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 500,000 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:

Does P have a factor X where 1 < X < P, and X and P are positive integers?

The question basically asks whether p is a prime number. If it is, then it won't have a factor x such that 1 < x < p (definition of a prime number).

(1) GCD (P^2, k) = k, where k is a prime number. Can p be a prime? Yes, consider p = k = 2. Can p be a non-prime? Yes, consider p = 4 and k = 2. Not sufficient.

(2) 36*20 + 2 < P < 36*20+6 --> p could be 36*20 + 3 = 723, 36*20 + 4 = 724, or 36*20 + 5 = 725. None of these numbers is prime: 723 is a multiple of 3 (sum of its digits is a multiple of 3), 724 is even and 725 is a multiple of 5. So, we can give a definite answer that p is not a prime number, therefore it must have a factor which is greater than 1 and less than p itself. Sufficient.

Does P have a factor X where 1 < X < P, and X and P are positive integers?

The question basically asks whether p is a prime number. If it is, then it won't have a factor x such that 1 < x < p (definition of a prime number).

(1) GCD (P^2, k) = k, where k is a prime number. Can p be a prime? Yes, consider p = k = 2. Can p be a non-prime? Yes, consider p = 4 and k = 2. Not sufficient.

(2) 36*20 + 2 < P < 36*20+6 --> p could be 36*20 + 3 = 723, 36*20 + 4 = 724, or 36*20 + 5 = 725. None of these numbers is prime: 723 is a multiple of 3 (sum of its digits is a multiple of 3), 724 is even and 725 is a multiple of 5. So, we can give a definite answer that p is not a prime number, therefore it must have a factor which is greater than 1 and less than p itself. Sufficient.

Re: Does P have a factor X where 1<X<P , and X and P are positive integers [#permalink]

Show Tags

15 Nov 2015, 09:37

Bunuel wrote:

Does P have a factor X where 1 < X < P, and X and P are positive integers?

The question basically asks whether p is a prime number. If it is, then it won't have a factor x such that 1 < x < p (definition of a prime number).

(1) GCD (P^2, k) = k, where k is a prime number. Can p be a prime? Yes, consider p = k = 2. Can p be a non-prime? Yes, consider p = 4 and k = 2. Not sufficient.

(2) 36*20 + 2 < P < 36*20+6 --> p could be 36*20 + 3 = 723, 36*20 + 4 = 724, or 36*20 + 5 = 725. None of these numbers is prime: 723 is a multiple of 3 (sum of its digits is a multiple of 3), 724 is even and 725 is a multiple of 5. So, we can give a definite answer that p is not a prime number, therefore it must have a factor which is greater than 1 and less than p itself. Sufficient.

Answer: B.

but what about X itself. for example, if X=721 and in this case it is not a factor of P?

Does P have a factor X where 1 < X < P, and X and P are positive integers?

The question basically asks whether p is a prime number. If it is, then it won't have a factor x such that 1 < x < p (definition of a prime number).

(1) GCD (P^2, k) = k, where k is a prime number. Can p be a prime? Yes, consider p = k = 2. Can p be a non-prime? Yes, consider p = 4 and k = 2. Not sufficient.

(2) 36*20 + 2 < P < 36*20+6 --> p could be 36*20 + 3 = 723, 36*20 + 4 = 724, or 36*20 + 5 = 725. None of these numbers is prime: 723 is a multiple of 3 (sum of its digits is a multiple of 3), 724 is even and 725 is a multiple of 5. So, we can give a definite answer that p is not a prime number, therefore it must have a factor which is greater than 1 and less than p itself. Sufficient.

Answer: B.

but what about X itself. for example, if X=721 and in this case it is not a factor of P?

Your question is not clear. First of all the question asks "Does P have a factor X where 1 < X < P..." plus, an integer is a factor of itself. For example, 721 is a factor of 721.
_________________

Re: Does P have a factor X where 1<X<P , and X and P are positive integers [#permalink]

Show Tags

09 Feb 2016, 18:34

manpreetsingh86 wrote:

Does P have a factor X where 1 < X < P, and X and P are positive integers?

(1) GCD (P^2, k) = k, where k is a prime number from this, we know that k is a factor of p^2. but we don't know whether k is a factor of P or not. what if k=p? what if k=p=1? p^2=1. since we need integers, there might be no x at all here. suppose we have p=9 k=3. then yes. it might be a number x that is a factor of p.

(2) 36*20 + 2 < P < 36*20+6 722 < P < 726 p can be 723, 724, 725. 724 is even, so it is divisible 725 ends in 5 so is divisible by 5 7+2+3=12, so divisible by 3 we see that all possible options of P have other factors. we can give a definite answer. B.

Re: Does P have a factor X where 1<X<P , and X and P are positive integers [#permalink]

Show Tags

16 Mar 2016, 04:05

Here all the values between 36*20+2 and 36*20+6 are non primes as it it possible to obtain the factors. Hence B is sufficient statement 2 can be discarded as p can be 3 and p can be 81 (for k=3) thus B is sufficient
_________________

Re: Does P have a factor X where 1<X<P , and X and P are positive integers [#permalink]

Show Tags

08 Oct 2017, 16:47

Bunuel wrote:

Does P have a factor X where 1 < X < P, and X and P are positive integers?

The question basically asks whether p is a prime number. If it is, then it won't have a factor x such that 1 < x < p (definition of a prime number).

(1) GCD (P^2, k) = k, where k is a prime number. Can p be a prime? Yes, consider p = k = 2. Can p be a non-prime? Yes, consider p = 4 and k = 2. Not sufficient.

(2) 36*20 + 2 < P < 36*20+6 --> p could be 36*20 + 3 = 723, 36*20 + 4 = 724, or 36*20 + 5 = 725. None of these numbers is prime: 723 is a multiple of 3 (sum of its digits is a multiple of 3), 724 is even and 725 is a multiple of 5. So, we can give a definite answer that p is not a prime number, therefore it must have a factor which is greater than 1 and less than p itself. Sufficient.

Does P have a factor X where 1 < X < P, and X and P are positive integers?

The question basically asks whether p is a prime number. If it is, then it won't have a factor x such that 1 < x < p (definition of a prime number).

(1) GCD (P^2, k) = k, where k is a prime number. Can p be a prime? Yes, consider p = k = 2. Can p be a non-prime? Yes, consider p = 4 and k = 2. Not sufficient.

(2) 36*20 + 2 < P < 36*20+6 --> p could be 36*20 + 3 = 723, 36*20 + 4 = 724, or 36*20 + 5 = 725. None of these numbers is prime: 723 is a multiple of 3 (sum of its digits is a multiple of 3), 724 is even and 725 is a multiple of 5. So, we can give a definite answer that p is not a prime number, therefore it must have a factor which is greater than 1 and less than p itself. Sufficient.

Answer: B.

Hi Bunuel..

How did u conclude that P is a prime number? The question asks whether p is prime. If p is prime it won't have a factor x such that 1 < x < p, if p is NOT prime it will have a factor x such that 1 < x < p. For example, prime number 7, does not have a factor x such that 1 < x < 7.

Pls help..thanks in advance

Where does it say that p is a prime?
_________________