Last visit was: 14 Aug 2024, 03:19 It is currently 14 Aug 2024, 03:19
Toolkit
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

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.

# Which of the following triples of numbers have the same

SORT BY:
Tags:
Show Tags
Hide Tags
Intern
Joined: 27 Oct 2013
Posts: 2
Own Kudos [?]: 171 [144]
Given Kudos: 0
Math Expert
Joined: 02 Sep 2009
Posts: 94937
Own Kudos [?]: 649478 [63]
Given Kudos: 86938
Math Expert
Joined: 02 Sep 2009
Posts: 94937
Own Kudos [?]: 649478 [25]
Given Kudos: 86938
General Discussion
Intern
Joined: 26 May 2013
Posts: 42
Own Kudos [?]: 72 [0]
Given Kudos: 243
Re: Which of the following triples of numbers have the same [#permalink]
zbvl wrote:
Which of the following triples of numbers have the same standard deviation as the numbers r, s, and t?

I. r-2, s-2, t-2
II. 0, r-s, t-s
III. r-4, s+5, t-1

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

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 (Avg-Number) 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+t-2r)/3, (r+t-2s)/3 and (r+s-2t)/3. If you try to compute the difference in I & II sets, you will notice that the difference remains same for the sets.
Alum
Joined: 12 Aug 2015
Posts: 2270
Own Kudos [?]: 3211 [0]
Given Kudos: 893
GRE 1: Q169 V154
Re: Which of the following triples of numbers have the same [#permalink]
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: 750
Own Kudos [?]: 1282 [0]
Given Kudos: 86
Concentration: Strategy
GPA: 3.71
Re: Which of the following triples of numbers have the same [#permalink]
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
Joined: 18 Jul 2015
Status:Emory Goizueta Alum
Posts: 3594
Own Kudos [?]: 5483 [0]
Given Kudos: 346
Re: Which of the following triples of numbers have the same [#permalink]
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.
Director
Joined: 28 Nov 2014
Posts: 750
Own Kudos [?]: 1282 [0]
Given Kudos: 86
Concentration: Strategy
GPA: 3.71
Re: Which of the following triples of numbers have the same [#permalink]
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?
Alum
Joined: 12 Aug 2015
Posts: 2270
Own Kudos [?]: 3211 [0]
Given Kudos: 893
GRE 1: Q169 V154
Re: Which of the following triples of numbers have the same [#permalink]
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 impliesSITUATIONS WHEN SD WILL BE SAME IRRESPECTIVE OF THE VALUE OF S,T,U

Regards
Stone Cold
Director
Joined: 28 Nov 2014
Posts: 750
Own Kudos [?]: 1282 [1]
Given Kudos: 86
Concentration: Strategy
GPA: 3.71
Re: Which of the following triples of numbers have the same [#permalink]
1
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.
Senior Manager
Joined: 04 Jan 2014
Posts: 271
Own Kudos [?]: 161 [0]
Given Kudos: 15
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]
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.
Alum
Joined: 12 Aug 2015
Posts: 2270
Own Kudos [?]: 3211 [0]
Given Kudos: 893
GRE 1: Q169 V154
Re: Which of the following triples of numbers have the same [#permalink]
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 =>
math-standard-deviation-87905.html

Regards
Stone Cold
Board of Directors
Joined: 18 Jul 2015
Status:Emory Goizueta Alum
Posts: 3594
Own Kudos [?]: 5483 [0]
Given Kudos: 346
Re: Which of the following triples of numbers have the same [#permalink]
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.
Manager
Joined: 04 May 2014
Posts: 110
Own Kudos [?]: 74 [4]
Given Kudos: 126
Location: India
WE:Sales (Mutual Funds and Brokerage)
Re: Which of the following triples of numbers have the same [#permalink]
1
Kudos
3
Bookmarks
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
10-15=-5
s
15-15=0
t
20-15=5
let us look at answer choices
r-2=10-2=8
s-2=15-2=13
t-2=20-2=18
Average of new set=8+13+18/3=45/3=15
the difference from mean
r-2
8-13=-5
s-2
13-13=0
t-2
18-13=5
the difference is same as the 1st set and hence SD will be same.

2nd option
0
r-s=10-15=-5
t-s=20-15=5
this set contains 0,-5 and 5 same as 1st set.
Intern
Joined: 12 Oct 2017
Posts: 27
Own Kudos [?]: 11 [0]
Given Kudos: 16
Re: Which of the following triples of numbers have the same [#permalink]
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 (r-2, s-2, t-2) = sd of (r,s,t) because set (r-2, s-2, t-2) obtained by subtract each term (r,s,t) by 2.
Sd of (0, r-s, t-s) = sd of (r,s,t) because set (o, r-s, t-s) obtained by subtract each term (r,s,t) by s.
Target Test Prep Representative
Joined: 04 Mar 2011
Affiliations: Target Test Prep
Posts: 3036
Own Kudos [?]: 6693 [2]
Given Kudos: 1646
Re: Which of the following triples of numbers have the same [#permalink]
1
Kudos
zbvl wrote:
Which of the following triples of numbers have the same standard deviation as the numbers r, s, and t?

I. r-2, s-2, t-2
II. 0, r-s, t-s
III. r-4, s+5, t-1

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. r-2, s-2, t-2

Since 2 is subtracted from r, s, and t, the standard deviation is the same as that of r, s, and t.

II. 0, r-s, t-s

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. r-4, s+5, t-1

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.

Senior Manager
Joined: 01 Mar 2015
Posts: 409
Own Kudos [?]: 945 [0]
Given Kudos: 42
Location: India
Re: Which of the following triples of numbers have the same [#permalink]
We know, if same thing is added or subtracted to all the terms, standard deviation does not change.
I. r-2, s-2, t-2 (Subtracted 2 from each term) Same
II. 0, r-s, t-s (Subtracted s from each term) Same
III. r-4, s+5, t-1 (no common thing subtracted) Different

Hence, OA is (C).
Non-Human User
Joined: 09 Sep 2013
Posts: 34420
Own Kudos [?]: 864 [0]
Given Kudos: 0
Re: Which of the following triples of numbers have the same [#permalink]
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]
Moderator:
Math Expert
94939 posts