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Re: Math: Number Theory [#permalink]
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31 Jan 2010, 11:06
Appreciate the very prompt response, walker. To your point re divisibility by 7: I'm having a hard time proving this algebraically, is it a fair statement to say that the only nonprime numbers of the form 6n1 and 6n+1 are the ones that are divisible by 7?
If so, a quick way to check whether a big number is prime would be to: 1) check whether it's of the form 6n1 or 6n+1 2) check whether it's divisible by 7
Is this correct?



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Re: Math: Number Theory [#permalink]
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01 Feb 2010, 16:46
Hey Bunuel, great post so far, just wondering when the Percent notes will go up in this section.



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Re: Math: Number Theory [#permalink]
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01 Feb 2010, 20:19
Got it, thank you both  walker and Bunuel.



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Re: Math: Number Theory [#permalink]
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21 Feb 2010, 06:09
This is just what i've been looking for !
Thanks



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Re: Math: Number Theory [#permalink]
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05 Mar 2010, 14:06
Bunuel wrote: The topic is done. At last!
I'll break it into several smaller ones in a day or two.
Any comments, advises and/or corrections are highly appreciated. What Topic are we talking abt??
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Re: Math: Number Theory [#permalink]
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05 Mar 2010, 14:41
I guess Bunuel meant Number Theory
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Re: Math: Number Theory [#permalink]
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08 Mar 2010, 21:28
Maybe a suggestion for the reciprocal section, this is a question I got tricked on in an early GMAT quant review
In which of the following pairs are the two numbers reciprocals of each other?
i. 3 and 1/3
ii. 1/17 and 1/17
iii. sqrt3 and sqrt3/3
a) i only b) ii only c) i and ii d) i and iii e) ii and iii
OA is D.



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Re: Math: Number Theory [#permalink]
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17 Mar 2010, 14:43
Hi Bunnel, I m confused about the extent of level for number properties.. do we have to remmeber eculer's, fermat's,wilson's theorem on prime number. Actually I found their application to be quite useful but m not sure whther there are other ways to solve the questions as well. eg difficult remainder questions and questions on HCF like if HCF of 2 numbers is 13 and their sum is 2080, how many such pairs are possible? do we see such questions on gmat?
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Re: Math: Number Theory [#permalink]
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17 Mar 2010, 15:07



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Re: Math: Number Theory [#permalink]
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17 Mar 2010, 15:29
So is there any way we can solve the above HCF question? Also does the number theory stated here is sufficient to cover the concepts asked?
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Re: Math: Number Theory [#permalink]
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01 Apr 2010, 10:03
this is a big help. thanks



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Re: Math: Number Theory [#permalink]
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05 Apr 2010, 21:45
This is amazing...thanks for all the great work guys!!
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Re: Math: Number Theory [#permalink]
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06 Apr 2010, 10:12
Thanks! It was very very helpful! Kudos! But I have a question:
How many powers of 900 are in 50!
Make the prime factorization of the number: \(900=2^2*3^2*5^2\), then find the powers of these prime numbers in the n!.
Find the power of 2: \(\frac{50}{2}+\frac{50}{4}+\frac{50}{8}+\frac{50}{16}+\frac{50}{32}=25+12+6+3+1=47\)
= \(2^{47}\)
Find the power of 3: \(\frac{50}{3}+\frac{50}{9}+\frac{50}{27}=16+5+1=22\)
=\(3^{22}\)
Find the power of 5: \(\frac{50}{5}+\frac{50}{25}=10+2=12\)
=\(5^{12}\)
We need all the prime {2,3,5} to be represented twice in 900, 5 can provide us with only 6 pairs, thus there is 900 in the power of 6 in 50!.
Why do we take just 5 from {2,3,5} and why do we need divide 12 by 2 to get the result?
Thanks in advance!



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Re: Math: Number Theory [#permalink]
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04 May 2010, 05:21
Thank you



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Re: Math: Number Theory [#permalink]
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10 May 2010, 16:51
sag wrote: Example: A company received $2 million in royalties on the first $10 million in sales and then $8 million in royalties on the next $100 million in sales. By what percent did the ratio of royalties to sales decrease from the first $10 million in sales to the next $100 million in sales?
Solution: Percent decrease can be calculated by the formula above: Percent=\frac{Change}{Original}*100=\frac{\frac{2}{10}\frac{10}{100}}{\frac{2}{10}}*100=50%, so the royalties decreased by 50%.
I could not get this , i think there is some error... Plzz explain..
as the same Q in Percent Part of Math book is giving an answer of 60 %.. There was a typo. I edited it in Percent section and forgot to edit it here. Now it's OK. Thanks. +1 for spotting this.
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Re: Math: Number Theory [#permalink]
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12 May 2010, 13:53
sag wrote: Example: A company received $2 million in royalties on the first $10 million in sales and then $8 million in royalties on the next $100 million in sales. By what percent did the ratio of royalties to sales decrease from the first $10 million in sales to the next $100 million in sales?
Solution: Percent decrease can be calculated by the formula above: Percent=\frac{Change}{Original}*100=\frac{\frac{2}{10}\frac{10}{100}}{\frac{2}{10}}*100=50%, so the royalties decreased by 50%.
I could not get this , i think there is some error... Plzz explain..
as the same Q in Percent Part of Math book is giving an answer of 60 %.. 2 million royalties on 10 million in sales is equivalent to 20 million royalties on 100 million sales (multiply both number by 10). Going down from 20 million royalties to 8 million royalties is a decrease of 60%.



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Re: Math: Number Theory [#permalink]
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16 May 2010, 00:24
Thanks Bunuel for all the efforts put in creating this. Really appreciate.



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Re: Math: Number Theory [#permalink]
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10 Jun 2010, 13:14
If a is a factor of bc, and gcd(a,b)=1, then a is a factor of c.
Can anyone please explain this rule??? I'm not sure what it means by gcd(a,b)=1.
Thanks a bunch and great summary !!!!!



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Re: Math: Number Theory [#permalink]
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10 Jun 2010, 15:00
bely202 wrote: If a is a factor of bc, and gcd(a,b)=1, then a is a factor of c.
Can anyone please explain this rule??? I'm not sure what it means by gcd(a,b)=1.
Thanks a bunch and great summary !!!!! \(gcd(a,b)=1\) means that greatest common divisor of \(a\) and \(b\) is 1, or in other words they are coprime, the don't share any common factor but 1. So if we are told that \(a\) is a factor of \(bc\) and \(a\) and \(b\) don't share any common factors, then it must be true that \(a\) is a factor of only \(c\). So if \(a=3\), \(b=5\) (\(a\) and \(b\) don't share any common factors but 1, \(gcd(a,b)=1\)), \(c=6\) \(bc=30\) > \(a=3\) is a factor of \(c=6\).
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Re: Math: Number Theory [#permalink]
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10 Jun 2010, 15:08
Thanks a lot of the detailed explanation !!!!




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