Hi All,

I have a very basic conceptual question about DS problems that I want to clarify. I should not be asking such question 1 week before the exam but I was stumped after reading the answer.

The question is:

If (Z)^n =1 what's Z = ?

a) n is a non zero integer

b) Z> 0

My understanding of statement A in this question...n is a non zero so for all values of Z^n=1

i.e wheter (1)^1 or whether (1)^5 the equation Z^n should always be equal to Z.

I mean we cannot consider if n is even or odd.....what that matter evey single value of n has to satisfy the Z^n=1 hence z= -1 is ruled out.

I am not sure I am able to put my thoughts in words... but let me try again ... here

irrespective of value of n the equal Z^n has to be always equal to 1.

Basically if shoudn't evenm consider the case of z= -1.



Please help!

Thanks
Saurabh Malpani

Saurabh,

I completely understand the difficulty in expressing thoughts as words. I battle with that daily, be it at work or at this forum. Nonetheless, I will try to explain how I would go about solving this problem, and maybe that will inadvertently answer your question. :)

Statement (I) to me means:

n can equal 1,2,64,-64,-2, etc. So, for all these figures of n, Z^n still has to equal 1. So, Z^-64=1 and Z^2=1. This leaves only 2 possible values for Z, 1 and -1. Basically, when n is an even exponent (such as 2) or a negative even exponent (such as -2), then Z has 2 values (1 and -1). However, when n is any other value other than 0 and what I just described above (such as 1 or -197), Z = 1. Therefore, as this leaves us with 2 solutions for Z, Statement (I) is insufficient. Note: Z could also be 0 for some of the values of n I mentioned above, but regardless, Statement I is insufficient.

Statement (II) is clearly insufficient on its own.

Together, we know that Z=1.

That might not answer your question, but I hope it helps.

Gmat 5/18 thanks for trying but I am still non convinced. Well statement 1 clearly tells that for any value of n the equation will hold true so why worry if n is even or odd.

Say 1^ 1 , or 1^2, or 1^3 .......1^n or any of the cases the equation Z^n =1 will hold true.

Whereas for
-1^ 1 , or -1^2, or -1^3 .......-1^n for only for few of the cases the equation Z^n =1 will hold true.

You know what as I writing the post I realoized where my reasoning is wrong. It always happens with me that when I start discussing I am better able to expore things that's y I prefer group studies than individual studies. Anyway,

My flaw was that I was considering that for n value of N the equation should hold. Where for some reason I failed to read it for e.x x>0 i.e x is any value greater than zero. Similalrly by saying that n is non negative integer it's like any value.

So dumb for me!! I guess just the day...

But I am glad I am able to eleiminate such stupid question today rather than on exam day!!!

Thanks GMAT 5/18 for reasoning out with me.

Saurabh Malpani

Saurabh,

I will continue to try!

You stated:

Gmat 5/18 thanks for trying but I am still non convinced. Well statement 1 clearly tells that for any value of n the equation will hold true so why worry if n is even or odd.

This is how I look at it. Statement (I) is telling is that n does not = 0. That is all it is stating. Nothing more, nothing less. This means n can be negative, positive, odd, even.

So, the question is, just by knowing that n does not = 0 and that z^n = 1, is this enough information for you to determine what z is? No. Depending on what n is, Z could be 1 or -1 or 0 (please refer to my examples above). So, you can cross off AD (I presume you use the AD/BCE grid or some form of it).

Then, we move to cross off B, and so on and so forth, leaving C.

In the end, to answer you question, why worry if n is even or odd......because if you don't, Z cannot be determined.

Hope this helps! If not, I am sure one of the brilliant GMAT instructors or forum participants will be along shortly to help us both!

Ah, it looks like whilst I was typing my last post, you figured it out. Excellent! Yes, much better today rather than on test day. :)

Meanwhile, my brain continues to hurt from the OG DS question 80 post I submitted earlier.

If you want to have a crack at it, I'd be very grateful. ;)

Hey dude! thank you very much for trying so patiently!! I really appreciate your contribution!!!!

Thanks a ton!

I have already responded to your post you can check out the problem was 1+1 is not 1 but 2
:)

Saurabh Malpani

Yes, a little embarrassed, but relieved at the same time. :)

Thanks!

Good job, but I just want to add a little insight. This is a problem that is greatly facilitated by rephrasing the question before addressing the statements.

If Z^n = 1, there are three possible scenarios:

1. Z = anything, n = 0
2. Z = 1, n = anything
3. Z = -1, n = EVEN exponent (this is the step most students miss!)

From here use your AD/BCE grid.
Statement (1) leaves Z = 1 or -1 (scenarios 2 and 3), so eliminate AD
Statement (2) leaves Z = 1 or anything (scenarios 1 and 2), so eliminate B
Together, only scenario 2 overlaps, so Z = 1. The correct answer is C.