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

It is currently 19 Sep 2014, 02:05

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 x is a positive integer and z is a non-negative integer

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Manager
Manager
avatar
Joined: 09 Feb 2012
Posts: 72
Location: India
Concentration: Marketing, Strategy
GMAT 1: 640 Q48 V31
GPA: 3.45
WE: Marketing (Pharmaceuticals and Biotech)
Followers: 1

Kudos [?]: 29 [1] , given: 41

If x is a positive integer and z is a non-negative integer [#permalink] New post 01 Mar 2012, 23:18
1
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (02:10) correct 40% (01:09) wrong based on 99 sessions
If x is a positive integer and z is a non-negative integer such that 2,066^z is a divisor of 3,176,793, what is the value of z^x - x^z?

A. -81
B. -1
C. 0
D. 1
E. It Cannot Be Determined


Source: http://www.PlatinumGMAT.com
[Reveal] Spoiler: OA

Last edited by pratikbais on 02 Mar 2012, 03:22, edited 2 times in total.
Manhattan GMAT Discount CodesKaplan GMAT Prep Discount CodesGMAT Pill GMAT Discount Codes
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23480
Followers: 3500

Kudos [?]: 26409 [0], given: 2710

Re: Exponential Mess [#permalink] New post 02 Mar 2012, 02:05
Expert's post
3
This post was
BOOKMARKED
pratikbais wrote:
If x is a positive integer and z is a non-negative integer such that (2,066)z is a divisor of, 176,793, what is the value of zx - xz?

A) -81
B) -1
C) 0
D) 1
E) It Cannot Be Determined

An odd number is never divisible by an even number. What value of z could make the expression (2,066)z equal to an odd number that is a factor of any number?


Source: http://www.PlatinumGMAT.com



pratikbais please format the questions properly. Thank you. The question should read:

If x is a positive integer and z is a non-negative integer such that 2,066^z is a divisor of 3,176,793, what is the value of z^x - x^z?
A. -81
B. -1
C. 0
D. 1
E. It Cannot Be Determined

3,176,793 is an odd number. The only way it to be a multiple of 2,066^z (even number in integer power) is when z=0, in this case 2,066^z=2,066^0=1 and 1 is a factor of every integer. Hence z=0 --> z^x-x^z=0^x-x^0=0-1=-1.

Answer: B.

Must know for the GMAT: a^0=1, for a\neq{0} - any nonzero number to the power of 0 is 1. Important note: the case of 0^0 is not tested on the GMAT.

Similar questions to practice:
tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029223
if-n-is-a-non-negative-integer-such-that-12n-is-a-divisor-of-101264.html

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 09 Feb 2012
Posts: 72
Location: India
Concentration: Marketing, Strategy
GMAT 1: 640 Q48 V31
GPA: 3.45
WE: Marketing (Pharmaceuticals and Biotech)
Followers: 1

Kudos [?]: 29 [0], given: 41

Re: If x is a positive integer and z is a non-negative integer [#permalink] New post 02 Mar 2012, 02:49
I think the question reads the same what you suggested Bunuel :-D

Yeah there is a typo in the sentence below the answer choices, sorry for that...
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23480
Followers: 3500

Kudos [?]: 26409 [0], given: 2710

Re: If x is a positive integer and z is a non-negative integer [#permalink] New post 25 Jun 2013, 04:55
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: 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

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 2423
Followers: 196

Kudos [?]: 38 [0], given: 0

Premium Member
Re: If x is a positive integer and z is a non-negative integer [#permalink] New post 02 Aug 2014, 04:33
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

Manager
Manager
User avatar
Joined: 22 Feb 2009
Posts: 229
Followers: 5

Kudos [?]: 34 [0], given: 132

GMAT ToolKit User CAT Tests
Re: If x is a positive integer and z is a non-negative integer [#permalink] New post 02 Aug 2014, 23:37
pratikbais wrote:
If x is a positive integer and z is a non-negative integer such that 2,066^z is a divisor of 3,176,793, what is the value of z^x - x^z?

A. -81
B. -1
C. 0
D. 1
E. It Cannot Be Determined


Source: http://www.PlatinumGMAT.com


Also, 2066^z = a number that ends with digit 6. If you multiply 6 *6*6*..... , it always end with 6 at the end. So 3176793 cannot be divided by 2066, then z= 0 -> B is the answer
_________________

.........................................................................
+1 Kudos please, if you like my post

Re: If x is a positive integer and z is a non-negative integer   [#permalink] 02 Aug 2014, 23:37
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic If x, y, and z are positive integers, is x - y - z positive ? clipea12 2 14 Sep 2014, 22:42
The positive integers x, y and z Countdown 0 03 Jul 2013, 04:08
2 Experts publish their posts in the topic If w, x, y, and z are non-negative integers, each less than abhi758 7 06 May 2010, 00:50
4 Experts publish their posts in the topic If x is a positive integer and z is a non-negative integer jade3 12 28 Nov 2009, 01:56
The positive integers x,y, and z are such that x is a factor uvs_mba 3 01 Nov 2006, 21:37
Display posts from previous: Sort by

If x is a positive integer and z is a non-negative integer

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| 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®.