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

It is currently 27 Aug 2014, 17:46

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:
1 KUDOS received
Manager
Manager
avatar
Joined: 18 Jan 2012
Posts: 51
Location: United States
Followers: 3

Kudos [?]: 78 [1] , given: 24

Re: Math: Number Theory [#permalink] New post 25 Sep 2012, 09:43
1
This post received
KUDOS
conty911 wrote:
Bunuel wrote:
NUMBER THEORY

Trailing zeros:
Trailing zeros are a sequence of 0's in the decimal representation (or more generally, in any positional representation) of a number, after which no other digits follow.

125000 has 3 trailing zeros;

The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula:

\frac{n}{5}+\frac{n}{5^2}+\frac{n}{5^3}+...+\frac{n}{5^k}, where k must be chosen such that 5^k<n.

It's easier if you look at an example:

How many zeros are in the end (after which no other digits follow) of 32!?
\frac{32}{5}+\frac{32}{5^2}=6+1=7 (denominator must be less than 32, 5^2=25 is less)

Hence, there are 7 zeros in the end of 32!

The formula actually counts the number of factors 5 in n!, but since there are at least as many factors 2, this is equivalent to the number of factors 10, each of which gives one more trailing zero.




I noticed in case the number (n) is multiple of 5^k and we have to find number of trailing zero zeroes, then it will be 5^k<=n rather 5^k<n

no of trailing zeros in 25! =6

\frac{25}{5}+\frac{25}{5^2}= 5+1;
Please correct me, clarify if i'm wrong. Thanks :)


The highest power of a prime number "k" that divides any number "n!" is given by the formula
n/K + n/k^2+n/k^3.. (until numerator becomes lesser than the denominator). Remember to truncate the remainders of each expression

E.g : The highest number of 2's in 10! is
10/2 + 10/4 + 10/8 = 5 + 2 + 1 = 8 (Truncate the reminder of each expression)

As a consequence of this, the number of zeros in n! is controlled by the presence of 5s.
Why ? 2 reasons

a) 10 = 5 x 2,
b) Also in any n!, the number of 5's are far lesser than the number of 2's.

Think about this example.
The number of cars that you make depends on the number of engines. You can have 100 engines and 1000 cars, but you can only make 100 cars (each car needs an engine !)

10 ! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Lets factorize each term ...
10! = (5 x 2) x(3x3)x(2x2x2)x7x(2x3)x(5)X(2x2)x1
the number of 5s = 2
The number of 2s = 7
The number of zeros in 10! = the total number of 5s = 2 (You may use a calc to check this10! = 3628800)

hence in any n! , the number of 5's control the number of zeros.

As a consequence of this, the number of 5's in any n! is
n/5 + n/25 + n/125 ..until numerator becomes lesser than denominator.

Again, i want to emphasize that this formuala only works for prime numbers !!
So to find the number of 10's in any n!, DO NOT DIVIDE by 10 ! (10 is not prime !)
i.e DONT do
n/10 + n/100 + n/1000 - THIS IS WRONG !!!
_________________

-----------------------------------------------------------------------------------------------------
IT TAKES QUITE A BIT OF TIME AND TO POST DETAILED RESPONSES.
YOUR KUDOS IS VERY MUCH APPRECIATED

-----------------------------------------------------------------------------------------------------

3 KUDOS received
Intern
Intern
User avatar
Status: Active
Joined: 30 Jun 2012
Posts: 38
Location: India
Followers: 4

Kudos [?]: 52 [3] , given: 36

Re: Math: Number Theory [#permalink] New post 27 Oct 2012, 01:00
3
This post received
KUDOS
I shall like to add one trick to find square of number :

To find square of a number (ab)^2 where a is tens digit and b is units digit =>

1. Multiply tens digit a by (a+1) i.e. a * (a+1) = A
2. Suffix 25 to the above derived result A and the new number will be A25

Example: what is 35^2?
Solution: 3 * (3+1) = 3*4 = 12 and so answer is 1225
_________________

Thanks and Regards!

P.S. +Kudos Please! in case you like my post. :)

2 KUDOS received
Intern
Intern
User avatar
Status: Active
Joined: 30 Jun 2012
Posts: 38
Location: India
Followers: 4

Kudos [?]: 52 [2] , given: 36

Re: Math: Number Theory [#permalink] New post 27 Oct 2012, 01:34
2
This post received
KUDOS
About Exponents and divisibility:



(a + b)^2 = a^2+ 2ab + b^2 Square of a Sum
(a - b)^2 = a^2 - 2ab + b^2 Square of a Diffe rence


a^n - b^n is always divisble by a-b i.e. irrespective of n being odd or even
Proof:
a^2 - b^2 = (a-b)(a+b)
a^3 - b^3 = (a-b)(a^2+ab+b^2)

Thus divisible by a- b in both cases where n = 2 i.e. even and 3 i.e. odd

a^n + b^n is divisble by a+b i.e. only if n = odd
Proof:
a^3 - b^3 = (a+b)(a^2-ab+b^2)
Thus divisible by a + b as n = 3 i.e. odd
_________________

Thanks and Regards!

