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Math: Number Theory

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Re: Math: Number Theory [#permalink] New post 01 Feb 2010, 19:19
Got it, thank you both - walker and Bunuel.
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Re: Math: Number Theory [#permalink] New post 21 Feb 2010, 05:09
This is just what i've been looking for !

Thanks
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Re: Math: Number Theory [#permalink] New post 05 Mar 2010, 13:06
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] New post 05 Mar 2010, 13:41
Expert's post
I guess Bunuel meant Number Theory
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Re: Math: Number Theory [#permalink] New post 08 Mar 2010, 20:28
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] New post 17 Mar 2010, 13:43
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] New post 17 Mar 2010, 14:07
Expert's post
gurpreetsingh wrote:
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?


I don't think that these theorems are needed for GMAT.
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Re: Math: Number Theory [#permalink] New post 17 Mar 2010, 14:29
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] New post 01 Apr 2010, 09:03
this is a big help. thanks
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Re: Math: Number Theory [#permalink] New post 05 Apr 2010, 20:45
This is amazing...thanks for all the great work guys!!
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Re: Math: Number Theory [#permalink] New post 06 Apr 2010, 09:12
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] New post 30 Apr 2010, 13:30
Expert's post
AloneAndInsufficient wrote:
Bunuel wrote:
NUMBER THEORY
• For GMAT it's good to memorize following values:
\sqrt{2}\approx{1.41}
\sqrt{3}\approx{1.73}
\sqrt{5}\approx{2.24}
\sqrt{7}\approx{2.45}
\sqrt{8}\approx{2.65}
\sqrt{10}\approx{2.83}


Anyone else notice that these are wrong?
They should be:
• For GMAT it's good to memorize following values:
\sqrt{2}\approx{1.41}
\sqrt{3}\approx{1.73}
\sqrt{5}\approx{2.24}
\sqrt{6}\approx{2.45}
\sqrt{7}\approx{2.65}
\sqrt{8}\approx{2.83}
\sqrt{10}\approx{3.16}


Thanks. Edited. +1 for spotting this.
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Re: Math: Number Theory [#permalink] New post 04 May 2010, 04:21
Thank you :)
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Re: Math: Number Theory [#permalink] New post 10 May 2010, 15:51
Expert's post
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] New post 12 May 2010, 12:53
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] New post 15 May 2010, 23:24
Thanks Bunuel for all the efforts put in creating this. Really appreciate.
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Re: Math: Number Theory [#permalink] New post 10 Jun 2010, 12:14
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] New post 10 Jun 2010, 14:00
Expert's post
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 co-prime, 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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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

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Re: Math: Number Theory [#permalink] New post 10 Jun 2010, 14:08
Thanks a lot of the detailed explanation !!!! :-D
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Re: Math: Number Theory [#permalink] New post 12 Jun 2010, 18:11
thanks for sharing!! :lol:
Re: Math: Number Theory   [#permalink] 12 Jun 2010, 18:11
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