Aug 25 09:00 AM PDT  12:00 PM PDT Join a FREE 1day verbal workshop and learn how to ace the Verbal section with the best tips and strategies. Limited for the first 99 registrants. Register today! Aug 25 08:00 PM PDT  11:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE. Aug 28 08:00 AM PDT  09:00 AM PDT Join a FREE live webinar with examPAL and Admissionado and learn how to master GMAT Critical Reasoning questions and the 6pointed star of MBA application essay glory. Save your spot today! Aug 30 08:00 PM PDT  11:00 PM PDT We'll be posting questions in DS/PS/SC/CR in competition mode. Detailed and quickest solution will get kudos. Will be collecting new links to all questions in this topic. Here you can also check links to fresh questions posted. Aug 31 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes. Sep 01 07:00 AM PDT  09:00 AM PDT Want to solve 700+ level Algebra questions within 2 minutes? Attend this free webinar to learn how to master the most challenging Inequalities and Absolute Values questions in GMAT Sep 02 08:00 PM PDT  11:00 PM PDT Sign Up, Get $49 Exam Pack 2 FREE. Train to be ready for Round 1 Deadlines with EMPOWERgmat's Score Booster Code: EP22019 Ends: September 2nd
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 13 Jun 2010
Posts: 14

Is the standard deviation of numbers w, x, y and z greater than 2?
[#permalink]
Show Tags
10 Aug 2010, 19:43
Question Stats:
58% (01:31) correct 42% (01:11) wrong based on 118 sessions
HideShow timer Statistics
Is the standard deviation of numbers w, x, y and z greater than 2? (1) w = 3 (2) The average of the four numbers is 8
Official Answer and Stats are available only to registered users. Register/ Login.




GMAT Tutor
Joined: 24 Jun 2008
Posts: 1834

Re: Is the standard deviation of numbers w, x, y and z greater than 2?
[#permalink]
Show Tags
10 Aug 2010, 21:04
gmatrant wrote: Is the standard deviation of numbers w,x,y and z greater than 2? 1) w=3 2) The average of the four numbers is 8 You might be able to see intuitively why the answer should be C here  if the average of our fourelement set is 8, and one of the elements is equal to 3, then at least one of our elements is pretty far from the mean. That's certainly going to guarantee something about our standard deviation  the standard deviation can't be all that small here. You can prove that the answer is C, at least if you remember how you find the standard deviation (not something you ever need to calculate on the GMAT, incidentally)  you find the distance from each element to the mean, square those distances, average these squares, then finally take the square root. If our mean is 8, and one of our elements is 3, then one of our distances to the mean is 5. So when we add the squares of the distances, our sum must be at least 5^2 = 25. We now take the average of this sum (so here divide by 4); this average is at least 25/4 = 6.25, and the square root of that is greater than 2. So if we use both statements, the standard deviation must be greater than 2, and the answer is C.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com




Director
Status: Apply  Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 18 Jul 2010
Posts: 602
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas

Re: Is the standard deviation of numbers w, x, y and z greater than 2?
[#permalink]
Show Tags
10 Aug 2010, 19:48
(1) w=3 does not say much, insuf (2) average = 8, so sum of all = 32 insuf 1+2 so sum of x, y, z = 29, does not give me a clue E
_________________
Consider kudos, they are good for health



Intern
Joined: 13 Jun 2010
Posts: 14

Re: Is the standard deviation of numbers w, x, y and z greater than 2?
[#permalink]
Show Tags
10 Aug 2010, 22:39
Thanks for the explanation Ian. C is the right answer.



Manager
Joined: 07 Aug 2010
Posts: 57

Re: Is the standard deviation of numbers w, x, y and z greater than 2?
[#permalink]
Show Tags
10 Oct 2010, 16:17
great clue by IanStewart C for the set to have a mean of 8 and smallest element to be 3 => sum of other 3 elements = 29 = 8*4  3 => set can be 3, 9, 10, 10 or can have any other 3 number whose sum is 29. whichever those number are, the sum of the difference between those numbers and mean is always 5. so sd = (5 + 5)/2 = 2.5 > 2
_________________
Click that thing  Give kudos if u like this



