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# Math: Number Theory

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Manager
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30 Dec 2010, 10:39
Thanks for this. It made my life easier! Kudossssssss!
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30 Dec 2010, 11:02
awesome work bunnel.I really appreciate u r work
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30 Dec 2010, 11:11
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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03 Jan 2011, 09:42
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.

• 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?

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03 Jan 2011, 09:52
1
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Expert's post
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.

• 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?

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=25, 5^3=125, ...
6^1=6, 6^2=36, 5^3=216, ...

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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03 Jan 2011, 11:22
As always, thank you , Bunuel!
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21 Jan 2011, 06:33
This is THE BEST thing anyone has ever posted. THANK YOU SO MUCH.
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01 Feb 2011, 07:29
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
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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01 Feb 2011, 07:34
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
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?
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01 Feb 2011, 10:07
WOW !!! Great !!!! +Kudo
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21 Feb 2011, 18:41
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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21 Feb 2011, 18:44
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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21 Feb 2011, 19:03
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).
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27 Feb 2011, 07:44
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.

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27 Feb 2011, 08:00
GMATD11 wrote:
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.

Sorry, don't have such a list.
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27 Feb 2011, 10:04
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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27 Feb 2011, 10:12
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 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 ...).
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27 Feb 2011, 11:55
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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03 Mar 2011, 05:14
Nice work mates....very informative source to kickkkk start my Prep.....
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06 Mar 2011, 05:50
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] 06 Mar 2011, 05:50

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