Value of Z

[sharath.nair]

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

1. n is a nonzero integer.
2. z is greater than 0.

Please post a solution for the same.

OA is C. I feel B should be alright.

Please clarify.

This is GMAT Prep question.

[albert.chi]

At first I thought that B would be sufficient as well, however this would allow 'z' to be anything, given that 'n' = 0.

So therefore, you need Statement (1) to rule that possibility out.

Hope that helps.

[sharath.nair]

Oh! shucks. I have to consider A and B separately! sometimes get mixed up.. Hope it does not screw me up day after on Test day!

[Ben Ku]

If z^n = 1, then we have a few different scenarios:
(a) z = 1 and n is any number
(b) z = -1 and n is any even integer
(c) z is any nonzero number, and n = 0

With Statement (1), we only rule out (c); it can still be (a) or (b), meaning z = 1 or -1.
With Statement (2), we only rule out (b); z can still be any positive number.

With both together, then the only possibility that works is (a), so z = a.

[adiagr]

If z^n = 1, then we have a few different scenarios:
(a) z = 1 and n is any number
(b) z = -1 and n is any even integer
(c) z is any nonzero number, and n = 0

With Statement (1), we only rule out (c); it can still be (a) or (b), meaning z = 1 or -1.
With Statement (2), we only rule out (b); z can still be any positive number.

With both together, then the only possibility that works is (a), so z = a.

Very nicely explained. I was missing "z= -1" case. Thanks a lot Ben.

Aditya

[RonPurewal]

If z^n = 1, then we have a few different scenarios:
(a) z = 1 and n is any number
(b) z = -1 and n is any even integer
(c) z is any nonzero number, and n = 0

With Statement (1), we only rule out (c); it can still be (a) or (b), meaning z = 1 or -1.
With Statement (2), we only rule out (b); z can still be any positive number.

With both together, then the only possibility that works is (a), so z = a.

Very nicely explained. I was missing "z= -1" case. Thanks a lot Ben.

Aditya

yep.

technically, in that case, n doesn't actually have to be an integer: you can raise -1 to any fractional power of the form (even/odd), and you'll still get 1.

that's a bit advanced for the gmat, but, if you understand it, then you can be quite confident that your understanding of fractional exponents (and your understanding of the exponential behavior of negative numbers) is solid.