Find all School-related info fast with the new School-Specific MBA Forum

It is currently 11 Feb 2016, 07:47
GMAT Club Tests

Close

GMAT Club Daily Prep

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 26 Jun 2011
Posts: 249
Location: India
GMAT 1: 760 Q51 V41
Followers: 12

Kudos [?]: 56 [0], given: 26

If z^n = 1, what is the value of z? [#permalink] New post 27 Dec 2011, 08:38
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

49% (01:34) correct 51% (00:35) wrong based on 310 sessions
If z^n = 1, what is the value of z?

(1) n is a nonzero integer.
(2) z > 0
[Reveal] Spoiler: OA

_________________

The chase begins ...

Expert Post
Magoosh Co-Founder
User avatar
Joined: 17 Sep 2011
Posts: 40
Schools: UC Berkeley (Haas) - Class of 2010
Followers: 24

Kudos [?]: 26 [0], given: 12

Re: If z^n = 1, what is the value of z? [#permalink] New post 27 Dec 2011, 10:03
Expert's post
1
This post was
BOOKMARKED
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.
_________________

Bhavin Parikh
Magoosh Test Prep

Image

Image

Manager
Manager
User avatar
Joined: 29 Jul 2011
Posts: 107
Location: United States
Followers: 5

Kudos [?]: 48 [0], given: 6

Re: If z^n = 1, what is the value of z? [#permalink] New post 11 Jan 2012, 14:47
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

Intern
Intern
avatar
Joined: 06 Dec 2010
Posts: 18
GMAT 1: Q V
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: If z^n = 1, what is the value of z? [#permalink] New post 11 Jan 2012, 19:48
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
1 KUDOS received
Manager
Manager
avatar
Joined: 16 Feb 2012
Posts: 237
Concentration: Finance, Economics
Followers: 6

Kudos [?]: 178 [1] , given: 121

GMAT ToolKit User
Re: If z^n = 1, what is the value of z? [#permalink] New post 29 Jun 2012, 04:50
1
This post received
KUDOS
3
This post was
BOOKMARKED
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.

Expert Post
4 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 31297
Followers: 5358

Kudos [?]: 62404 [4] , given: 9455

Re: If z^n = 1, what is the value of z? [#permalink] New post 29 Jun 2012, 04:59
4
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
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 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.

For more on number theory and exponents check: math-number-theory-88376.html

DS questions on exponents: search.php?search_id=tag&tag_id=39
PS questions on exponents: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

Hope it helps.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
avatar
Joined: 29 Nov 2012
Posts: 902
Followers: 12

Kudos [?]: 709 [0], given: 543

Re: If z^n = 1, what is the value of z? [#permalink] New post 04 Feb 2013, 19:50
Statement 1 is insufficient here are some examples

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.

Examples 2^0 = 1 , 3^0 = 1

not sufficient

together n can't be 0 and Z has to be greater than 1 only one case

1^1 is the answer sufficient. Answer Choice C
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios gmat-prep-software-analysis-and-what-if-scenarios-146146.html

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 8214
Followers: 417

Kudos [?]: 111 [0], given: 0

Top 10 in overall
Re: If z^n = 1, what is the value of z? [#permalink] New post 07 Jan 2015, 16:13
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
e-GMAT Representative
User avatar
Joined: 04 Jan 2015
Posts: 338
Followers: 82

Kudos [?]: 634 [0], given: 83

Re: If z^n = 1, what is the value of z? [#permalink] New post 08 Jan 2015, 04:48
Expert's post
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 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. :-D

Hope this helps.

Japinder
_________________

https://e-gmat.com/courses/quant-live-prep/

Image

Intern
Intern
User avatar
Joined: 17 Jul 2013
Posts: 26
Location: India
Concentration: Strategy, International Business
GPA: 3.5
WE: Consulting (Computer Software)
Followers: 0

Kudos [?]: 7 [0], given: 80

Re: If z^n = 1, what is the value of z? [#permalink] New post 21 Mar 2015, 21:11
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..
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 31297
Followers: 5358

Kudos [?]: 62404 [1] , given: 9455

Re: If z^n = 1, what is the value of z? [#permalink] New post 22 Mar 2015, 05:13
1
This post received
KUDOS
Expert's post
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 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...
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
User avatar
Joined: 17 Jul 2013
Posts: 26
Location: India
Concentration: Strategy, International Business
GPA: 3.5
WE: Consulting (Computer Software)
Followers: 0

Kudos [?]: 7 [0], given: 80

Re: If z^n = 1, what is the value of z? [#permalink] New post 22 Mar 2015, 05:23
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.. :)
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 31297
Followers: 5358

Kudos [?]: 62404 [0], given: 9455

Re: If z^n = 1, what is the value of z? [#permalink] New post 22 Mar 2015, 05:24
Expert's post
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.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 8214
Followers: 417

Kudos [?]: 111 [0], given: 0

Top 10 in overall
Re: If z^n = 1, what is the value of z? [#permalink] New post 22 Sep 2015, 00:06
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern
Intern
avatar
Joined: 21 Apr 2015
Posts: 9
Schools: ISB '17
GMAT 1: 700 Q48 V38
Followers: 0

Kudos [?]: 1 [0], given: 39

If z^n = 1, what is the value of z? [#permalink] New post 12 Oct 2015, 09:29
Bunuel wrote:
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.


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
If z^n = 1, what is the value of z?   [#permalink] 12 Oct 2015, 09:29
    Similar topics Author Replies Last post
Similar
Topics:
If Z^n =1, what is Z ? dreamchase 0 22 Sep 2015, 00:06
1 If z^n=1, what is the value of z? Hyppo 4 12 Jun 2011, 13:07
Experts publish their posts in the topic If z^n = 1, what is the value of z? tradinggenius 4 24 Jan 2011, 07:02
7 Experts publish their posts in the topic If z1, z2, z3,..., zn is a series of consecutive positive swethar 7 02 Mar 2010, 08:23
6 Experts publish their posts in the topic If z1, z2, z3, ..., zn is a series of consecutive positive TheRob 11 19 Aug 2009, 06:35
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.