Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 02 Jul 2015, 15:58

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is the standard deviation of the numbers X, Y and Z equal to

Author Message
TAGS:
Director
Joined: 29 Nov 2012
Posts: 926
Followers: 12

Kudos [?]: 480 [4] , given: 543

Is the standard deviation of the numbers X, Y and Z equal to [#permalink]  17 Jan 2013, 05:15
4
KUDOS
5
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

78% (01:34) correct 22% (00:48) wrong based on 137 sessions
Is the standard deviation of the numbers X, Y and Z equal to the standard deviation of 10,15 and 20?

(1) Z - X = 10
(2) Z - Y = 5
[Reveal] Spoiler: OA

_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Math Expert
Joined: 02 Sep 2009
Posts: 28252
Followers: 4464

Kudos [?]: 45049 [9] , given: 6640

Re: Is the standard deviation of the numbers X, Y and Z equal to [#permalink]  17 Jan 2013, 05:25
9
KUDOS
Expert's post
3
This post was
BOOKMARKED
Is the standard deviation of the numbers X, Y and Z equal to the standard deviation of 10, 15 and 20?

(1) Z - X = 10. No info about y. Not sufficient.
(2) Z - Y = 5. . No info about x. Not sufficient.

(1)+(2) From above x = z - 10 and y = z - 5, so the set in ascending order is {z-10, z-5, z}. Now, if we add or subtract a constant to each term in a set the standard deviation will not change. Adding 20-z to each term in the set we get {10, 15, 20}. So, the standard deviation of {z-10, z-5, z} is equal to that of {10, 15, 20}. Sufficient.

Hope it's clear.
_________________
Director
Joined: 29 Nov 2012
Posts: 926
Followers: 12

Kudos [?]: 480 [0], given: 543

Re: Is the standard deviation of the numbers X, Y and Z equal to [#permalink]  17 Jan 2013, 05:46
Bunuel wrote:
Is the standard deviation of the numbers X, Y and Z equal to the standard deviation of 10, 15 and 20?

(1) Z - X = 10. No info about y. Not sufficient.
(2) Z - Y = 5. . No info about x. Not sufficient.

(1)+(2) From above x = z - 10 and y = z - 5, so the set in ascending order is {z-10, z-5, z}. Now, if we add or subtract a constant to each term in a set the standard deviation will not change. Adding 20-z to each term in the set we get {10, 15, 20}. So, the standard deviation of {z-10, z-5, z} is equal to that of {10, 15, 20}. Sufficient.

Hope it's clear.

Sweet Trick to solve the question, very helpful!
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5682
Location: Pune, India
Followers: 1413

Kudos [?]: 7328 [3] , given: 186

Re: Is the standard deviation of the numbers X, Y and Z equal to [#permalink]  17 Jan 2013, 20:10
3
KUDOS
Expert's post
fozzzy wrote:
Is the standard deviation of the numbers X, Y and Z equal to the standard deviation of 10,15 and 20?

(1) Z - X = 10
(2) Z - Y = 5

Another way to look at SD is to think in terms of a number line. SD calculates the dispersion of numbers from the mean. The SD of two sets will be the same if the relative placement of numbers from the respective means is the same.

This is what 10, 15 and 20 will look like on a number line
10 .... 15 .... 20
(15 is the mean and 10 and 20 are 5 steps away from the mean. Each dot is a number between 10 and 15 and between 15 and 20)

(1) Z - X = 10
This is what Z and X will look like on the number line
X ......... Z

(2) Z - Y = 5
This is what Z and Y will look like on the number line
Y .... Z

Together, their relative placement on the number line looks like this:
X .... Y .... Z

This matches the placement of 10, 15 and 20 and hence the SD will be the same in the two cases.

