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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
Posts: 104
Followers: 2

Kudos [?]: 60 [2] , given: 0

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

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14 Mar 2008, 23:31
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This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 550

Kudos [?]: 3565 [0], given: 360

Re: GmatSet29 Q3 [#permalink]

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14 Mar 2008, 23:43
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 [?]: 60 [0], given: 0

Re: GmatSet29 Q3 [#permalink]

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14 Mar 2008, 23:53
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: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 550

Kudos [?]: 3565 [0], given: 360

Re: GmatSet29 Q3 [#permalink]

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14 Mar 2008, 23:56
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 [?]: 60 [0], given: 0

Re: GmatSet29 Q3 [#permalink]

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20 Mar 2008, 10:38
sorry for the late reply

OA = E
tnx
Re: GmatSet29 Q3   [#permalink] 20 Mar 2008, 10:38
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If n is an integer and x^(n) x^(-n) = 0, what is the value

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