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

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Manager
Joined: 26 Jun 2007
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If n is an integer and x^(n) x^(-n) = 0, what is the value [#permalink]

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15 Mar 2008, 00:31
2
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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
CEO
Joined: 17 Nov 2007
Posts: 3586
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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Kudos [?]: 3976 [0], given: 360

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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
Joined: 26 Jun 2007
Posts: 104
Followers: 2

Kudos [?]: 67 [0], given: 0

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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
CEO
Joined: 17 Nov 2007
Posts: 3586
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 574

Kudos [?]: 3976 [0], given: 360

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15 Mar 2008, 00:56
Excellent question!!! +2

x=-1 works for even n. Therefore, E
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Manager
Joined: 26 Jun 2007
Posts: 104
Followers: 2

Kudos [?]: 67 [0], given: 0

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20 Mar 2008, 11:38

OA = E
tnx
Re: GmatSet29 Q3   [#permalink] 20 Mar 2008, 11:38
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