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If x is an integer, how many even numbers does set (0, x ,

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If x is an integer, how many even numbers does set (0, x , [#permalink]

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22 Nov 2007, 06:03
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If x is an integer, how many even numbers does set (0, x , x^2, ..., x^9) contain?

1) The mean of the set is even
2) The standard deviation of the set is 0

Can someone explain to me how we can determine whether the sum of the series is odd or even by looking at Statement 1? For example, does x have to be odd for 0 + x + x^2 + ...+ x^9 to be odd? Why? Thanks.
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22 Nov 2007, 07:14
GK_Gmat wrote:
If x is an integer, how many even numbers does set (0, x , x^2, ..., x^9) contain?

1) The mean of the set is even
2) The standard deviation of the set is 0

Can someone explain to me how we can determine whether the sum of the series is odd or even by looking at Statement 1? For example, does x have to be odd for 0 + x + x^2 + ...+ x^9 to be odd? Why? Thanks.

Im sure I am wrong - but if the SD is 0 - doesn't that mean all the numbers are the same? So if 0 is included, x = 0

Edit - I see A as being suff now... D

Last edited by alrussell on 22 Nov 2007, 07:26, edited 1 time in total.
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22 Nov 2007, 07:19
This is what I think:

1) suff. because the mean is the sum of all number and then divided by the number of numbers. the sum in this case should be even:

sum/# of #'s = even

therefore: sum = (# of #'s) even

The only way you can have the sum of even is when x is even. you can try it. if X is odd, you will not have the total sum as even.

e+o+o+o+o+o+o+o+o+o= odd
e+e+e+e+e+e+e+e+e+e= even

by the way, 0 is even

2) suff. because this means that all the numbers are the same. therefore, when counting from 0 up to x^9, that should be 10 even numbers.

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22 Nov 2007, 11:57
If x is an integer, how many even numbers does set (0, x , x^2, ..., x^9) contain?

1) The mean of the set is even
2) The standard deviation of the set is 0

FROM ONE

the set is composed of x and its exponantials + 0 , the sum of the whole set is even.............you can answer the question ...........suff
from 2

sd = 0 ,....x = 0 ..suff

i say D
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22 Nov 2007, 12:30
GK_Gmat wrote:
If x is an integer, how many even numbers does set (0, x , x^2, ..., x^9) contain?

1) The mean of the set is even
2) The standard deviation of the set is 0

Can someone explain to me how we can determine whether the sum of the series is odd or even by looking at Statement 1? For example, does x have to be odd for 0 + x + x^2 + ...+ x^9 to be odd? Why? Thanks.

if the mean is even, then definitely the sum is also even because even divided by odd or even only be even. only # of elements can be even or odd.

also got D.

1: since there are 10 elements (and out of 10, 9 are power of x), the sum of x and its powers should be even. if x is odd, the sum of x and its powers cannot be even. so x must be even and eventually all are even.

2: SD 0 means all are zero because the set has 0 as an element. when a set has 0 as an element and its SD is 0, then all elements must be 0. so all elements are even.

D.
Re: DS: Even numbers   [#permalink] 22 Nov 2007, 12:30
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