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If x is an integer, how many even numbers does set (0, x, [#permalink]
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24 Dec 2010, 10:13
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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
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Last edited by Bunuel on 12 Oct 2012, 09:42, edited 1 time in total.
Edited the question.



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Re: How many even #'s does set X contain? Source: GMAT Club Test [#permalink]
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24 Dec 2010, 13:25
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.



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Re: How many even #'s does set X contain? Source: GMAT Club Test [#permalink]
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25 Dec 2010, 08:06
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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.
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Re: How many even #'s does set X contain? Source: GMAT Club Test [#permalink]
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25 Dec 2010, 15:20
Nice explenation guys.
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Re: How many even #'s does set X contain? Source: GMAT Club Test [#permalink]
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01 Oct 2012, 11:49
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



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Re: How many even #'s does set X contain? Source: GMAT Club Test [#permalink]
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01 Oct 2012, 12:22
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.
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Re: How many even #'s does set X contain? Source: GMAT Club Test [#permalink]
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12 Oct 2012, 09:36
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.



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Re: How many even #'s does set X contain? Source: GMAT Club Test [#permalink]
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12 Oct 2012, 09:39



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Re: If x is an integer, how many even numbers does set (0, x, [#permalink]
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23 Oct 2012, 02:34
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Tricky Question ... nice explanation bunuel... I didnt c zero in set..selected option E..
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Re: If x is an integer, how many even numbers does set (0, x, [#permalink]
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09 Jul 2013, 14:59



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Re: If x is an integer, how many even numbers does set (0, x, [#permalink]
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13 Sep 2014, 21:01
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 )



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