u+ 1 when you know s.d. of s,t,u is d, what will be your answer?



Current Student
Joined: 12 Aug 2015
Posts: 2518

Re: Which of the following triples of numbers have the same
[#permalink]
Show Tags
27 Aug 2016, 11:52
Keats wrote: abhimahna wrote: Keats wrote: Bunuel: Please confirm  When there is a different constant added to a list of numbers, does the standard deviation change? For example: a, b, and c have s.d. 'x' Will a+3, b+7, c+3 have s.d. 'x'? Adding or subtracting doesn't change the standard deviation while multiplying or dividing does. Looks like you have not read my question clearly. I understand adding/subtracting doesn't effect s.d. But if I ask you to calculate s.d. for below a) s+1, t + 6, u +4 b) s+1, t+ 1, u+ 1 when you know s.d. of s,t,u is d, what will be your answer? HI THERE..! The Thing is => The stem has asked that when will the SD remain the same. It implies SITUATIONS WHEN SD WILL BE SAME IRRESPECTIVE OF THE VALUE OF S,T,URegards Stone Cold
_________________



Director
Joined: 28 Nov 2014
Posts: 806
Concentration: Strategy
GPA: 3.71

Re: Which of the following triples of numbers have the same
[#permalink]
Show Tags
27 Aug 2016, 13:45
stonecold wrote: HI THERE..! The Thing is => The stem has asked that when will the SD remain the same. It impliesSITUATIONS WHEN SD WILL BE SAME IRRESPECTIVE OF THE VALUE OF S,T,U
Regards Stone Cold
Thanks stonecold. As far as this question is concerned, I have no doubts. I just wanted to extend the learning and point that if we add/subtract same constant to r,s, and t there will be no change in the standard deviation and it will remain the same as that of r,s, and t. However, if we add random constant to each r,s, and t then the standard deviation will definitely CHANGE. However, we will have to do calculation to it! So the case is that it should be the *same constant* that is added to r,s, and t. I hope I am able to convey my point.



Manager
Joined: 04 Jan 2014
Posts: 112
GMAT 1: 660 Q48 V32 GMAT 2: 630 Q48 V28 GMAT 3: 680 Q48 V35

Re: Which of the following triples of numbers have the same
[#permalink]
Show Tags
27 Aug 2016, 14:14
Keats wrote: abhimahna wrote: Keats wrote: Bunuel: Please confirm  When there is a different constant added to a list of numbers, does the standard deviation change? For example: a, b, and c have s.d. 'x' Will a+3, b+7, c+3 have s.d. 'x'? Adding or subtracting doesn't change the standard deviation while multiplying or dividing does. Looks like you have not read my question clearly. I understand adding/subtracting doesn't effect s.d. But if I ask you to calculate s.d. for below a) s+1, t + 6, u +4 b) s+1, t+ 1, u+ 1 when you know s.d. of s,t,u is d, what will be your answer? For a, standard deviation will change since different constant is added to each term. For b, standard deviation will not change since same constant is added to each term.



Current Student
Joined: 12 Aug 2015
Posts: 2518

Which of the following triples of numbers have the same
[#permalink]
Show Tags
27 Aug 2016, 15:20
Keats wrote: stonecold wrote: HI THERE..! The Thing is => The stem has asked that when will the SD remain the same. It impliesSITUATIONS WHEN SD WILL BE SAME IRRESPECTIVE OF THE VALUE OF S,T,U
Regards Stone Cold
Thanks stonecold. As far as this question is concerned, I have no doubts. I just wanted to extend the learning and point that if we add/subtract same constant to r,s, and t there will be no change in the standard deviation and it will remain the same as that of r,s, and t. However, if we add random constant to each r,s, and t then the standard deviation will definitely CHANGE. However, we will have to do calculation to it! So the case is that it should be the *same constant* that is added to r,s, and t. I hope I am able to convey my point. This Will clear Any Doubts you have Regarding Standard Deviation => mathstandarddeviation87905.html Regards Stone Cold
_________________



