Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46264

Question Stats:
35% (01:20) correct 65% (00:53) wrong based on 48 sessions
HideShow timer Statistics
Set \(A=\{ 32x, \ 3x, \ 3, \ 3+x, \ 3+2x\}\), where \(x\) is an integer. Is the standard deviation of set A more than the standard deviation of set \(B=\{32x, \ 3x, \ 3, \ 3+x, \ 3+2x, \ y\}\) (1) The standard deviation of set A is positive. (2) \(y=3\).
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
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: 46264

Re M2842 [#permalink]
Show Tags
16 Sep 2014, 01:31
Official Solution: (1) The standard deviation of set A is positive. We know that the standard deviation of any set is more than or equal to zero. The standard deviation of a set is zero only when the set consists of identical elements. So, this statement implies that set A does NOT consists of identical elements or that \(x\) does not equal to zero. Still this statement is not sufficient to answer the question. (2) \(y=3\). The mean of set A is 3. Now, if \(x \neq 0\) for example if \(x=1\), then the standard deviation of B would be smaller than the standard deviation A, since the elements of B would be less widespread than the element of set A. But if \(x=0\), then \(A=\{3, \ 3, \ 3, \ 3, \ 3\}\) and \(B=\{3, \ 3, \ 3, \ 3, \ 3, \ 3\}\), so both will have the standard deviation of zero. Not sufficient. (1)+(2) Since from (1) \(x \neq 0\), then adding a new element which equals to the mean will shrink the standard deviation, thus \(SD(A) \gt SD(B)\). Sufficient. 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



Manager
Joined: 17 Oct 2016
Posts: 93
Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38 GMAT 2: 680 Q48 V35
GPA: 3.05
WE: Pharmaceuticals (Health Care)

Re: M2842 [#permalink]
Show Tags
24 Jul 2017, 13:23
can someone please explain why mean of set A is 3? thanks a ton
_________________
Sometimes you have to burn yourself to the ground before you can rise like a phoenix from the ashes.
Dr. Pratik



Math Expert
Joined: 02 Sep 2009
Posts: 46264

Re: M2842 [#permalink]
Show Tags
24 Jul 2017, 21:04



Manager
Joined: 17 Oct 2016
Posts: 93
Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38 GMAT 2: 680 Q48 V35
GPA: 3.05
WE: Pharmaceuticals (Health Care)

Re: M2842 [#permalink]
Show Tags
24 Jul 2017, 21:09
fitzpratik wrote: can someone please explain why mean of set A is 3? thanks a ton I understood, As the terms are equally spaced out, Median = Mean. so as median is 3, Mean is 3. Am I right?
_________________
Sometimes you have to burn yourself to the ground before you can rise like a phoenix from the ashes.
Dr. Pratik



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1345

Re: M2842 [#permalink]
Show Tags
24 Jul 2017, 21:19
fitzpratik wrote: I understood, As the terms are equally spaced out, Median = Mean. so as median is 3, Mean is 3. Am I right? Yes, you're right. It's an equally spaced set (going up by x from one term to the next), so the median, which is 3, must also be the mean.
_________________
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



Manager
Joined: 17 Oct 2016
Posts: 93
Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38 GMAT 2: 680 Q48 V35
GPA: 3.05
WE: Pharmaceuticals (Health Care)

Re: M2842 [#permalink]
Show Tags
25 Jul 2017, 00:22
Thanks Bunuel and IanStewart
_________________
Sometimes you have to burn yourself to the ground before you can rise like a phoenix from the ashes.
Dr. Pratik



Moderator
Joined: 29 Jan 2015
Posts: 804
Location: India
WE: General Management (NonProfit and Government)

Re: M2842 [#permalink]
Show Tags
03 Feb 2018, 01:53
Bunuel wrote: Official Solution:
(1) The standard deviation of set A is positive. We know that the standard deviation of any set is more than or equal to zero. The standard deviation of a set is zero only when the set consists of identical elements. So, this statement implies that set A does NOT consists of identical elements or that \(x\) does not equal to zero. Still this statement is not sufficient to answer the question. (2) \(y=3\). The mean of set A is 3. Now, if \(x \neq 0\) for example if \(x=1\), then the standard deviation of B would be smaller than the standard deviation A, since the elements of B would be less widespread than the element of set A. But if \(x=0\), then \(A=\{3, \ 3, \ 3, \ 3, \ 3\}\) and \(B=\{3, \ 3, \ 3, \ 3, \ 3, \ 3\}\), so both will have the standard deviation of zero. Not sufficient. (1)+(2) Since from (1) \(x \neq 0\), then adding a new element which equals to the mean will shrink the standard deviation, thus \(SD(A) \gt SD(B)\). Sufficient.
Answer: C Hi Bunuel, Can you please elaborate statement 2 a little more? Even if x is 1 or higher, shouldn't the SD of the set B = the SD of set A as Y which is 3 is the same value as mean and the spread is pretty much the same. Thanks.
_________________
If you liked my post, kindly give me a Kudos. Thanks.



Intern
Joined: 10 Jun 2017
Posts: 23

Re: M2842 [#permalink]
Show Tags
21 Apr 2018, 05:31
Hi Bunnel,
Sets A and B are equal, except for the term Y in set B.
Now, regardless of the value of X, if you don't consider the term Y in set B, the SD would be the same, correct? Because Set B = Set A
Now if we add the term 3 to Set B, the distance of Y to the average is 0, then the addition of the term to the set has no impact on the SD since the distance is zero. Thus, regardless of the value of X, the SD in both sets A and B are equal.
Could u please tell me where did I go wrong?
Thanks a lot