Intern
Joined: 15 Mar 2015
Posts: 24

Re: Is the standard deviation of numbers w, x, y and z greater than 2?
[#permalink]
Show Tags
10 Jan 2016, 20:00
I would say the following:
St1) w=3
If all were equal, then SD, would be: w=3, x=3, y=3, z=3 SD=0 If all were different: w=3, x=0, y=3, z=6 SD>2
Insufficient
St2) Avg of w,x,y,z = 8
If all were equal, then SD, would be: w=2, x=2, y=2, z=2 SD=0 If all were different: w=4, x=0, y=0, z=12 SD>2
Insufficient
St1 and St2)
If all were equal, then SD, would be: w=3, x=4, y=3, z=4 SD=0 If all were different: w=3, x=4, y=3, z=12 SD>2
Insufficient



Math Expert
Joined: 02 Sep 2009
Posts: 57272

Re: Is the standard deviation of numbers w, x, y and z greater than 2?
[#permalink]
Show Tags
10 Jan 2016, 22:24
cfpenteado wrote: I would say the following:
St1) w=3
If all were equal, then SD, would be: w=3, x=3, y=3, z=3 SD=0 If all were different: w=3, x=0, y=3, z=6 SD>2
Insufficient
St2) Avg of w,x,y,z = 8
If all were equal, then SD, would be: w=2, x=2, y=2, z=2 SD=0 If all were different: w=4, x=0, y=0, z=12 SD>2
Insufficient
St1 and St2)
If all were equal, then SD, would be: w=3, x=4, y=3, z=4 SD=0 If all were different: w=3, x=4, y=3, z=12 SD>2
Insufficient In your examples the average is never 8. Plus SD of 3, 4, 3, 4 is ~3, not 0.
_________________



Intern
Joined: 15 Mar 2015
Posts: 24

Is the standard deviation of numbers w, x, y and z greater than 2?
[#permalink]
Show Tags
10 Jan 2016, 23:19
Bunuel wrote: cfpenteado wrote: I would say the following:
St1) w=3
If all were equal, then SD, would be: w=3, x=3, y=3, z=3 SD=0 If all were different: w=3, x=0, y=3, z=6 SD>2
Insufficient
St2) Avg of w,x,y,z = 8
If all were equal, then SD, would be: w=2, x=2, y=2, z=2 SD=0 If all were different: w=4, x=0, y=0, z=12 SD>2
Insufficient
St1 and St2)
If all were equal, then SD, would be: w=3, x=4, y=3, z=4 SD=0 If all were different: w=3, x=4, y=3, z=12 SD>2
Insufficient
In your examples the average is never 8. Plus SD of 3, 4, 3, 4 is ~3, not 0. St1) w=3 If all were equal, then SD, would be: w=3, x=3, y=3, z=3 SD=0 If all were different: w=3, x=0, y=3, z=6 SD>2 Insufficient St2) Avg of w,x,y,z = 8 If all were equal, then SD, would be: w=8, x=8, y=8, z=8 SD=0 If all were different: w=4, x=0, y=0, z=36 SD>2 Insufficient St1 and St2) w=3 so the rest will have to sum up to 29. I think by any way I try the set will always have a SD > 2 (more scattered data) an example: w=3, x=5, y=12, z=12 avg = 8 SD > 2 always. In my opinion, SD always > 2. so C I think. Also, corrected my second statement. Thanks Bunuel Sorry Guys, I rushed on this one.



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7766
GPA: 3.82

Re: Is the standard deviation of numbers w, x, y and z greater than 2?
[#permalink]
Show Tags
12 Jan 2016, 00:55
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. Is the standard deviation of numbers w, x, y and z greater than 2? (1) w = 3 (2) The average of the four numbers is 8 In the original condition, there are 4 variables(w,x,y,z), which should match with the number equations. So you need 4 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer. When 1) & 2), standard deviation(d)=root((xaverage)^2 is average). So, d=root{[(38)^2+(x8)^2+(y8)^2+(z8)^2]/4}, which is always yes and sufficient. Therefore, the answer is C. For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 1 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



NonHuman User
Joined: 09 Sep 2013
Posts: 12091

Re: Is the standard deviation of numbers w, x, y and z greater than 2?
[#permalink]
Show Tags
24 Feb 2018, 08:39
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 numbers w, x, y and z greater than 2?
[#permalink]
24 Feb 2018, 08:39