For more on number line concepts of SD, check: http://www.veritasprep.com/blog/2012/06 ... deviation/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Senior Manager Joined: 13 Aug 2012 Posts: 464 Concentration: Marketing, Finance GMAT 1: Q V0 GPA: 3.23 Followers: 17 Kudos [?]: 276 [0], given: 11 Re: Is the standard deviation of the numbers X, Y and Z equal to [#permalink] 23 Jan 2013, 05:36 fozzzy wrote: Is the standard deviation of the numbers X, Y and Z equal to the standard deviation of 10,15 and 20? (1) Z - X = 10 (2) Z - Y = 5 1. From the information we know that the gap between Z and X is 10 so we can think of any number with that gap... {5,Y,15} or {10,Y,20} or {50,Y,60}, etc. These sets are similar to the given {10,15,20} in such away that the first and last term are of a distance of 10. Notice that the middle number of {10,15,20} is 15 which is equal to the average = 20+10+15/3 = 15. Now, we do not know the middle number or Y or {X,Y,Z}. If Y is equal to the average then it will have an SD equal to the SD of {10,15,20}. If Y is not equal to the average, then our SD will be greater. INSUFFICIENT! 2. From the information we know that Y and Z are of 5 away from each other {X,15,20} or {X,16,21}, etc. These sets are similar to {10,15,20} in terms of the distance of 2nd to the last term. But, we need to know X to know how spread out are the numbers. If X -Y is 5 then the SD will be the same. If not then the SD will not be the same. INSUFFICIENT! Together: {X,Y,Z} = {i, i+5, i+10} SD is the same with {10,15,20} where i=10: {10, 10+5, 10+10} Answer: C _________________ Impossible is nothing to God. Manager Joined: 04 Dec 2011 Posts: 81 Schools: Smith '16 (I) Followers: 0 Kudos [?]: 15 [0], given: 13 Re: Is the standard deviation of the numbers X, Y and Z equal to [#permalink] 17 Mar 2013, 00:05 well I thought the same way and was going to mark C But I stopped thinking of another case Y....Z.........X I.e this case satisfies the 2 conditions difference between Y and Z is 5 and difference between Z and X is 10, will SD be same in this case too? Sounds a bit stupid, but need to know why this approach is incorrect? _________________ Life is very similar to a boxing ring. Defeat is not final when you fall down… It is final when you refuse to get up and fight back! 1 Kudos = 1 thanks Nikhil Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5682 Location: Pune, India Followers: 1413 Kudos [?]: 7328 [1] , given: 186 Re: Is the standard deviation of the numbers X, Y and Z equal to [#permalink] 17 Mar 2013, 19:29 1 This post received KUDOS Expert's post nikhil007 wrote: well I thought the same way and was going to mark C But I stopped thinking of another case Y....Z.........X I.e this case satisfies the 2 conditions difference between Y and Z is 5 and difference between Z and X is 10, will SD be same in this case too? Sounds a bit stupid, but need to know why this approach is incorrect? Z - X = 10 implies that Z is greater than X by 10 which means Z MUST be to the right of X on the number line. It doesn't matter whether Z and X are both positive, both negative or one positive one negative. You cannot put Z to the left of X on the number line and still have Z - X = 10. This is the reason using number line is a good idea because it gives you a lot of clarity. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5682
Location: Pune, India
Followers: 1413

Kudos [?]: 7328 [1] , given: 186

Re: Is the standard deviation of the numbers X, Y and Z equal to [#permalink]  17 Mar 2013, 19:36
1
KUDOS
Expert's post
nikhil007 wrote:
well I thought the same way and was going to mark C
But I stopped thinking of another case

Y....Z.........X
I.e this case satisfies the 2 conditions difference between Y and Z is 5 and difference between Z and X is 10, will SD be same in this case too?
Sounds a bit stupid, but need to know why this approach is incorrect?

Also, SD of 10, 15, 20 will not be the same as SD of Y....Z.........X (e.g. 5, 10, 20). The distance of the numbers from the mean is not the same in the two cases.

SD of 10, 15, 20 will be the same as SD of 20, 25, 30 or of 41, 46, 51 or of -16, -11, -6 etc.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 01 Feb 2013 Posts: 10 Location: United States Concentration: Finance, Technology GPA: 3 WE: Analyst (Computer Software) Followers: 0 Kudos [?]: 9 [0], given: 9 Re: Is the standard deviation of the numbers X, Y and Z equal to [#permalink] 30 Apr 2013, 09:47 I feel like this problem was easier for me to solve when having this in mind "Is x, y, and Z -- 10, 15, and 20". And then just on C putting z = 20 and calculate. However I realized that it is unnecessary since you can tell that C is sufficient. _________________ Goal: 25 KUDOZ and higher scores for everyone! Intern Joined: 18 Nov 2011 Posts: 37 Concentration: Strategy, Marketing GMAT Date: 06-18-2013 GPA: 3.98 Followers: 0 Kudos [?]: 9 [0], given: 0 Re: Is the standard deviation of the numbers X, Y and Z equal to [#permalink] 30 Apr 2013, 15:52 Is the 700-level rating accurate? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5682 Location: Pune, India Followers: 1413 Kudos [?]: 7328 [1] , given: 186 Re: Is the standard deviation of the numbers X, Y and Z equal to [#permalink] 30 Apr 2013, 21:45 1 This post received KUDOS Expert's post hitman5532 wrote: Is the 700-level rating accurate? I would say 650 - 700. Note that there are certain complications: 1. The concept of SD is not very intuitive to many people which makes this question hard. Once you understand it, you feel its simple. 2. X, Y and Z are not given to be positive so subtraction puts people off sometimes since they feel they have to account for positive as well as negative numbers. Its all in the perception. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 5357
Followers: 310

Kudos [?]: 60 [0], given: 0

Re: Is the standard deviation of the numbers X, Y and Z equal to [#permalink]  13 May 2014, 04:47
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: Is the standard deviation of the numbers X, Y and Z equal to   [#permalink] 13 May 2014, 04:47
Similar topics Replies Last post
Similar
Topics:
2 Is the standard deviation of numbers w,x,y and z greater 5 10 Aug 2010, 18:43
1 Each of the numbers w, x, y, and z is equal to either 0 or 5 19 Jul 2008, 18:18
3 is the standard deviation of number w,x,y,z greater than 2 3 10 Jun 2008, 22:07
Each of the number of w,x,y,z is equal to either 0 or 1. 1 22 Mar 2008, 17:10
A list w,x,y,z, standard deviation d = sqrt( ((w-m)^2 + 8 02 Mar 2006, 11:06
Display posts from previous: Sort by