P.S. +Kudos Please! in case you like my post. :)

Intern
Intern
avatar
Joined: 14 May 2011
Posts: 10
Followers: 0

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

Re: Math: Number Theory [#permalink] New post 12 Dec 2012, 02:26
Hi,

I'm not sure whether I undertood the below rule correctly:

"Integer ending with 0, 1, 5 or 6, in the integer power k>0, has the same last digit as the base".

55^2 = 3025 - the last digit is same as the base (5) so the above rule works.
55^10 = 253295162119141000 - the last digit is not same as the base (5) so the above rule doesn't work.

Please help if I have misunderstood the rule.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22141
Followers: 3405

Kudos [?]: 24884 [0], given: 2697

Re: Math: Number Theory [#permalink] New post 12 Dec 2012, 02:33
Expert's post
klueless7825 wrote:
Hi,

I'm not sure whether I undertood the below rule correctly:

"Integer ending with 0, 1, 5 or 6, in the integer power k>0, has the same last digit as the base".

55^2 = 3025 - the last digit is same as the base (5) so the above rule works.
55^10 = 25329516211914100[b]0[/b] - the last digit is not same as the base (5) so the above rule doesn't work.

Please help if I have misunderstood the rule.


5 in any positive integer power has 5 as the units digit.

5^1=5;
5^2=25;
5^3=125
...
5^10=253,295,162,119,140,625 (your result was just rounded).

Hope it's clear.
_________________

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

Intern
Intern
avatar
Joined: 25 Dec 2012
Posts: 2
Followers: 0

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

Re: Math: Number Theory [#permalink] New post 25 Dec 2012, 07:33
Thanks for the post!
Expert Post
BSchool Forum Moderator
avatar
Joined: 27 Aug 2012
Posts: 1103
Followers: 77

Kudos [?]: 479 [0], given: 102

Premium Member CAT Tests
Re: Math: Number Theory [#permalink] New post 27 Dec 2012, 10:02
Expert's post
Now this is a huge man..it's really BIG and I think one of the most critical areas tested in GMAT Quant.

You've really done a mammoth job Bunuel..Hats Off..... :)

Kudos !
_________________

UPDATED : e-GMAT SC Resources-Consolidated || ALL RC Resources-Consolidated || ALL SC Resources-Consolidated || UPDATED : AWA compilations-109 Analysis of Argument Essays || NEW !!! GMAC's IR Prep Tool

GMAT Club guide - OG 11-12-13 || Veritas Blog || Manhattan GMAT Blog


KUDOS please, if you like the post or if it helps :-)

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22141
Followers: 3405

Kudos [?]: 24884 [0], given: 2697

Re: Math: Number Theory [#permalink] New post 10 Jul 2013, 23:05
Expert's post
Intern
Intern
avatar
Joined: 07 Jul 2013
Posts: 31
Location: India
Concentration: Finance, Economics
GMAT Date: 08-19-2013
GPA: 3.2
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 8 [0], given: 7

Re: Math: Number Theory [#permalink] New post 12 Jul 2013, 02:12
Great Post. thanks a lot
Intern
Intern
avatar
Joined: 04 Sep 2013
Posts: 17
Followers: 0

Kudos [?]: 0 [0], given: 4

Re: Math: Number Theory [#permalink] New post 15 Sep 2013, 09:04
Hi!!! can you explain the number line?? and how we can figure out the radicals on it???
Intern
Intern
avatar
Joined: 30 Apr 2013
Posts: 16
Location: India
Followers: 5

Kudos [?]: -1 [0], given: 21

Re: Math: Number Theory [#permalink] New post 02 Oct 2013, 19:39
Awesome post.
Bunuel, you are great. Love your posts.
_________________

GMAT RC Vocab - No nonsense(Only for GMAT)
gmat-rc-vocab-no-nonsense-only-for-gmat-162129.html#p1283165

Quant Document to revise a week before exam - Mixedbag
document-to-revise-a-week-before-exam-mixedbag-162145.html

Best questions to revise few days before exam- Mixed bag(25)
best-questions-to-revise-few-days-before-exam-mixed-bag-162124.html#p1283141

Intern
Intern
avatar
Joined: 04 Sep 2013
Posts: 17
Followers: 0

Kudos [?]: 0 [0], given: 4

Re: Math: Number Theory [#permalink] New post 14 Oct 2013, 09:47
can someone explain me this property:

If a is a factor of bc, and gcd(a,b)=1, then a is a factor of c.

