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# IF Z^n=1 What is the value of Z ST1 n is nonzero integer ST2

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Joined: 05 Oct 2005
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IF Z^n=1 What is the value of Z ST1 n is nonzero integer ST2 [#permalink]

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28 Nov 2005, 10:50
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IF Z^n=1 What is the value of Z

ST1 n is nonzero integer
ST2 Z is bigger than 0

thanks
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SVP
Joined: 28 May 2005
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28 Nov 2005, 12:52
Z^n=1

it can be having 3 values

if n is not equal to zero, then z^n = z^0 or n=0

or z can be equal to 1 or -1

now statement 1) says n is non zero, it is insufficient because z can be 1 or -1

statement 2 ) says z>0 it also leaves with 2 value of z, 1 or any thing if n is not equal to 0.

but if we combine both the statement we get z = 1

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Director
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Re: DS OG 1O TH 262 [#permalink]

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28 Nov 2005, 17:30
mand-y wrote:
:) IF Z^n=1 What is the value of Z

ST1 n is nonzero integer
ST2 Z is bigger than 0

thanks

St1) If n is a nonzero integer, Z should be 1 or -1.
St2) Z is positive.
St1&2) Z is 1.[/b]
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GMAT Club Legend
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28 Nov 2005, 19:49
If z^n = 1,

- n = 0 and z is any value
- n is any value, z is 1
- n is 2 or multiple of 2, z is 1 or -1

(1) n is nonzero. So n can be 1 or -1 and z is 1, or n can be 2 or -2 and z is 1 or -1. Not sufficient.

(2) z is bigger than 0. To satisfy the given equation, z can be any positive value and n is 0, or z is -1 and n is 2, or z is 1 and n is any value. Not sufficient.

Using (1) and (2), n is non-zero, z is positive, so z can be 1 and n is a odd power (1,3,5..) or z can be 1 and n = any value,

Ans: C

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VP
Joined: 06 Jun 2004
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28 Nov 2005, 20:23
Yup, C for me.

Concur with ywilfred's working

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28 Nov 2005, 20:23
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