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If x is an integer, how many even numbers does set (0, x , [#permalink]
22 Nov 2007, 05:03

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

100% (04:29) correct
0% (00:00) wrong based on 2 sessions

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.

Re: DS: Even numbers [#permalink]
22 Nov 2007, 06:14

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, 06:26, edited 1 time in total.

Re: DS: Even numbers [#permalink]
22 Nov 2007, 11:30

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.

gmatclubot

Re: DS: Even numbers
[#permalink]
22 Nov 2007, 11:30