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

 It is currently 05 Jul 2015, 23:27

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:
Manager
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]  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
Joined: 25 Apr 2006
Posts: 50
Followers: 0

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

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
Joined: 10 Oct 2005
Posts: 531
Location: US
Followers: 1

Kudos [?]: 17 [0], given: 0

yes 5 it is...

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

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

22=11*2 neither is divisible by square and 22 isn't prime...
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
Similar topics Replies Last post
Similar
Topics:
If n=4p, where p is a prime number greater than 2, how many 5 23 Feb 2008, 18:36
how many prime numbers are integer multiples of 16 ? 1. 0 2. 9 04 Feb 2008, 18:49
7 If n=4p, where p is a prime number greater than 2, how many 18 23 Jan 2008, 11:07
If n=4p, where p is a prime number greater than 2, how many 8 16 Jan 2007, 10:31
If n = 4p where p is a prime number > 2, how many diff 2 16 Dec 2006, 19:21
Display posts from previous: Sort by