???
Intern
Intern
avatar
Joined: 10 Jun 2013
Posts: 10
GMAT 1: 700 Q49 V35
GPA: 3.54
Followers: 0

Kudos [?]: 12 [0], given: 8

Re: Math: Number Theory [#permalink] New post 14 Oct 2013, 10:18
Quite informative and descriptive... all at one place :)
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22141
Followers: 3405

Kudos [?]: 24884 [0], given: 2697

Re: Math: Number Theory [#permalink] New post 17 Oct 2013, 02:33
Expert's post
skamran wrote:
can someone explain me this property:

If a is a factor of bc, and gcd(a,b)=1, then a is a factor of c.

???


Say a=2, b=3 (gcd(a,b)=gcd(2,3)=1), and c=4.

a=2 IS a factor of bc=12, and a=2 IS a factor of c.

OR: if a is a factor of bc and NOT a factor of b, then it must be a factor of c.

Hope it's clear.
_________________

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

Intern
Intern
avatar
Joined: 04 Sep 2013
Posts: 17
Followers: 0

Kudos [?]: 0 [0], given: 4

Re: Math: Number Theory [#permalink] New post 17 Oct 2013, 15:52
Bunuel wrote:
skamran wrote:
can someone explain me this property:

If a is a factor of bc, and gcd(a,b)=1, then a is a factor of c.

???


Say a=2, b=3 (gcd(a,b)=gcd(2,3)=1), and c=4.

a=2 IS a factor of bc=12, and a=2 IS a factor of c.

OR: if a is a factor of bc and NOT a factor of b, then it must be a factor of c.

Hope it's clear.



Yeh Thanks alot!!!
Intern
Intern
User avatar
Joined: 17 Jan 2012
Posts: 30
Location: India
Concentration: General Management, International Business
GMAT 1: 650 Q48 V31
WE: Information Technology (Telecommunications)
Followers: 0

Kudos [?]: 9 [0], given: 13

Re: Math: Number Theory [#permalink] New post 29 Oct 2013, 20:06
Hello Bunuel,

• \sqrt{x^2}=|x|, when x\leq{0}, then \sqrt{x^2}=-x and when x\geq{0}, then \sqrt{x^2}=x

• When the GMAT provides the square root sign for an even root, such as \sqrt{x} or \sqrt[4]{x}, then the only accepted answer is the positive root.

Isn't both of these points contradict each other?

If I consider second point as valid then how can \sqrt{x^2}=|x|, when x\leq{0}, then \sqrt{x^2}=-x be said ?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22141
Followers: 3405

Kudos [?]: 24884 [0], given: 2697

Re: Math: Number Theory [#permalink] New post 29 Oct 2013, 23:31
Expert's post
Phoenix22 wrote:
Hello Bunuel,

• \sqrt{x^2}=|x|, when x\leq{0}, then \sqrt{x^2}=-x and when x\geq{0}, then \sqrt{x^2}=x

• When the GMAT provides the square root sign for an even root, such as \sqrt{x} or \sqrt[4]{x}, then the only accepted answer is the positive root.

Isn't both of these points contradict each other?

If I consider second point as valid then how can \sqrt{x^2}=|x|, when x\leq{0}, then \sqrt{x^2}=-x be said ?


The point here is that square root function can not give negative result: wich means that \sqrt{some \ expression}\geq{0}.

So \sqrt{x^2}\geq{0}. But what does \sqrt{x^2} equal to?

Let's consider following examples:
If x=5 --> \sqrt{x^2}=\sqrt{25}=5=x=positive;
If x=-5 --> \sqrt{x^2}=\sqrt{25}=5=-x=positive.

So we got that:
\sqrt{x^2}=x, if x\geq{0};
\sqrt{x^2}=-x, if x<0.

What function does exactly the same thing? The absolute value function! That is why \sqrt{x^2}=|x|
_________________

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

Intern
Intern
avatar
Joined: 03 Nov 2013
Posts: 2
Followers: 0

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

Re: Math: Number Theory [#permalink] New post 06 Nov 2013, 17:51
this is insanely helpful..thank you so much!!
Intern
Intern
avatar
Joined: 15 Dec 2013
Posts: 3
Followers: 0

Kudos [?]: 0 [0], given: 4

GMAT ToolKit User
Re: Math: Number Theory [#permalink] New post 13 Jan 2014, 19:57
Bunuel wrote:
LAST DIGIT OF A POWER

Determining the last digit of (xyz)^n:

1. Last digit of (xyz)^n is the same as that of z^n;
2. Determine the cyclicity number c of z;
3. Find the remainder r when n divided by the cyclisity;
4. When r>0, then last digit of (xyz)^n is the same as that of z^r and when r=0, then last digit of (xyz)^n is the same as that of z^c, where c is the cyclisity number.

