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Re: Math: Number Theory [#permalink]
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30 Dec 2010, 10:02
awesome work bunnel.I really appreciate u r work



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Re: Math: Number Theory [#permalink]
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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



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Re: Math: Number Theory [#permalink]
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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 216^32is the last digit 6? What is the last digit of 111^56is the last digit 1?
Any clarification would be helpful.
Thanks for all your help.



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Re: Math: Number Theory [#permalink]
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03 Jan 2011, 08:52
resh924 wrote: 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 216^32is the last digit 6? What is the last digit of 111^56is the last digit 1?
Any clarification would be helpful.
Thanks for all your help. First of all: last digit of 345^27 is the same as that of 5^27 (the same for 216^32 and 111^56); Next: 1 in any integer power is 1; 5^1= 5, 5^2=2 5, 5^3=12 5, ... 6^1= 6, 6^2=3 6, 5^3=21 6, ... So yes, integer ending with 0, 1, 5 or 6, in the integer power k>0, has the same last digit as the base: thus 0, 1, 5, and 6 respectively. Hope it's clear.
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Re: Math: Number Theory [#permalink]
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03 Jan 2011, 10:22
As always, thank you , Bunuel!



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



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Re: Math: Number Theory [#permalink]
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01 Feb 2011, 06:34



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Re: Math: Number Theory [#permalink]
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01 Feb 2011, 09:07
WOW !!! Great !!!! +Kudo



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Re: Math: Number Theory [#permalink]
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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?



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Re: Math: Number Theory [#permalink]
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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



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Re: Math: Number Theory [#permalink]
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21 Feb 2011, 18:03



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Re: Math: Number Theory [#permalink]
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27 Feb 2011, 06:44
Hi Bunuel, I need the list of number theory questions from OG12 and OG11 for both Ps and DS.Have you listed them some where. Thanks in Advance
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Re: Math: Number Theory [#permalink]
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27 Feb 2011, 07:00



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Re: Math: Number Theory [#permalink]
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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
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Re: Math: Number Theory [#permalink]
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27 Feb 2011, 09:12
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 uniqueprimefactorization 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 ...).
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New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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? Extrahard Quant Tests with Brilliant Analytics



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Re: Math: Number Theory [#permalink]
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27 Feb 2011, 10:55
If a is a factor of bc, and gcd(a,b)=1, then a is a factor of c. any particular example.
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Re: Math: Number Theory [#permalink]
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03 Mar 2011, 04:14
Nice work mates....very informative source to kickkkk start my Prep.....



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Re: Math: Number Theory [#permalink]
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06 Mar 2011, 04:50
Can someone please explain the following: 1. "Special Cases" section in "Evenly Spaced Integers" 2. Last digit of a power Thanks.
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Re: Math: Number Theory [#permalink]
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27 May 2011, 07:21
thank you for the great post. I currently use the GMAT Toolkit app, which I highly recommend, when can I expect this update? In addition, when will the Manhattan GMAT books be updated to the app? Thanks,




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