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

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Intern
Joined: 14 Sep 2010
Posts: 17
If z^n = 1, what is the value of z?  [#permalink]

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24 Jan 2011, 08:02
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55% (hard)

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60% (01:14) correct 40% (01:19) wrong based on 176 sessions

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

(1) n is a non zero integer
(2) z > 0
Intern
Joined: 13 Oct 2010
Posts: 21
Location: Milpitas, CA
Re: Gmat Prep Number Properties  [#permalink]

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24 Jan 2011, 08:10
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1
(1) n is a non-zero integer implies n can be positive or negative integer, which is NOT SUFFICIENT to find z.

(2) z > 0 implies that z is any positive value, which is again NOT SUFFICIENT.

Combining (1) and (2), we have n is a non-zero integer and z > 0. So, the only possible value of z = 1, and n can be any positive integer, say, 1, 2, 3, 4....
Hence, combining the statements the question can be answered.

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Anurag Mairal, Ph.D., MBA
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Intern
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Re: Gmat Prep Number Properties  [#permalink]

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24 Jan 2011, 08:16
I guess my question is , why cant it be B by itself ? Because for the equation to equal 1, what other value can z have knowing its positive, and in that case what would n equal to?

Can you give an example of b insufficient

Thanks
Intern
Joined: 13 Oct 2010
Posts: 21
Location: Milpitas, CA
Re: Gmat Prep Number Properties  [#permalink]

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24 Jan 2011, 08:21
I guess my question is , why cant it be B by itself ? Because for the equation to equal 1, what other value can z have knowing its positive, and in that case what would n equal to?

Can you give an example of b insufficient

Thanks

Since z > 0, so z can be 2, 3, 4, 5, 6...or even any fractional value say, $$\frac{1}{2}$$, $$\frac{3}{4}$$...
Now if we take n = 0, then $$2^0 = 1$$
$$3^0 = 1$$
Similarly $$(\frac{1}{2})^0 = 1$$
We don't have any unique value of z. So, statement 2 alone is NOT SUFFICIENT.
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Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
+91-99201 32411 (India)

Math Expert
Joined: 02 Sep 2009
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Re: Gmat Prep Number Properties  [#permalink]

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24 Jan 2011, 08:24
1
If z^n = 1, what is the value of z?
1) n is a non zero integer
2) z > 0

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 n 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 $$n$$ can equal to 1 only. Sufficient.

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Re: If z^n = 1, what is the value of z?  [#permalink]

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16 Jan 2019, 03:07
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Re: If z^n = 1, what is the value of z?   [#permalink] 16 Jan 2019, 03:07
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