GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Oct 2019, 01:41 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Does P have a factor X where 1<X<P , and X and P are positive integers

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

Hide Tags

Senior Manager  Joined: 13 Jun 2013
Posts: 266
Does P have a factor X where 1<X<P , and X and P are positive integers  [#permalink]

Show Tags

2
15 00:00

Difficulty:   95% (hard)

Question Stats: 42% (02:21) correct 58% (02:17) wrong based on 235 sessions

HideShow timer Statistics

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

(2) 36*20 + 2 < P < 36*20+6

Originally posted by manpreetsingh86 on 19 Nov 2014, 05:24.
Last edited by Bunuel on 19 Nov 2014, 05:25, edited 1 time in total.
Edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 58435
Re: Does P have a factor X where 1<X<P , and X and P are positive integers  [#permalink]

Show Tags

1
3
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.

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58435
Re: Does P have a factor X where 1<X<P , and X and P are positive integers  [#permalink]

Show Tags

1
1
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.

Similar questions to practice:
if-x-is-an-integer-does-x-have-a-factor-n-such-that-100670.html
does-the-integer-k-have-a-factor-p-such-that-1-p-k-126735.html
for-any-integer-n-greater-than-1-n-denotes-the-product-of-168575.html
does-integer-n-have-2-factors-x-y-such-that-1-x-y-n-165983.html
if-z-is-an-integer-is-z-prime-128732.html

Hope this helps.
_________________
Intern  Joined: 01 Oct 2015
Posts: 1
GMAT 1: 610 Q47 V28 Re: Does P have a factor X where 1<X<P , and X and P are positive integers  [#permalink]

Show Tags

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.

but what about X itself. for example, if X=721 and in this case it is not a factor of P?
Math Expert V
Joined: 02 Sep 2009
Posts: 58435
Re: Does P have a factor X where 1<X<P , and X and P are positive integers  [#permalink]

Show Tags

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.

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.
_________________
Board of Directors P
Joined: 17 Jul 2014
Posts: 2509
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: Does P have a factor X where 1<X<P , and X and P are positive integers  [#permalink]

Show Tags

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.
Current Student D
Joined: 12 Aug 2015
Posts: 2567
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: Does P have a factor X where 1<X<P , and X and P are positive integers  [#permalink]

Show Tags

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
_________________
Manager  B
Joined: 19 Aug 2016
Posts: 75
Re: Does P have a factor X where 1<X<P , and X and P are positive integers  [#permalink]

Show Tags

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.

Hi Bunuel..

How did u conclude that P is a prime number?

Pls help..thanks in advance
Math Expert V
Joined: 02 Sep 2009
Posts: 58435
Re: Does P have a factor X where 1<X<P , and X and P are positive integers  [#permalink]

Show Tags

zanaik89 wrote:
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.

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?
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 13241
Re: Does P have a factor X where 1<X<P , and X and P are positive integers  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: Does P have a factor X where 1<X<P , and X and P are positive integers   [#permalink] 19 Jan 2019, 12:03
Display posts from previous: Sort by

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

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

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