If n is an integer and x^(n) x^(-n) = 0, what is the value

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If n is an integer and x^(n) x^(-n) = 0, what is the value [#permalink]

15 Mar 2008, 00:31

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If n is an integer and x^(n) – x^(-n) = 0, what is the value of x ?
(1) x is an integer.
(2) n ≠ 0

Pls Explain

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Re: GmatSet29 Q3 [#permalink]

15 Mar 2008, 00:43

B

1. x is an integer: 5^{0} - 5^{-0} = 0 and 7^0 - 7^{-0} = 0. insuff.

2. n ≠ 0: we have to consider two possibilities: x=1 and x=0.

x=1: 1^n - 1^{-n} = 0 works perfect.
x=0: 0^n - 0^{-n} = 0 does not work because 0^{-n} is undefined for n>0 as well as 0^{n} is undefined for n<0.
Therefore, x=1.
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Manager

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Re: GmatSet29 Q3 [#permalink]

15 Mar 2008, 00:53

walker wrote:

B

1. x is an integer: and . insuff.

2. n ≠ 0: we have to consider two possibilities: x=1 and x=0.

x=1: works perfect.
x=0: does not work because is undefined for n>0 as well as is undefined for n<0.
Therefore, x=1.

thats what i thought - B is not the OA im afraid

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Concentration: Entrepreneurship, Other

Schools: Chicago (Booth) - Class of 2011

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Re: GmatSet29 Q3 [#permalink]

15 Mar 2008, 00:56

Excellent question!!! +2

x=-1 works for even n. Therefore, E
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Re: GmatSet29 Q3 [#permalink]

20 Mar 2008, 11:38

sorry for the late reply

OA = E
tnx

Re: GmatSet29 Q3 [#permalink] 20 Mar 2008, 11:38

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If n is an integer and x^(n) x^(-n) = 0, what is the value

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If n is an integer and x^(n) x^(-n) = 0, what is the value

If n is an integer and x^(n) x^(-n) = 0, what is the value

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