Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Statement 1 is insufficient because Z could be 1 or -1. Let's say n is 2. 1^2 = 1 and (-1)^2 = 1

Statement 2 is insufficient because if n = 0, then Z could be one of many numbers, such as 1 or 2. If Z = 1, 1^0 = 1. If Z = 2, 2^0 = 1. Any non-zero number raised to 0 equals 1.

Statements 1 and 2 combined are sufficient because with statement 1, we know Z is either 1 or -1 and with statement 2 we know Z is greater than 0. So Z must be 1. _________________

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

Show Tags

11 Jan 2012, 15:47

Rephrase: The only possibilities here are Z^0 = 1, where Z is any integer. Also, Z = 1 and n is any integer, including 0.

1. n!=0. This means that Z=1 and n=1 or Z=-1 and n=2. insuff 2. Z>0. This means that Z could be anything positive and n=0. insuff

Together, Z=positive. For the stem to be satisfied, Z has to be 1 regardless of value of n. Suff. _________________

I am the master of my fate. I am the captain of my soul. Please consider giving +1 Kudos if deserved!

DS - If negative answer only, still sufficient. No need to find exact solution. PS - Always look at the answers first CR - Read the question stem first, hunt for conclusion SC - Meaning first, Grammar second RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min

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

Show Tags

11 Jan 2012, 20:48

First rephrase, the value of z^n = 1 in the following three situations: i)Z is anything, and n is 0 ii)Z is -1 or 1 and n is even iii)z is 1 and n is odd.

a) this gets rid of the first option, but z can still be -1 or 1 - Not Sufficient b) No information about n, so z could be 1 but it could also be any other positive number with n = 0.

Together only the third option is left; n is not zero, and z is 1. so C

Zero raised to any power is zero and any number raised to the power of 0 equals one? Is that the rule of it is reversed?

I'm not sure understand the red part in your post above.

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 \(z\) 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 \(z\) can equal to 1 only. Sufficient.

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

Show Tags

07 Jan 2015, 17:13

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Zero raised to any power is zero and any number raised to the power of 0 equals one? Is that the rule of it is reversed?

This is not a difficult question by itself, but clarity of approach matters a lot in getting it right. The low accuracy for this question suggests that most students could not think through this question clearly.

At eGMAT, we strongly advocate that in DS Questions,the student should first analyze the question statement thoroughly and only then move on to analyzing the two statements. You'll see how elegantly this question will simplify with this approach.

We are given that z^n = 1. So, what cases are possible for the value of z and n?

Case 1: z = 1; n has any integral value Case 2: z = -1; n is an even integer Case 3: z has any non-zero value; n = 0

Please note that only after this analysis are we going to the first Statement.

As per the first statement, n is a non-zero integer This rules out Case 3. However, this still leaves out Case 1 and 2. So, z can either be equal to 1 or z can be equal to -1. So, Statement 1 alone is not sufficient.

As per the second statement, z > 0 This rules out Case 2. However, Case 1 and 3 still remain. Again, we have not been able to determine a unique value of z. So, Statement 2 alone is not sufficient either.

Combining both the Statements, From Statement 1, z could either be 1 or -1 From Statement 2, z > 0 Therefore, only possible value of z is 1.

Thus, by combining both the statements together, we have been able to determine a unique value of z. So, the correct answer is Choice C.

Takeaway: The correct answer is only a byproduct of a clear approach.

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

Show Tags

21 Mar 2015, 22:11

Bunuel wrote:

(1) n is a non zero integer --> \(1^{any \ integer}=1\) and also \((-1)^{even}=1\), so \(z\) 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 \(z\) can equal to 1 only. Sufficient.

Answer: C.

Can we take \((\sqrt{1})^2\) as a plug in value to check these statements..

(1) n is a non zero integer --> \(1^{any \ integer}=1\) and also \((-1)^{even}=1\), so \(z\) 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 \(z\) can equal to 1 only. Sufficient.

Answer: C.

Can we take \((\sqrt{1})^2\) as a plug in value to check these statements..

\(\sqrt{1}=1\), so are you asking whether we can plug 1 for n? Well, yes we can... _________________

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

Show Tags

22 Sep 2015, 01:06

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

\(\sqrt{1}=1\), so are you asking whether we can plug 1 for n? Well, yes we can...

Oh.. ya.. I forgot that the square root of a perfect number is always +ve.

\(\sqrt{36}\) = 6 (not -6)

So \(\sqrt{1}\) = 1 (not -1)

I had +/- 1 in my head while combining statements I and II together.

Thanks for your clarification..

Any even root from any postie number is positive.

Apologies if I am asking a stupid question but I re-phrased the question stem "If \(z^n = 1\), what is the value of z" to "If \(z = 1^(^1^/^n^)\)", what is the value of z" and after doing this, statement 1 looks sufficient to answer the question. For any non-zero integer value of n, z will always be 1. Please let me know where am I making a mistake? Thanks in advance!

Regards, Gaurav

gmatclubot

If z^n = 1, what is the value of z?
[#permalink]
12 Oct 2015, 10:29

Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...

As you leave central, bustling Tokyo and head Southwest the scenery gradually changes from urban to farmland. You go through a tunnel and on the other side all semblance...

Ghibli studio’s Princess Mononoke was my first exposure to Japan. I saw it at a sleepover with a neighborhood friend after playing some video games and I was...