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

It is currently 21 Sep 2014, 04:12

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

Math: Number Theory

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 18 Oct 2010
Posts: 3
Followers: 0

Kudos [?]: 2 [0], given: 1

Re: Math: Number Theory [#permalink] New post 19 Nov 2010, 01:18
Quote:
But:
Not all number which yield a remainder of 1 or 5 upon division by 6 are prime, so vise-versa of above property is not correct. For example 25 yields a remainder of 1 upon division be 6 and it's not a prime number.

Hope it's clear.

Understood Sir!
.. i'll just use it one way; i.e, if i'm told that n is a prime number>3, then i can express it as 6n+1 or 6n+5

I think I just got a bit too excited about it that I forgot to thoroughly test it thru... :oops:

thx again for the prompt reply!

Raj
Senior Manager
Senior Manager
avatar
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 333
Followers: 1

Kudos [?]: 68 [0], given: 193

Re: Math: Number Theory [#permalink] New post 05 Dec 2010, 15:36
(a^m)^n=a^{mn} ----------1

(2^2)^2 = 2^2*^2 =2^4

a^m^n=a^{(m^n)} and not (a^m)^n ------------------2

2^2^2 = 2^(2^2) = 2^4

If above example is correct then whats the difference 1 & 2. Please clarify
thanks
_________________

I'm the Dumbest of All !!

Retired Moderator
User avatar
Joined: 02 Sep 2010
Posts: 807
Location: London
Followers: 76

Kudos [?]: 483 [0], given: 25

GMAT ToolKit User GMAT Tests User Reviews Badge
Re: Math: Number Theory [#permalink] New post 05 Dec 2010, 19:36
shrive555 wrote:
(a^m)^n=a^{mn} ----------1

(2^2)^2 = 2^2*^2 =2^4

a^m^n=a^{(m^n)} and not (a^m)^n ------------------2

2^2^2 = 2^(2^2) = 2^4

If above example is correct then whats the difference 1 & 2. Please clarify
thanks



I think its just that you have taken a bad example here. Consider a=2, m=3, b=2

(a^m)^n=(2^3)^2=8^2=64
a^{(m^n)}=2^{(3^2)}=2^9=512
_________________

Math write-ups
1) Algebra-101 2) Sequences 3) Set combinatorics 4) 3-D geometry

My GMAT story

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 333
Followers: 1

Kudos [?]: 68 [0], given: 193

Re: Math: Number Theory [#permalink] New post 05 Dec 2010, 21:16
shrouded1 wrote:
shrive555 wrote:
(a^m)^n=a^{mn} ----------1

(2^2)^2 = 2^2*^2 =2^4

a^m^n=a^{(m^n)} and not (a^m)^n ------------------2

2^2^2 = 2^(2^2) = 2^4

If above example is correct then whats the difference 1 & 2. Please clarify
thanks



I think its just that you have taken a bad example here. Consider a=2, m=3, b=2

(a^m)^n=(2^3)^2=8^2=64
a^{(m^n)}=2^{(3^2)}=2^9=512



In question would that be given explicitly ... i mean the Brackets ( )
_________________

I'm the Dumbest of All !!

Manager
Manager
avatar
Joined: 21 Jul 2010
Posts: 56
Followers: 1

Kudos [?]: 7 [0], given: 3

GMAT ToolKit User
Re: Math: Number Theory [#permalink] New post 30 Dec 2010, 09:39
Thanks for this. It made my life easier! Kudossssssss!
Manager
Manager
avatar
Joined: 08 Jun 2010
Posts: 172
Followers: 1

Kudos [?]: 6 [0], given: 10

Re: Math: Number Theory [#permalink] New post 30 Dec 2010, 10:02
awesome work bunnel.I really appreciate u r work
Manager
Manager
avatar
Joined: 08 Jun 2010
Posts: 172
Followers: 1

Kudos [?]: 6 [0], given: 10

Re: Math: Number Theory [#permalink] New post 30 Dec 2010, 10:11
we need more in GMAT math book.It contain awesome post but few.you are providing all this stuff for free.I hardly believe it.but it's true.
+10
Intern
Intern
avatar
Joined: 04 Dec 2010
Posts: 4
Followers: 0

Kudos [?]: 2 [0], given: 12

Re: Math: Number Theory [#permalink] New post 03 Jan 2011, 08:42
Bunuel,

For determining last digit of a power for numbers 0, 1, 5, and 6, I am not clear on how to determine the last digit.

Your post says:
• Integer ending with 0, 1, 5 or 6, in the integer power k>0, has the same last digit as the base.

What is the last digit of 345^27 ---is the last digit 5?
What is the last digit of 216^32----is the last digit 6?
What is the last digit of 111^56---is the last digit 1?

Any clarification would be helpful.

Thanks for all your help.
Intern
Intern
avatar
Joined: 04 Dec 2010
Posts: 4
Followers: 0

Kudos [?]: 2 [0], given: 12

Re: Math: Number Theory [#permalink] New post 03 Jan 2011, 10:22
As always, thank you , Bunuel! :-D
Senior Manager
Senior Manager
User avatar
Joined: 03 Mar 2010
Posts: 446
Schools: Kelley,Tepper,Carlson,Kenan Flager,Broad
Followers: 4

Kudos [?]: 114 [0], given: 22

GMAT Tests User
Re: Math: Number Theory [#permalink] New post 21 Jan 2011, 05:33
This is THE BEST thing anyone has ever posted. THANK YOU SO MUCH.
_________________

My dad once said to me: Son, nothing succeeds like success.

