Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 14 Nov 2010
Posts: 1

If x is an integer, how many even numbers does set (0, x, [#permalink]
Show Tags
Updated on: 12 Oct 2012, 10:42
Question Stats:
46% (01:18) correct 54% (01:16) wrong based on 340 sessions
HideShow timer Statistics
If x is an integer, how many even numbers does set (0, x, x^2, x^3,.... x^9) contain? (1) The mean of the set is even (2) The standard deviation of the set is 0
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by lhskev on 24 Dec 2010, 11:13.
Last edited by Bunuel on 12 Oct 2012, 10:42, edited 1 time in total.
Edited the question.



Manager
Joined: 25 Jun 2010
Posts: 88

Re: How many even #'s does set X contain? Source: GMAT Club Test [#permalink]
Show Tags
24 Dec 2010, 14:25
Statement 1: Mean = Even => 0+x+x^2+x^3+...+x^9/10 = even
If X is odd, then 0+x+x^2+x^3+...+x^9 = 0 + Odd + Odd + .. + odd (total 9 times Odd) = Odd So, x is Even, There for all the members of the set are Even.  Sufficient
Statement 2: The standard deviation of the set is 0 => All the members are 0 => All the members are Even
 Sufficient
Hence, answer is D.



Math Expert
Joined: 02 Sep 2009
Posts: 46129

Re: How many even #'s does set X contain? Source: GMAT Club Test [#permalink]
Show Tags
25 Dec 2010, 09:06
lhskev wrote: If X is an integer, how many even numbers does set (0, x, x^2, x^3,.... x^9) contain?
(1) The mean of the set is even (2) The standard deviation of the set is 0
Can someone please explain how to get to this answer?
Thank you. If x is an integer, how many even numbers does set (0, x, x^2, x^3,.... x^9) contain?We have the set with 10 terms: {0, x, x^2, x^3, ..., x^9}. Note that if \(x=odd\) then the set will contain one even (0) and 9 odd terms (as if \(x=odd\), then \(x^2=odd\), \(x^3=odd\), ..., \(x^9=odd\)) and if \(x=even\) then the set will contain all even terms (as if \(x=even\), then \(x^2=even\), \(x^3=even\), ..., \(x^9=even\)). Also note that: standard deviation is always more than or equal to zero: \(SD\geq{0}\). SD is 0 only when the list contains all identical elements (or which is same only 1 element). (1) The mean of the set is even > mean=sum/10=even > sum=10*even=even > 0+x+x^2+x^3+...+x^9=even > x+x^2+x^3+...+x^9=even > x=even (if x=odd then the sum of 9 odd numbers would be odd) > all 10 terms in the set are even. Sufficient. (2) The standard deviation of the set is 0 > all 10 terms are identical > as the first term is 0, then all other terms must equal to zero > all 10 terms in the set are even. Sufficient. Answer: D.
_________________
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: 27 Jul 2010
Posts: 172
Location: Prague
Schools: University of Economics Prague

Re: How many even #'s does set X contain? Source: GMAT Club Test [#permalink]
Show Tags
25 Dec 2010, 16:20
Nice explenation guys.
_________________
You want somethin', go get it. Period!



Manager
Joined: 05 Aug 2011
Posts: 64
Location: United States
Concentration: General Management, Sustainability

Re: How many even #'s does set X contain? Source: GMAT Club Test [#permalink]
Show Tags
01 Oct 2012, 12:49
Bunuel wrote: lhskev wrote: If X is an integer, how many even numbers does set (0, x, x^2, x^3,.... x^9) contain?
(1) The mean of the set is even (2) The standard deviation of the set is 0
Can someone please explain how to get to this answer?
Thank you. If x is an integer, how many even numbers does set (0, x, x^2, x^3,.... x^9) contain?We have the set with 10 terms: {0, x, x^2, x^3, ..., x^9}. Note that if \(x=odd\) then the set will contain one even (0) and 9 odd terms (as if \(x=odd\), then \(x^2=odd\), \(x^3=odd\), ..., \(x^9=odd\)) and if \(x=even\) then the set will contain all even terms (as if \(x=even\), then \(x^2=even\), \(x^3=even\), ..., \(x^9=even\)). Also note that: standard deviation is always more than or equal to zero: \(SD\geq{0}\). SD is 0 only when the list contains all identical elements (or which is same only 1 element). (1) The mean of the set is even > mean=sum/10=even > sum=10*even=even > 0+x+x^2+x^3+...+x^9=even > x+x^2+x^3+...+x^9=even > x=even (if x=odd then the sum of 9 odd numbers would be odd) > all 10 terms in the set are even. Sufficient. (2) The standard deviation of the set is 0 > all 10 terms are identical > as the first term is 0, then all other terms must equal to zero > all 10 terms in the set are even. Sufficient. Answer: D. I am a little confused about statement 1) especially if x is odd. For eg: consider x=3. Now if there are 3 elements in the set, they are (0,3,9). The mean of the set will be (0+3+9)/3=4 which is EVEN Now consider 4 terms in this series with x=3 the set will be (0,3,9,27) then the mean would be (0+3+9+27)/4 = 39/4 which is not even. So x could be odd and still have the Mean of the set to be even. So A is insufficient. What am I missing, thanks