• Integer ending with 0, 1, 5 or 6, in the integer power k>0, has the same last digit as the base.
• Integers ending with 2, 3, 7 and 8 have a cyclicity of 4.
• Integers ending with 4 (eg. (xy4)^n) have a cyclisity of 2. When n is odd (xy4)^n will end with 4 and when n is even (xy4)^n will end with 6.
• Integers ending with 9 (eg. (xy9)^n) have a cyclisity of 2. When n is odd (xy9)^n will end with 9 and when n is even (xy9)^n will end with 1.

Example: What is the last digit of 127^{39}?
Solution: Last digit of 127^{39} is the same as that of 7^{39}. Now we should determine the cyclisity of 7:

1. 7^1=7 (last digit is 7)
2. 7^2=9 (last digit is 9)
3. 7^3=3 (last digit is 3)
4. 7^4=1 (last digit is 1)
5. 7^5=7 (last digit is 7 again!)
...

So, the cyclisity of 7 is 4.

Now divide 39 (power) by 4 (cyclisity), remainder is 3.So, the last digit of 127^{39} is the same as that of the last digit of 7^{39}, is the same as that of the last digit of 7^3, which is 3.



Congratulation and thank you very much for the post, but in the LAST DIGIT OF A POWER i have an issue, when i try to solve the last digit of (456)^35 with the process i just don't get the correct answers, with the process above gives me 6^4 which is 1296=6 and with calculator its 0, can you explain me that case?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22141
Followers: 3405

Kudos [?]: 24884 [0], given: 2697

Re: Math: Number Theory [#permalink] New post 14 Jan 2014, 00:56
Expert's post
mandrake15 wrote:
Bunuel wrote:
LAST DIGIT OF A POWER

Determining the last digit of (xyz)^n:

1. Last digit of (xyz)^n is the same as that of z^n;
2. Determine the cyclicity number c of z;
3. Find the remainder r when n divided by the cyclisity;
4. When r>0, then last digit of (xyz)^n is the same as that of z^r and when r=0, then last digit of (xyz)^n is the same as that of z^c, where c is the cyclisity number.

• Integer ending with 0, 1, 5 or 6, in the integer power k>0, has the same last digit as the base.
• Integers ending with 2, 3, 7 and 8 have a cyclicity of 4.
• Integers ending with 4 (eg. (xy4)^n) have a cyclisity of 2. When n is odd (xy4)^n will end with 4 and when n is even (xy4)^n will end with 6.
• Integers ending with 9 (eg. (xy9)^n) have a cyclisity of 2. When n is odd (xy9)^n will end with 9 and when n is even (xy9)^n will end with 1.

Example: What is the last digit of 127^{39}?
Solution: Last digit of 127^{39} is the same as that of 7^{39}. Now we should determine the cyclisity of 7:

1. 7^1=7 (last digit is 7)
2. 7^2=9 (last digit is 9)
3. 7^3=3 (last digit is 3)
4. 7^4=1 (last digit is 1)
5. 7^5=7 (last digit is 7 again!)
...

So, the cyclisity of 7 is 4.

Now divide 39 (power) by 4 (cyclisity), remainder is 3.So, the last digit of 127^{39} is the same as that of the last digit of 7^{39}, is the same as that of the last digit of 7^3, which is 3.



Congratulation and thank you very much for the post, but in the LAST DIGIT OF A POWER i have an issue, when i try to solve the last digit of (456)^35 with the process i just don't get the correct answers, with the process above gives me 6^4 which is 1296=6 and with calculator its 0, can you explain me that case?


Any integer with 6 as its units digit in any positive integer power has the units digit of 6 (integers ending with 0, 1, 5 or 6, in the integer power k>0, has the same last digit as the base.). For example, (xxx6)^(positive integer) has the units digit of 6.

The reason you get 0 as the units digit of (456)^35 is because it's a huge number and simple calculator rounds the result.

Exact result is: 1,158,162,485,059,181,044,784,824,077,056,791,483,879,723,809,565,243,305,114,019,731,744,476,935,058,125,438,332,149,170,176.

1 trigintillion 158 novemvigintillion 162 octovigintillion 485 septenvigintillion 59 sexvigintillion 181 quinvigintillion 44 quattuorvigintillion 784 trevigintillion 824 duovigintillion 77 unvigintillion 56 vigintillion 791 novemdecillion 483 octodecillion 879 septendecillion 723 sexdecillion 809 quindecillion 565 quattuordecillion 243 tredecillion 305 duodecillion 114 undecillion 19 decillion 731 nonillion 744 octillion 476 septillion 935 sextillion 58 quintillion 125 quadrillion 438 trillion 332 billion 149 million 170 thousand 176

Hope it's clear.
_________________

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] 14 Jan 2014, 00:56
    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
32 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  [ 148 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®.