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

There are only 3 scenarios that exist in which Z^n = 1.

Scenario 1: Z^n = 1, if n =0 . Any variable or number to the power of zero(0) is 1....so, Z^0 = 1
Scenario 2: Z^n = 1, if Z = 1.
Scenario 3: Z^n = 1 , if Z is (-1) AND n is even.

Stmt 1: n is a non zero integer.
So n is not equal to zero. ( scenario 1 is not the case and does not say anything on the other possibilities. So it is Insufficient

Stmt 2: Z>0, implying that Z can be any positive number( not integer - which does not make an difference either) ....1, 2, 3, 3.5 , 4.99 .. and the list goes on...so it is insufficient as well.

Lets combine Stmts 1 and 2.
Given that n is not equal to Zero(0) and Z is postive and for Z^n = 1, then Z must be equal to positive 1 as specified in Scenario 2 above...thus sufficient and C it is.
Hope that helps.

The explanation above is great. Thanks Haaress.

Ayankm, if you still have any trouble understanding that explanation, review the step-by-step video solution. This is GMATPrep question 1225

Best of luck,
-Patrick

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

a. n is a nonzero integer
b. z > 0

z^n = 1
lets see in what all conditions can z^n can be equal to 1

if Z is an integer and n = 0 -------------condition_1
or Z = +/-1 with n as even power -------------condition_2

statement a) n != 0 which means condition_1 is ruled out.
leaves condition2 but this gives us +/- 1 not sufficient

statement b) z>0, this means z could be 1,2,3,4...

combine statement a and b
gives z = 1

hence (C)

st 1: z=1,-1
st 2: z>0
c

well, I think statement 2 alone can be sufficient

Given Z^n = 1 and z>0

The only possible integer of Z here can be 1 unless there are logarithms involved.

Please clarify...

hemanthquartz1 wrote:well, I think statement 2 alone can be sufficient

Given Z^n = 1 and z>0

The only possible integer of Z here can be 1 unless there are logarithms involved.

Please clarify...

Z can take any value if n=0

ex:

2^ 0 =1
3^0 =1
4^0=1
.
.
.

So we cannot determine the unique value of Z - statement 2 insufficient
HTH!!

Got it. Thank you.

IMO, Statement 1 alone is sufficient to answer whereas Statement B alone is not sufficient........ Hence A BTW OA ??

real2008 wrote:IMO, Statement 1 alone is sufficient to answer whereas Statement B alone is not sufficient........ Hence A BTW OA ??

Hi Real,
Statement 1 is not sufficient because z and n could be 1 and 2, but they could also be -1 and 2. We don't know what z is from statement 1.

The official answer is C. This is GMATPrep Question 1225 (detailed solution, video solution)

thanks Patrick_GMATFix!

u r correct.

Please call me Patrick