Director
Joined: 22 Mar 2011
Posts: 605
WE: Science (Education)

Re: How many even #'s does set X contain? Source: GMAT Club Test [#permalink]
Show Tags
01 Oct 2012, 13:22
ace312 wrote: Bunuel wrote: lhskev wrote: If X is an integer, how many even numbers does set (0, x, x^2, x^3,.... x^9) contain?
(1) The mean of the set is even (2) The standard deviation of the set is 0
Can someone please explain how to get to this answer?
Thank you. If x is an integer, how many even numbers does set (0, x, x^2, x^3,.... x^9) contain?We have the set with 10 terms: {0, x, x^2, x^3, ..., x^9}. Note that if \(x=odd\) then the set will contain one even (0) and 9 odd terms (as if \(x=odd\), then \(x^2=odd\), \(x^3=odd\), ..., \(x^9=odd\)) and if \(x=even\) then the set will contain all even terms (as if \(x=even\), then \(x^2=even\), \(x^3=even\), ..., \(x^9=even\)). Also note that: standard deviation is always more than or equal to zero: \(SD\geq{0}\). SD is 0 only when the list contains all identical elements (or which is same only 1 element). (1) The mean of the set is even > mean=sum/10=even > sum=10*even=even > 0+x+x^2+x^3+...+x^9=even > x+x^2+x^3+...+x^9=even > x=even (if x=odd then the sum of 9 odd numbers would be odd) > all 10 terms in the set are even. Sufficient. (2) The standard deviation of the set is 0 > all 10 terms are identical > as the first term is 0, then all other terms must equal to zero > all 10 terms in the set are even. Sufficient. Answer: D. I am a little confused about statement 1) especially if x is odd. For eg: consider x=3. Now if there are 3 elements in the set, they are (0,3,9). The mean of the set will be (0+3+9)/3=4 which is EVEN Now consider 4 terms in this series with x=3 the set will be (0,3,9,27) then the mean would be (0+3+9+27)/4 = 39/4 which is not even. So x could be odd and still have the Mean of the set to be even. So A is insufficient. What am I missing, thanks consider x=3. Now if there are 3 elements in the set  You cannot have 3 elements. The set must contain \(0, 3, 3^2,3^3,3^4,...,3^9\)  \(10\) elements.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Intern
Joined: 01 Jun 2012
Posts: 1

Re: How many even #'s does set X contain? Source: GMAT Club Test [#permalink]
Show Tags
12 Oct 2012, 10:36
Can you please explain why we are considering 0 as even, because 0 is mostly treated as nether even nor odd. Hence 2) is insufficient.



Math Expert
Joined: 02 Sep 2009
Posts: 46129

Re: How many even #'s does set X contain? Source: GMAT Club Test [#permalink]
Show Tags
12 Oct 2012, 10:39



Senior Manager
Joined: 06 Aug 2011
Posts: 361

Re: If x is an integer, how many even numbers does set (0, x, [#permalink]
Show Tags
23 Oct 2012, 03:34
Tricky Question ... nice explanation bunuel... I didnt c zero in set..selected option E..
_________________
Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !



Math Expert
Joined: 02 Sep 2009
Posts: 46129

Re: If x is an integer, how many even numbers does set (0, x, [#permalink]
Show Tags
09 Jul 2013, 15:59



Manager
Joined: 23 Jan 2013
Posts: 164
Concentration: Technology, Other
GMAT Date: 01142015
WE: Information Technology (Computer Software)

Re: If x is an integer, how many even numbers does set (0, x, [#permalink]
Show Tags
13 Sep 2014, 22:01
For Stmt A ?
Does it mean if x = odd , then sum is odd , the mean would be = Sum / numbers ( 9 ) in this case which would be
Mean = Sum ( Odd )  == Odd .. so X can only be even here ... 9 ( Odd )



NonHuman User
Joined: 09 Sep 2013
Posts: 6995

Re: If x is an integer, how many even numbers does set (0, x, [#permalink]
Show Tags
05 May 2018, 05:06
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If x is an integer, how many even numbers does set (0, x,
[#permalink]
05 May 2018, 05:06






