Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Aug 2014, 02:10

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

How many numbers from 2 to 50 are not prime and are such

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Joined: 25 Apr 2006
Posts: 50
Followers: 0

Kudos [?]: 2 [0], given: 0

How many numbers from 2 to 50 are not prime and are such [#permalink] New post 27 May 2006, 13:22
How many numbers from 2 to 50 are not prime and are such that neither the number nor double the number is divisible by a perfect square greater than 1?
Manager
Manager
User avatar
Joined: 25 Apr 2006
Posts: 50
Followers: 0

Kudos [?]: 2 [0], given: 0

 [#permalink] New post 27 May 2006, 13:33
Solution

Five.

Since the number is not prime and is not divisible by a square greater than 1, it must be divisible by two different primes. If it were divisible by only one prime, it would either be prime itself or be divisible by the square of that prime.

Since double the number is not divisible by a square, the original number is also not divisible by 2; otherwise, its double is divisible by 4, the square of 2. Therefore, only numbers that are the product of at least two distinct primes greater than 2 satisfy the problem.

The only ones that are less than 50 are (3)(5) = 15, (3)(7) = 21, (3)(11) = 33, (3)(13) = 39, and (5)(7) = 35, so five numbers satisfy the conditions of the problem.
Director
Director
avatar
Joined: 10 Oct 2005
Posts: 532
Location: US
Followers: 1

Kudos [?]: 8 [0], given: 0

GMAT Tests User
 [#permalink] New post 27 May 2006, 22:40
yes 5 it is...

15, 21, 33, 35, and 39
Intern
Intern
avatar
Joined: 23 Feb 2006
Posts: 40
Followers: 0

Kudos [?]: 0 [0], given: 0

 [#permalink] New post 31 May 2006, 06:19
How about 22?
22=11*2 neither is divisible by square and 22 isn't prime...
My answer is 26
Primes are 3 5 7 11 17 23 29 31 37 41 43 47 = 12 primes
2^x: 4 8 16 32 = 4 numbers
3^x:9 27 = 2 numbers
2*3^x: 18 = 1 number
5^x:25 = 1 numbers
2*5^x:50= 1 numbers
6^x:36= 1 numbers
7^x:49= 1 numbers
Summing up we get=(50-2+1)-(12+4+2+1+1+1+1+1)=49-12-11=26
  [#permalink] 31 May 2006, 06:19
    Similar topics Author Replies Last post
Similar
Topics:
8 Experts publish their posts in the topic How many different prime numbers are factors of the positive xyzgmat 11 08 Oct 2010, 16:50
how many prime numbers are integer multiples of 16 ? 1. 0 2. blog 9 04 Feb 2008, 18:49
How many different prime numbers are factors of the positive gmacvik 4 22 Oct 2006, 22:37
A is a prime number (A>2). If C = A^3, by how many HIMALAYA 6 14 Aug 2005, 19:44
How many prime numbers are in a set of 10 positive cloudz9 2 04 Jun 2005, 15:12
Display posts from previous: Sort by

How many numbers from 2 to 50 are not prime and are such

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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

Powered by phpBB © phpBB Group and phpBB SEO

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®.