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If x is an integer, how many even numbers does set (0, x, [#permalink]
 24 Dec 2010, 11:13
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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
Last edited by Bunuel on 12 Oct 2012, 10:42, 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]
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.
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Re: How many even #'s does set X contain? Source: GMAT Club Test [#permalink]
25 Dec 2010, 09:06
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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]
25 Dec 2010, 16:20
Nice explenation guys.
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Re: How many even #'s does set X contain? Source: GMAT Club Test [#permalink]
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
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Re: How many even #'s does set X contain? Source: GMAT Club Test [#permalink]
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 - 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]
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.
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Re: How many even #'s does set X contain? Source: GMAT Club Test [#permalink]
12 Oct 2012, 10:39
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Re: If x is an integer, how many even numbers does set (0, x, [#permalink]
23 Oct 2012, 03:34
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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,
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23 Oct 2012, 03:34
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