Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 14 Sep 2010
Posts: 17

If z^n = 1, what is the value of z?
[#permalink]
Show Tags
24 Jan 2011, 08:02
Question Stats:
57% (01:14) correct 43% (01:15) wrong based on 748 sessions
HideShow timer Statistics
If z^n = 1, what is the value of z? (1) n is a non zero integer (2) z > 0
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 59147

Re: If z^n = 1, what is the value of z?
[#permalink]
Show Tags
29 Jun 2012, 05:59
Stiv wrote: If z^n = 1, what is the value of z?
(1) n is a nonzero integer. (2) z > 0
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 nonzero 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. For more on number theory and exponents check: mathnumbertheory88376.htmlDS questions on exponents: search.php?search_id=tag&tag_id=39PS questions on exponents: search.php?search_id=tag&tag_id=60Tough and tricky DS exponents and roots questions with detailed solutions: toughandtrickyexponentsandrootsquestions125967.htmlTough and tricky PS exponents and roots questions with detailed solutions: toughandtrickyexponentsandrootsquestions125956.htmlHope it helps.
_________________



Magoosh CoFounder
Joined: 17 Sep 2011
Posts: 41
Schools: UC Berkeley (Haas)  Class of 2010

Re: If z^n = 1, what is the value of z?
[#permalink]
Show Tags
27 Dec 2011, 11:03
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 nonzero 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.
_________________




Manager
Joined: 16 Feb 2012
Posts: 144
Concentration: Finance, Economics

Re: If z^n = 1, what is the value of z?
[#permalink]
Show Tags
29 Jun 2012, 05:50
If z^n = 1, what is the value of z? (1) n is a nonzero integer. (2) z > 0 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?
_________________
Kudos if you like the post!
Failing to plan is planning to fail.



eGMAT Representative
Joined: 04 Jan 2015
Posts: 3142

Re: If z^n = 1, what is the value of z?
[#permalink]
Show Tags
08 Jan 2015, 05:48
Stiv wrote: If z^n = 1, what is the value of z?
(1) n is a nonzero integer. (2) z > 0
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 nonzero 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 nonzero 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. Hope this helps. Japinder
_________________



Intern
Joined: 13 Oct 2010
Posts: 17
Location: Milpitas, CA

Re: Gmat Prep Number Properties
[#permalink]
Show Tags
24 Jan 2011, 08:10
(1) n is a nonzero integer implies n can be positive or negative integer, which is NOT SUFFICIENT to find z. (2) z > 0 implies that z is any positive value, which is again NOT SUFFICIENT. Combining (1) and (2), we have n is a nonzero integer and z > 0. So, the only possible value of z = 1, and n can be any positive integer, say, 1, 2, 3, 4.... Hence, combining the statements the question can be answered.
_________________
Anurag Mairal, Ph.D., MBA GMAT Expert, Admissions and Career Guidance Gurome, Inc. 18005664043 (USA) +9199201 32411 (India) http://www.facebook.com/Gurome



Math Expert
Joined: 02 Sep 2009
Posts: 59147

Re: If z^n = 1, what is the value of z?
[#permalink]
Show Tags
22 Mar 2015, 06:13
suhasancd wrote: 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 nonzero 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...
_________________



Intern
Joined: 14 Sep 2010
Posts: 17

Re: Gmat Prep Number Properties
[#permalink]
Show Tags
24 Jan 2011, 08:16
I guess my question is , why cant it be B by itself ? Because for the equation to equal 1, what other value can z have knowing its positive, and in that case what would n equal to?
Can you give an example of b insufficient
Thanks



Intern
Joined: 13 Oct 2010
Posts: 17
Location: Milpitas, CA

Re: Gmat Prep Number Properties
[#permalink]
Show Tags
24 Jan 2011, 08:21
tradinggenius wrote: I guess my question is , why cant it be B by itself ? Because for the equation to equal 1, what other value can z have knowing its positive, and in that case what would n equal to?
Can you give an example of b insufficient
Thanks Since z > 0, so z can be 2, 3, 4, 5, 6...or even any fractional value say, \(\frac{1}{2}\), \(\frac{3}{4}\)... Now if we take n = 0, then \(2^0 = 1\) \(3^0 = 1\) Similarly \((\frac{1}{2})^0 = 1\) We don't have any unique value of z. So, statement 2 alone is NOT SUFFICIENT.
_________________
Anurag Mairal, Ph.D., MBA GMAT Expert, Admissions and Career Guidance Gurome, Inc. 18005664043 (USA) +9199201 32411 (India) http://www.facebook.com/Gurome



Intern
Joined: 17 Jul 2013
Posts: 17
Location: India
Concentration: Strategy, International Business
GPA: 3.5
WE: Consulting (Computer Software)

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 nonzero 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..



Intern
Joined: 17 Jul 2013
Posts: 17
Location: India
Concentration: Strategy, International Business
GPA: 3.5
WE: Consulting (Computer Software)

Re: If z^n = 1, what is the value of z?
[#permalink]
Show Tags
22 Mar 2015, 06:23
Bunuel wrote: \(\sqrt{1}=1\), 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..



Math Expert
Joined: 02 Sep 2009
Posts: 59147

Re: If z^n = 1, what is the value of z?
[#permalink]
Show Tags
22 Mar 2015, 06:24
suhasancd wrote: Bunuel wrote: \(\sqrt{1}=1\), 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.
_________________



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15476
Location: United States (CA)

Re: If z^n = 1, what is the value of z?
[#permalink]
Show Tags
09 Sep 2015, 18:19
Hi All, This exponent rule 'concept' is something of a classic in the realm of standardized testing  it serves as a relatively simple way to assess a Test Taker's 'thoroughness of understanding' on a specific concept: Here, the concept is "using exponent rules, and one number raised to one exponent, how many different ways can you get to the number 1?" The first ('obvious') answer is "1 raised to any power = 1" eg. 1^2, 1^50, 1^(3), etc. There are OTHER possibilities though. If your base is 1, then any EVEN exponent will lead us to a total of 1... eg. (1)^2, (1)^4, (1)^(2), etc. Finally, raising any number to the '0 power' will also give us a total of 1... eg. 1^0, 537^0, (13)^0, etc. When dealing with this specific situation, it's important to pay careful attention to the information that you're given. What do you really know about the 'base' and the 'power' involved? If you don't know anything, then you have to consider all of the above possibilities. GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



NonHuman User
Joined: 09 Sep 2013
Posts: 13612

Re: If z^n = 1, what is the value of z?
[#permalink]
Show Tags
16 Jan 2019, 03:07
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.
_________________




Re: If z^n = 1, what is the value of z?
[#permalink]
16 Jan 2019, 03:07






