It is currently 24 Feb 2018, 11:30

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Math: Number Theory

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 12 Sep 2017
Posts: 5
Re: Math: Number Theory [#permalink]

Show Tags

New post 22 Sep 2017, 04:11
Thank you Bunuel and everyone for their contribution here :)
Intern
Intern
avatar
B
Joined: 01 Apr 2017
Posts: 6
GMAT 1: 720 Q48 V40
Re: Math: Number Theory [#permalink]

Show Tags

New post 14 Oct 2017, 03:51
Nothing is better than this
Intern
Intern
avatar
B
Status: hope for the best, prepare for the worst
Joined: 13 Dec 2015
Posts: 6
Location: Pakistan
Concentration: General Management, International Business
GPA: 3.19
Re: Math: Number Theory [#permalink]

Show Tags

New post 26 Dec 2017, 14:39
How many powers of 900 are in 50!? the statement written in following question wa
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!
what does it mean?
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43896
Re: Math: Number Theory [#permalink]

Show Tags

New post 26 Dec 2017, 20:11
abbas57 wrote:
How many powers of 900 are in 50!? the statement written in following question wa
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!
what does it mean?


I tried to elaborate this in the posts below:
https://gmatclub.com/forum/math-number- ... ml#p678298
https://gmatclub.com/forum/math-number- ... ml#p710819
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 14 Jul 2015
Posts: 4
Re: Math: Number Theory [#permalink]

Show Tags

New post 28 Dec 2017, 12:13
Finding the power of non-prime in n!:

How many powers of 900 are in 50!

Make the prime factorization of the number: 900=22∗32∗52900=22∗32∗52, then find the powers of these prime numbers in the n!.

Find the power of 2:
502+504+508+5016+5032502+504+508+5016+5032=25+12+6+3+1=47=25+12+6+3+1=47

= 247247

Find the power of 3:
503+509+5027=16+5+1=22503+509+5027=16+5+1=22

=322322

Find the power of 5:
505+5025=10+2=12505+5025=10+2=12

=512512

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!.

Hi Bunuel,
I read the explanation you gave to defoue but couldn't apply it to the above example of 900. Could you please elaborate?

Thanks.
Intern
Intern
avatar
B
Joined: 14 Jul 2015
Posts: 4
Re: Math: Number Theory [#permalink]

Show Tags

New post 28 Dec 2017, 12:18
I just read the remaining explanations...got it! Sorry
Intern
Intern
avatar
Joined: 05 Jan 2018
Posts: 1
Re: Math: Number Theory [#permalink]

Show Tags

New post 05 Jan 2018, 05:18
A die is rolled 14 times.
a) What is the probability that we obtain exactly one 6?
b) What is the probability that we obtain 4 times 4, 2 times 6 and 8 times 3?
Please help with this home assingment , I will be grateful, thank you!
Intern
Intern
avatar
B
Joined: 18 May 2016
Posts: 12
GMAT ToolKit User CAT Tests
Math: Number Theory [#permalink]

Show Tags

New post 22 Feb 2018, 20:16
Bunuel

Excellent Post!

Edit suggestions:
1. 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.

If p = a = b = 2, the above point fails
as p will be a factor of ab and a and b


2. Take the last digit, double it, and subtract it from the rest of the number, if the answer is divisible by 7 (including 0), then the number is divisible by 7.

I think you should change the underlined "number" to digits for better understanding
and then provide an example of the working
eg. 203/7
Last digit -> 3
Double it -> 3*2 = 6
Rest of the digits = 20 -> 20-6 = 14
Answer (14) -> Divisible by 7 -> Yes

3. Verifying the primality (checking whether the number is a prime) of a given number n can be done by trial division ...

Wouldn't it be easier & faster to just use another method that you've mentioned earlier in the post?
all prime numbers above 3 are of the form 6n−1 or 6n+1
-> Divide a number by 6 and +1/-1 to check if it is a prime

Please verify

Thanks
P
Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43896
Re: Math: Number Theory [#permalink]

Show Tags

New post 22 Feb 2018, 21:30
1
This post received
KUDOS
Expert's post
ppnimkar wrote:
Bunuel

Excellent Post!

Edit suggestions:
1. 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.

If p = a = b = 2, the above point fails
as p will be a factor of ab and a and b


2. Take the last digit, double it, and subtract it from the rest of the number, if the answer is divisible by 7 (including 0), then the number is divisible by 7.

I think you should change the underlined "number" to digits for better understanding
and then provide an example of the working
eg. 203/7
Last digit -> 3
Double it -> 3*2 = 6
Rest of the digits = 20 -> 20-6 = 14
Answer (14) -> Divisible by 7 -> Yes

3. Verifying the primality (checking whether the number is a prime) of a given number n can be done by trial division ...

Wouldn't it be easier & faster to just use another method that you've mentioned earlier in the post?
all prime numbers above 3 are of the form 6n−1 or 6n+1
-> Divide a number by 6 and +1/-1 to check if it is a prime

Please verify

Thanks
P


Thank you for your suggestions.

1. x or y means x or y or both. So, everything is correct there.

2. I don't think it would be better.

3. Any prime number p, which is greater than 3, could be expressed as \(p=6n+1\) or \(p=6n+5\) or \(p=6n-1\), where n is an integer greater than 1.

Any prime number p, which is greater than 3, when divided by 6 can only give the remainder of 1 or 5 (remainder cannot be 2 or 4 as in this case p would be even and the remainder cannot be 3 as in this case p would be divisible by 3).

So, any prime number p, which is greater than 3, could be expressed as \(p=6n+1\) or \(p=6n+5\) or \(p=6n-1\), where n is an integer greater than 1.

But:
Not all number which yield a remainder of 1 or 5 upon division by 6 are primes, so vise-versa of the above property is not true. For example 25 yields the remainder of 1 upon division be 6 and it's not a prime number.

_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Re: Math: Number Theory   [#permalink] 22 Feb 2018, 21:30

Go to page   Previous    1   2   3   4   5   6   7   8   9   10   11   [ 209 posts ] 

Display posts from previous: Sort by

Math: Number Theory

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.