Intern
Intern
User avatar
Joined: 29 Nov 2010
Posts: 4
Followers: 0

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

Re: Math: Number Theory [#permalink] New post 01 Feb 2011, 06:29
Hi Folks,

I am having a small confusion between two concepts for which one of my practice Q went wrong.
During my elementary school I have studied BODMAS
B - Brackets
O - Of
D- Division
M-Mulitplication
A- Addition
S- Substraction

I tried with this approach and it went wrong, while i was going through this again i happened to see a difference between PEMDAS & BODMAS (Multiplication order is different) .

Can somebody help me to understand which one i should follow.

Thanks
Humble GMAT ASPIRANT :?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23500
Followers: 3508

Kudos [?]: 26577 [0], given: 2713

Re: Math: Number Theory [#permalink] New post 01 Feb 2011, 06:34
Expert's post
gmat709 wrote:
Hi Folks,

I am having a small confusion between two concepts for which one of my practice Q went wrong.
During my elementary school I have studied BODMAS
B - Brackets
O - Of
D- Division
M-Mulitplication
A- Addition
S- Substraction

I tried with this approach and it went wrong, while i was going through this again i happened to see a difference between PEMDAS & BODMAS (Multiplication order is different) .

Can somebody help me to understand which one i should follow.

Thanks
Humble GMAT ASPIRANT :?


The rule mentioned in the initial post is correct.

Anyway: what difference are you talking about? Can you give an example?
_________________

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: 17 Aug 2010
Posts: 90
Followers: 1

Kudos [?]: 5 [0], given: 22

GMAT Tests User
Re: Math: Number Theory [#permalink] New post 01 Feb 2011, 09:07
WOW !!! Great !!!! :thumbup: +Kudo
Intern
Intern
avatar
Joined: 23 Jan 2011
Posts: 8
Followers: 0

Kudos [?]: 1 [0], given: 3

Re: Math: Number Theory [#permalink] New post 21 Feb 2011, 17:41
Quote:
If is a prime number and is a factor of then is a factor of or is a factor of .


2 is a prime number. 2 is a factor of 12*16. This implies that 2 is a factor of both 12 and 16. Am I missing something here?
Intern
Intern
avatar
Joined: 23 Jan 2011
Posts: 8
Followers: 0

Kudos [?]: 1 [0], given: 3

Re: Math: Number Theory [#permalink] New post 21 Feb 2011, 17:44
Quote:
If p is a prime number and p is a factor of ab then p is a factor of a or p is a factor of b.


Sorry did not quote the post correctly
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23500
Followers: 3508

Kudos [?]: 26577 [0], given: 2713

Re: Math: Number Theory [#permalink] New post 21 Feb 2011, 18:03
Expert's post
bugSniper wrote:
Quote:
If p is a prime number and p is a factor of ab then p is a factor of a or p is a factor of b.


Sorry did not quote the post correctly


This is inclusive *or* (as almost always on the GMAT): p is a factor of a or p is a factor of b (or both).
_________________

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

Senior Manager
Senior Manager
avatar
Joined: 10 Nov 2010
Posts: 268
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
Followers: 5

Kudos [?]: 49 [0], given: 22

GMAT Tests User
Re: Math: Number Theory [#permalink] New post 27 Feb 2011, 06:44
Hi Bunuel,

I need the list of number theory questions from OG-12 and OG-11 for both Ps and DS.Have you listed them some where.

Thanks in Advance
_________________

The proof of understanding is the ability to explain it.

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23500
Followers: 3508

Kudos [?]: 26577 [0], given: 2713

Re: Math: Number Theory [#permalink] New post 27 Feb 2011, 07:00
Expert's post
Senior Manager
Senior Manager
avatar
Joined: 10 Nov 2010
Posts: 268
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
Followers: 5

Kudos [?]: 49 [0], given: 22

GMAT Tests User
Re: Math: Number Theory [#permalink] New post 27 Feb 2011, 09:04
Any nonzero natural number n can be factored into primes, written as a product of primes or powers of primes. Moreover, this factorization is unique except for a possible reordering of the factors.

Pls give me the example of bold face text because i am not sure what does it exactly means.

Thanks
_________________

The proof of understanding is the ability to explain it.

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23500
Followers: 3508

Kudos [?]: 26577 [0], given: 2713

Re: Math: Number Theory [#permalink] New post 27 Feb 2011, 09:12
Expert's post
GMATD11 wrote:
Any nonzero natural number n can be factored into primes, written as a product of primes or powers of primes. Moreover, this factorization is unique except for a possible reordering of the factors.

Pls give me the example of bold face text because i am not sure what does it exactly means.

Thanks


It's called the fundamental theorem of arithmetic (or the unique-prime-factorization theorem) which states that any integer greater than 1 can be written as a unique product of prime numbers.

For example: 60=2^2*3*5 --> 60 can be written as a product of primes (powers of primes) only in this unique way (you can just reorder the multiples and write 3*2^2*5 or 2^2*5*3 ...).
_________________

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

Re: Math: Number Theory   [#permalink] 27 Feb 2011, 09:12
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic Number theory..... pzazz12 3 05 Oct 2010, 04:39
33 Experts publish their posts in the topic Math: Number Theory - Percents Bunuel 43 22 Mar 2010, 14:24
8 Experts publish their posts in the topic Math: Number Theory (broken into smaller topics) Bunuel 7 10 Mar 2010, 05:20
NUMBER THEORY vcbabu 5 03 Feb 2009, 10:11
1 NUMBER THEORY vcbabu 2 02 Feb 2009, 10:38
Display posts from previous: Sort by

Math: Number Theory

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page   Previous    1   2   3   4   5   6   7   8    Next  [ 151 posts ] 



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®.