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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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?

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.

HBS: Reimagining Capitalism: Business and Big Problems : Growing income inequality, poor or declining educational systems, unequal access to affordable health care and the fear of continuing economic distress...

I am not panicking. Nope, Not at all. But I am beginning to wonder what I was thinking when I decided to work full-time and plan my cross-continent relocation...

Over the last week my Facebook wall has been flooded with most positive, almost euphoric emotions: “End of a fantastic school year”, “What a life-changing year it’s been”, “My...