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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.
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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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
22 Nov 2007, 07:19
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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.
Answer should be D
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.
Answer should be D
