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

1. n is a non zero integer.

2. z > 0.

The official answer is C - both statements are needed.

I chose A because:
- Since n is non zero, the only value z^n =1 is when z =1.
Am I wrong?

Thanks
Lee

Hi guys

I thought the question for a long time, and after posting the question, I realised my mistake, but I couldn't delete the post.

For z^n = 1, and n being a non zero integer, there are 3 possible ways.
a. 1^1 = 1
b. 1^- 1 = 1
c. - 1^2 = 1

Statement 1 not conclusive. Z could be 1 or -1.

Statement 2: z > 0.

==> we need both statements to solve for z.
Answer: C.

absolutely correct.

no reason to delete the post - and very good reasons to keep it (it will help other students who come on here searching for this problem)

Without knowing that z is an integer how come the answer isn't E?

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

1. n is a non zero integer.

2. z > 0.


z = (1^(1/2)) and n = 2 works

and so does:

z = 1 and n = 1

Ron , any thoughts

1^(1/2) is still 1, as is 1^(anything else).
therefore, these two examples comprise just one value, not two values, for z.

Hi folks,

from
A) n is a non-zero integer ; agreed that z could be either +/- 1 for n=2 and thus not sufficient.

but, from
B) z >0 ; the only solution for z^n=1 in this case would be z=1 , as only 1 raised to a power n (where n is any no.) would give the result as 1.

In that case shouldn't B be the answer ? and not C.

Thanks.

its E

example verifying :

Z=5
n=10

the calculation does not give E

SK

steven, please go back and read the explanation in this thread. The correct answer is C. Your numbers do not work in the stated question.

_________________
Jamie Nelson
ManhattanGMAT Instructor

The answer can't be B because (any number) ^ 0 = 1.

yes.
a slight amendment -- this should read "any number except 0", because the expression 0^0 is not actually defined. (any other number to the 0 power is indeed 1, though.)

Sorry To dig an old post but Can you explain to me why the answer is not B? if Z > 1. With this condition there is only 1 value of Z, which is 1 right? 1^(anything) = 1, this satisfies the condition in the questions. Please help.

there are 3 different ways for z^n to be 1:

#1: z = 1, and n can be any value at all.

#2: z = -1, and n can be an even integer. (n can also be a fraction of the form even/odd, but i know that the gmat is not going to get that mathematically advanced.)

#3: z = any number except 0, and n = 0. (note that 0^0 is undefined, but (anything else)^0 is equal to 1.)



this rules out case #3 above, but cases #1 and #2 are still in play. so, z could be either 1 or -1, so the statement is insufficient.




this rules out case #2, but cases #1 and #3 are still in play. so, insufficient (z can be any value in the world except 0, because of statement 3).

--

together:
statement (1) rules out case #3
statement (2) rules out case #2
so we're left with case #1
so z = 1
sufficient.

Wow ... I just love the documentation on this site - I wasted 1 hour trying to figure out why option A is the wrong answer and it took less than a minute to understand it from this site. Kudos.

thanks for the kind words. that's why we made the forum!
glad it's helping you out.

(“documentation” is an interesting choice of words to describe the content on the forum.)

I missed the point that n is a nonzero integer, and thought that any positive number can be reduced to 1 by putting a fraction, value of n, in the power, since the fraction in the power decreses the number, and hence chose the answer E. (Thats wrong)

Even if (1) says that 'n', is a non zero any number the answer would still be the same (C).
You may try to see the (4)^0.0001=1.0001 and so on. You may put any number with any fraction power it reaches towards 1 but never takes the value as 1 (asymptotic in nature). Though GMAT does not check this but wanted to share.

using conventional way:
(1) N is a non zero integer (Say -2, -1, 1, 2) all these values would give you the value of Z only (-1 and 1) : Not sufficient
(2) Z is greater than zero ( say 1, 2, and 3) that will give
1^n= 1, 2^n = 1, and 3^n = 1. All these would be true with n = 0. but n is not given. hence Not sufficient. Though I think, except '0', there are no other number , which will satisfy the equation. But since it is not told, I think we can not assume and choose (B) as an answer.

Taking both together we get following values

Z= 1, n = -2: => 1^-2 = 1 : TRUE
Z=1, n = -1 => 1^-1 = 1 : TRUE
Z=1, n=1 => 1^1 = 1 : TRUE
Z=1, n=2 => 1^2 = 1 : TRUE
Z=2, n=-2 => 2^-2 = 1 : FALSE
Z=2, n=-1 => 2^-1 =1 : FALSE
Z=2, n=1 => 2^1=1 : FALSE

So except 'Z=1', all values of Z> 1 results a FALSE. Hence we get Z=1 as the answer using both the condition. Hence (C) is the right answer.