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# If z^n = 1, what is the value of z?

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Manager
Joined: 09 Sep 2004
Posts: 165
Followers: 1

Kudos [?]: 1 [1] , given: 0

If z^n = 1, what is the value of z? [#permalink]  22 Nov 2004, 09:14
1
KUDOS
00:00

Difficulty:

65% (hard)

Question Stats:

44% (01:55) correct 56% (00:45) wrong based on 103 sessions
If z^n = 1, what is the value of z?

(1) n is a nonzero integer.
(2) z > 0

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-z-n-1-what-is-the-value-of-z-135081.html
[Reveal] Spoiler: OA
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Director
Joined: 31 Aug 2004
Posts: 610
Followers: 3

Kudos [?]: 59 [0], given: 0

z^n = 1

happens if z=1 whatever n value, OR if n=0 whatever z value

Statement 1 : n is a nonzero integer, so z= 1 enough

Statement 2 : z>0 could be z=1 or not so not enough

My choice is A
Senior Manager
Joined: 19 Oct 2004
Posts: 318
Location: Missouri, USA
Followers: 1

Kudos [?]: 32 [0], given: 0

Ill go with E..

statement 1.. if n=1, z=1, of n=2, then z= +1 or -1. hence, insuff.

statement 2-- very much insuff. no doubt.

combining, Z^n=1, since n is not 0, there is no way of finding out Z ..
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Senior Manager
Joined: 19 May 2004
Posts: 291
Followers: 1

Kudos [?]: 11 [2] , given: 0

2
KUDOS
I'll pick C here.

1) Z could be +1 or (-1) .. we don't know.

2) Z>0 so n=0 or z=1.

together, Z=1.
Director
Joined: 03 Nov 2004
Posts: 867
Followers: 1

Kudos [?]: 21 [0], given: 0

After reading this I have a fundamental question - since this question can be rewritten as z= 1^1/n, isn't z always 1
Manager
Joined: 09 Sep 2004
Posts: 165
Followers: 1

Kudos [?]: 1 [0], given: 0

After reading this I have a fundamental question - since this question can be rewritten as z= 1^1/n, isn't z always 1

rthothad - z can be 1 or -1 if n is even.

Yep the ans is C.
GMAT Club Legend
Joined: 09 Sep 2013
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Kudos [?]: 70 [0], given: 0

Re: Z^n = 1, What is the value of Z? 1. n is a nonzero integer [#permalink]  13 Sep 2013, 06:32
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Re: If z^n = 1, what is the value of z? [#permalink]  13 Sep 2013, 07:56
Expert's post
If z^n = 1, what is the value of z?

(1) n is a non zero integer --> $$1^{any \ integer}=1$$ and also $$(-1)^{even}=1$$, so $$z$$ can be 1 or -1. Not sufficient.

(2) z > 0 --> any nonzero number to the power of 0 is 1, so if $$n=0$$ then $$z$$ can be any non-zero number (any positive number in our case as given that $$z>0$$). Not sufficient.

(1)+(2) $$n$$ is a nonzero integer and $$z>0$$ implies that $$z$$ can equal to 1 only. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-z-n-1-what-is-the-value-of-z-135081.html
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Re: If z^n = 1, what is the value of z?   [#permalink] 13 Sep 2013, 07:56
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