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
2
This post received KUDOS
26
This post was BOOKMARKED
Question Stats:
59% (00:36) correct 41% (00:36) wrong based on 636 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: 43862

Re: Which of the following triples of numbers have the same [#permalink]
Show Tags
01 Nov 2013, 06:16
13
This post received KUDOS
Expert's post
14
This post was BOOKMARKED
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.
_________________
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



Math Expert
Joined: 02 Sep 2009
Posts: 43862

Re: Which of the following triples of numbers have the same [#permalink]
Show Tags
01 Nov 2013, 06:23
1
This post received KUDOS
Expert's post
9
This post was BOOKMARKED
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.
_________________
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: 26 May 2013
Posts: 65

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.



Retired Moderator
Joined: 12 Aug 2015
Posts: 2424
GRE 1: 323 Q169 V154

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
_________________
Getting into HOLLYWOOD with an MBA Stone Cold's Mock Tests for GMATQuant(700+)



Current Student
Joined: 28 Nov 2014
Posts: 916
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: Aiming MBA
Joined: 18 Jul 2015
Posts: 3076
Location: India
Concentration: Healthcare, Technology
GPA: 3.65
WE: Information Technology (Health Care)

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.
_________________
How I improved from V21 to V40! ? How to use this forum in THE BEST way?



Current Student
Joined: 28 Nov 2014
Posts: 916
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?



Retired Moderator
Joined: 12 Aug 2015
Posts: 2424
GRE 1: 323 Q169 V154

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
_________________
Getting into HOLLYWOOD with an MBA Stone Cold's Mock Tests for GMATQuant(700+)



Current Student
Joined: 28 Nov 2014
Posts: 916
Concentration: Strategy
GPA: 3.71

Re: Which of the following triples of numbers have the same [#permalink]
Show Tags
27 Aug 2016, 13:45
1
This post received KUDOS
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: 120
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.



Retired Moderator
Joined: 12 Aug 2015
Posts: 2424
GRE 1: 323 Q169 V154

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
_________________
Getting into HOLLYWOOD with an MBA Stone Cold's Mock Tests for GMATQuant(700+)



Board of Directors
Status: Aiming MBA
Joined: 18 Jul 2015
Posts: 3076
Location: India
Concentration: Healthcare, Technology
GPA: 3.65
WE: Information Technology (Health Care)

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.
_________________
How I improved from V21 to V40! ? How to use this forum in THE BEST way?



Current Student
Joined: 28 Nov 2014
Posts: 916
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.



Manager
Joined: 14 May 2017
Posts: 55

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: 166
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
1
This post was BOOKMARKED
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: 39

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: 1986

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
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: Which of the following triples of numbers have the same
[#permalink]
27 Nov 2017, 10:55






