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

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

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New post 24 Jan 2011, 08:02
2
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A
B
C
D
E

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

(1) n is a non zero integer
(2) z > 0
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Re: Gmat Prep Number Properties  [#permalink]

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New post 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.

The correct answer is C.

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Re: Gmat Prep Number Properties  [#permalink]

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New post 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
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Re: Gmat Prep Number Properties  [#permalink]

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New post 24 Jan 2011, 08:21
tradinggenius wrote:
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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Re: Gmat Prep Number Properties  [#permalink]

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New post 24 Jan 2011, 08:24
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tradinggenius wrote:
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.

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

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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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