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:
Re: If r and s are positive integers, is r/s an integer? [#permalink]
23 Feb 2012, 07:26
4
This post received KUDOS
Expert's post
6
This post was BOOKMARKED
If r and s are positive integers, is r/s an integer?
(1) Every factor of s is also a factor of r. If every factor of s is also factor of r, then in fraction r/s, s will just be reduced and we get an integer. Sufficient.
(2) Every prime factor of s is also a prime factor of r. The powers of prime factors of s could be higher than powers of prime factors of r. eg 25/125=1/5 not an integer. Not sufficient.
Re: If r and s are positive integers, is r/s an integer? [#permalink]
11 Apr 2012, 12:40
Expert's post
Galiya wrote:
i mean this one (2) Every prime factor of s is also a prime factor of r.
There is an example given in my post which satisfies the given condition and doesn't give an integer value of r/s.
(2) Every prime factor of s is also a prime factor of r. The powers of prime factors of s could be higher than powers of prime factors of r.
For example: if s=5^3 and r=5^2 then every prime of 125 (in fact its only prime 5) IS also a prime of 25 but r/s=25/125 is not an integer. _________________
Re: If r and s are positive integers, is r/s an integer? [#permalink]
24 Aug 2012, 01:04
Expert's post
KAS1 wrote:
What if S>R? It doesn't say that R>S. It just says they are positive integers.
For first statement: R>S = 20/10 = 2 --> Integer S>R = 10/20 = .5 --> Not an integer
For the second statement: R>S = 50/5 = 10 --> Integer S>R = 5/50 = .5 --> Not an integer
That is why I picked E. Can you please explain why my reasoning is incorrect? Thanks!
For the first statement s cannot be greater than r. If every factor of s is also factor of r, then \(r\geq{s}\). Your example, (r=10 and s=20), is not possible, because 4 is a factor of s but not a factor of r.
Re: If a and b are positive integers, is ‘a’ a multiple of b? [#permalink]
25 Sep 2012, 10:24
1
This post was BOOKMARKED
ankit0411 wrote:
If a and b are positive integers, is ‘a’ a multiple of b?
(1) Every prime factor of b is also a prime factor of a (2) Every factor of b is also a factor of a
(1) Consider for example \(a = 2\cdot3=6\) and \(b = 2^2\cdot3=12\), so obviously \(a\) is not a multiple of \(b.\) If \(a = 12\) and \(b = 6\), then of course \(a\) is a multiple of \(b.\) Not sufficient.
(2) \(b\) is a factor of itself, so it is also a factor of \(a\), which means that \(a\) is a multiple of \(b.\) Sufficient.
Answer B. _________________
PhD in Applied Mathematics Love GMAT Quant questions and running.
Re: If r and s are positive integers, is r/s an integer? [#permalink]
12 Jan 2014, 05:35
BANON wrote:
If r and s are positive integers, is r/s an integer?
(1) Every factor of s is also a factor of r. (2) Every prime factor of s is also a prime factor of r.
Basically, the question asks us if s is a factor of r.
1) This is significant, because we are told something about every factor of s. Let's say the products of the factors of s = n, then 1) gives us n*r.. is n*r/n an integer? Of course.. So 1) is sufficient
2) This only tells us a fraction of the information that 1) tells us, since 2) restricts the factors to primes.. But we don't know if s has other factors that are NOT shared by r, and thus 2) is insufficient..
Re: If r and s are positive integers, is r/s an integer? [#permalink]
04 May 2014, 10:23
Bunuel wrote:
If r and s are positive integers, is r/s an integer?
(1) Every factor of s is also a factor of r. If every factor of s is also factor of r, then in fraction r/s, s will just be reduced and we get an integer. Sufficient.
(2) Every prime factor of s is also a prime factor of r. The powers of prime factors of s could be higher than powers of prime factors of r. eg 25/125=1/5 not an integer. Not sufficient.
Answer: A.
Hope it's clear.
Hi Bunuel,
If we look at the two statements above: (1) Every factor of s is also a factor of r. (2) Every prime factor of s is also a prime factor of r.
I'm having a hard time differentiating the two statements. I realize that one is talking about PF and one is talking about All Factors, but how can we assume that in statement 2, S could have it's factors raised to a higher value. Isn't the verbiage between 1 and 2 identical?
Re: If r and s are positive integers, is r/s an integer? [#permalink]
05 May 2014, 01:40
Expert's post
russ9 wrote:
Bunuel wrote:
If r and s are positive integers, is r/s an integer?
(1) Every factor of s is also a factor of r. If every factor of s is also factor of r, then in fraction r/s, s will just be reduced and we get an integer. Sufficient.
(2) Every prime factor of s is also a prime factor of r. The powers of prime factors of s could be higher than powers of prime factors of r. eg 25/125=1/5 not an integer. Not sufficient.
Answer: A.
Hope it's clear.
Hi Bunuel,
If we look at the two statements above: (1) Every factor of s is also a factor of r. (2) Every prime factor of s is also a prime factor of r.
I'm having a hard time differentiating the two statements. I realize that one is talking about PF and one is talking about All Factors, but how can we assume that in statement 2, S could have it's factors raised to a higher value. Isn't the verbiage between 1 and 2 identical?
No, they are not identical.
(2) says that r and s have the same primes but this does not mean that r and s have the same factors. For, example, 2, 4, 8, 16, ..., 2^n all have the same prime: 2. But they certainly do not share all their factors: the factors of 8 (1, 2, 4, 8) are not the same as the factors of 4 (1, 2, 4).
Re: If r and s are positive integers, is r/s an integer? [#permalink]
26 Jul 2014, 10:21
Factors of 4 is 1, 2 and 4. Factors of 6 is 1, 2, 3 and 6. Therefore, your example is not a true representation of statement 1. If every factor of s is also a factor of r, then what it is really saying is that r is a multiple of s, i.e. Factor of \(s=4\) is 1, 2 and 4. Factor of \(r=8\) is 1, 2, 4 and 8, while \(r=12\) has factors 1, 2, 3, 4, 6 and 12. Since multiples are defined as whole numbers, it is sufficient.
Statement 2 is not sufficient since it is simply stating that each prime factor of s is also a prime factor of r. It does not state how many of each prime factor is present.
Re: If r and s are positive integers, is r/s an integer? [#permalink]
24 Jun 2015, 03:40
Hi, I answered E to this question because I thought that "every factor of s is also factor of r" does not mean that every factor of r is also a factor of s. and that is r (6) and s (4) could be an answer: every factor of s (1 and 2) are factors of r but not all factors of r are necessarily factors of s. what am i missreading? thanks!!
Re: If r and s are positive integers, is r/s an integer? [#permalink]
24 Jun 2015, 03:44
1
This post received KUDOS
Expert's post
petu wrote:
Hi, I answered E to this question because I thought that "every factor of s is also factor of r" does not mean that every factor of r is also a factor of s. and that is r (6) and s (4) could be an answer: every factor of s (1 and 2) are factors of r but not all factors of r are necessarily factors of s. what am i missreading? thanks!!
If s = 4 and r = 6, then 4, a factor of s = 4, is NOT a factor of r = 6. _________________
You know what’s worse than getting a ding at one of your dreams schools . Yes its getting that horrid wait-listed email . This limbo is frustrating as hell . Somewhere...
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Wow! MBA life is hectic indeed. Time flies by. It is hard to keep track of the time. Last week was high intense training Yeah, Finance, Accounting, Marketing, Economics...