Board of Directors
Status: Emory Goizueta Alum
Joined: 18 Jul 2015
Posts: 3598

Re: Which of the following triples of numbers have the same
[#permalink]
Show Tags
27 Aug 2016, 21:54
Keats wrote: abhimahna wrote: Keats wrote: Bunuel: Please confirm  When there is a different constant added to a list of numbers, does the standard deviation change? For example: a, b, and c have s.d. 'x' Will a+3, b+7, c+3 have s.d. 'x'? Adding or subtracting doesn't change the standard deviation while multiplying or dividing does. Looks like you have not read my question clearly. I understand adding/subtracting doesn't effect s.d. But if I ask you to calculate s.d. for below a) s+1, t + 6, u +4 b) s+1, t+ 1, u+ 1 when you know s.d. of s,t,u is d, what will be your answer? What I meant was adding or subtracting a constant term doesn't change the SD. Its like an AP, when you add or subtract a constant term to each o the term of an AP, it never changes. Hence, in your options above, in a) you are adding a different rem to each of the terms, So SD will change but in b) since you are adding a constant term to each of the terms, it would not have any impact. I hope its clear now.
_________________
My LinkedIn abhimahna.  My GMAT Story: From V21 to V40  My MBA Journey: My 10 years long MBA DreamMy Secret Hacks: Best way to use GMATClub  Importance of an Error Log!Verbal Resources: All SC Resources at one place  All CR Resources at one placeGMAT Club Inbuilt Error Log Functionality  View More  Best Reply Functionality on GMAT Club!New Visa Forum  Ask all your Visa Related Questions  here  Have OPT questions?  Post them here. Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for freeCheck our new About Us Page here.  Blog: Subscribe to Question of the Day BlogNew! Executive Assessment (EA) Exam  All you need to know!



Director
Joined: 28 Nov 2014
Posts: 806
Concentration: Strategy
GPA: 3.71

Re: Which of the following triples of numbers have the same
[#permalink]
Show Tags
27 Aug 2016, 23:10
Thanks abhimahna. Also thank you stonecold for sharing the standard deviation link. It is useful.



Intern
Joined: 14 May 2017
Posts: 38

Re: Which of the following triples of numbers have the same
[#permalink]
Show Tags
20 Nov 2017, 18:32
In case of doubt, we can just put in a value and solve this question.



Manager
Joined: 03 May 2014
Posts: 145
Location: India
WE: Sales (Mutual Funds and Brokerage)

Re: Which of the following triples of numbers have the same
[#permalink]
Show Tags
22 Nov 2017, 00:31
SD=difference of values from the mean(this is simplified definition but will serve the purpose) Calculations are not required but we will do them to get the idea Let r=10 s=15 t=20 mean=10+15+20/3=15 Difference of each value from mean r 1015=5 s 1515=0 t 2015=5 let us look at answer choices r2=102=8 s2=152=13 t2=202=18 Average of new set=8+13+18/3=45/3=15 the difference from mean r2 813=5 s2 1313=0 t2 1813=5 the difference is same as the 1st set and hence SD will be same.
2nd option 0 rs=1015=5 ts=2015=5 this set contains 0,5 and 5 same as 1st set. hence answer is C.



Intern
Joined: 12 Oct 2017
Posts: 34

Re: Which of the following triples of numbers have the same
[#permalink]
Show Tags
23 Nov 2017, 08:17
The rule is "the standard deviation of a set will not change If we add/ subtract a constant to each term in a set" => Sd of (r2, s2, t2) = sd of (r,s,t) because set (r2, s2, t2) obtained by subtract each term (r,s,t) by 2. Sd of (0, rs, ts) = sd of (r,s,t) because set (o, rs, ts) obtained by subtract each term (r,s,t) by s. Hence, the answer is C.



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2799

Re: Which of the following triples of numbers have the same
[#permalink]
Show Tags
27 Nov 2017, 10:55
zbvl wrote: Which of the following triples of numbers have the same standard deviation as the numbers r, s, and t?
I. r2, s2, t2 II. 0, rs, ts III. r4, s+5, t1
A. I only B. II only C. I and II only D. I and III only E. I, II, and III We may recall the rule that when we add or subtract the same constant to a set of numbers the standard deviation does not change. Let’s analyze each Roman Numeral: I. r2, s2, t2 Since 2 is subtracted from r, s, and t, the standard deviation is the same as that of r, s, and t. II. 0, rs, ts If we subtract s from r, s, and t, we have r  s, s  s = 0, and t  s, thus the standard deviation is the same as that of r, s, and t. III. r4, s+5, t1 We see that since we subtract/add different numbers to r, s, and t, we do not have the same standard deviation as that of r, s, and t. Answer: C
_________________
5star rated online GMAT quant self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews



Intern
Joined: 09 Nov 2016
Posts: 48
Location: India

Re: Which of the following triples of numbers have the same
[#permalink]
Show Tags
21 Aug 2018, 16:48
Hi Bunuel, Is this question of Must be category or Could be category? Its not explicitly mentioned in Question. I am assuming it to be Must be Question. Is this understanding correct? Thanks in advance!



NonHuman User
Joined: 09 Sep 2013
Posts: 15386

Re: Which of the following triples of numbers have the same
[#permalink]
Show Tags
23 Aug 2019, 22:56
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.
_________________




Re: Which of the following triples of numbers have the same
[#permalink]
23 Aug 2019, 22:56




