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

 It is currently 24 Aug 2016, 19:40

### 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

# If r and s are positive integers, is r/s an integer?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 20 Feb 2012
Posts: 41
Followers: 1

Kudos [?]: 297 [3] , given: 6

If r and s are positive integers, is r/s an integer? [#permalink]

### Show Tags

23 Feb 2012, 08:13
3
KUDOS
10
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

59% (01:29) correct 41% (00:37) wrong based on 513 sessions

### HideShow timer Statistics

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.
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 34420
Followers: 6251

Kudos [?]: 79415 [6] , given: 10016

Re: If r and s are positive integers, is r/s an integer? [#permalink]

### Show Tags

23 Feb 2012, 08:26
6
KUDOS
Expert's post
9
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.

Hope it's clear.
_________________
Manager
Joined: 16 Jan 2011
Posts: 103
Followers: 11

Kudos [?]: 135 [0], given: 13

Re: If r and s are positive integers, is r/s an integer? [#permalink]

### Show Tags

11 Apr 2012, 13:30
i mean this one
(2) Every prime factor of s is also a prime factor of r.
Math Expert
Joined: 02 Sep 2009
Posts: 34420
Followers: 6251

Kudos [?]: 79415 [0], given: 10016

Re: If r and s are positive integers, is r/s an integer? [#permalink]

### Show Tags

11 Apr 2012, 13:40
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.
_________________
Manager
Joined: 22 Mar 2012
Posts: 87
Location: United States (NY)
Concentration: General Management, Marketing
GMAT 1: Q V
GPA: 3.1
WE: Accounting (Other)
Followers: 0

Kudos [?]: 33 [0], given: 27

Re: If r and s are positive integers, is r/s an integer? [#permalink]

### Show Tags

23 Aug 2012, 21:14
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!
Math Expert
Joined: 02 Sep 2009
Posts: 34420
Followers: 6251

Kudos [?]: 79415 [0], given: 10016

Re: If r and s are positive integers, is r/s an integer? [#permalink]

### Show Tags

24 Aug 2012, 02:04
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.

Hope it's clear.
_________________
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 90

Kudos [?]: 818 [0], given: 43

Re: If a and b are positive integers, is ‘a’ a multiple of b? [#permalink]

### Show Tags

25 Sep 2012, 11:24
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.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Intern
Joined: 29 Dec 2011
Posts: 38
Followers: 0

Kudos [?]: 40 [0], given: 29

DS : X and Y are two positive integers [#permalink]

### Show Tags

24 Oct 2012, 23:25
Hi,

I'm trying to figure out this one.

X and Y are two positive integers. Is x divided by y an integer?

(1) All of Y's factors are also factors of X.

(2) Each prime factor of Y is also a prime factor of X.

A, B, C, D or E?

Thanks.
Moderator
Joined: 02 Jul 2012
Posts: 1230
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 110

Kudos [?]: 1253 [0], given: 116

Re: DS : X and Y are two positive integers [#permalink]

### Show Tags

24 Oct 2012, 23:33
elegan wrote:
Hi,

I'm trying to figure out this one.

X and Y are two positive integers. Is x divided by y an integer?

(1) All of Y's factors are also factors of X.

(2) Each prime factor of Y is also a prime factor of X.

A, B, C, D or E?

Thanks.

1) Y itself is a factor of Y. Hence Y is also a factor of X. Sufficient

2)Suppose X = 2 and Y = 8. Answer is No. If Y = 2 and X =8 answer is yes. Insufficient

Kudos Please... If my post helped.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Manager
Joined: 12 Jan 2013
Posts: 244
Followers: 4

Kudos [?]: 58 [0], given: 47

Re: If r and s are positive integers, is r/s an integer? [#permalink]

### Show Tags

12 Jan 2014, 06:35
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..

So A is correct
Senior Manager
Joined: 15 Aug 2013
Posts: 328
Followers: 0

Kudos [?]: 43 [0], given: 23

Re: If r and s are positive integers, is r/s an integer? [#permalink]

### Show Tags

04 May 2014, 11:23
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.

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?
Math Expert
Joined: 02 Sep 2009
Posts: 34420
Followers: 6251

Kudos [?]: 79415 [0], given: 10016

Re: If r and s are positive integers, is r/s an integer? [#permalink]

### Show Tags

05 May 2014, 02:40
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.

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).

Does this make sense?
_________________
Intern
Joined: 14 May 2014
Posts: 26
Concentration: General Management, Operations
GPA: 3.15
Followers: 0

Kudos [?]: 26 [0], given: 1

Re: If r and s are positive integers, is r/s an integer? [#permalink]

### Show Tags

26 Jul 2014, 11:21
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.
Intern
Joined: 30 Mar 2015
Posts: 15
Followers: 1

Kudos [?]: 13 [0], given: 5

Re: If r and s are positive integers, is r/s an integer? [#permalink]

### Show Tags

24 Jun 2015, 04:40
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!!
Math Expert
Joined: 02 Sep 2009
Posts: 34420
Followers: 6251

Kudos [?]: 79415 [1] , given: 10016

Re: If r and s are positive integers, is r/s an integer? [#permalink]

### Show Tags

24 Jun 2015, 04:44
1
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.
_________________
Intern
Joined: 07 Mar 2014
Posts: 16
Location: India
Followers: 2

Kudos [?]: 23 [2] , given: 9

Re: If r and s are positive integers, is r/s an integer? [#permalink]

### Show Tags

26 Oct 2015, 03:37
2
KUDOS
r and s are positive integers.

$$\frac{r}{s}$$ is an integer?

Statement 1

Every factor of s is also a factor of r

Hence sufficient

Statement 2

every prime factor of s is also a prime factor of r

case 1
r = 10 therefore prime factors 2 * 5
s = 10 therefore prime factors 2 * 5

$$\frac{r}{s} = \frac{10}{10}= integer$$

case 2
r = 10 therefore prime factors 2 * 5
s= 20 therefore prime factors 2 * 5

$$\frac{r}{s} = \frac{10}{20}\neq{integer}$$

hence not sufficient

Director
Joined: 12 Aug 2015
Posts: 945
Followers: 14

Kudos [?]: 129 [0], given: 255

Re: If r and s are positive integers, is r/s an integer? [#permalink]

### Show Tags

16 Mar 2016, 05:49
Superb Question
remember here that two number may be entirely different but have the same prie factors
statement 1 is sufficient as all the factors are same
but two is not sufficient as PRIME factors are same
hence A
_________________

Give me a hell yeah ...!!!!!

Senior Manager
Joined: 10 Jul 2015
Posts: 267
GMAT 1: 770 Q47 V48
WE: Education (Education)
Followers: 17

Kudos [?]: 149 [0], given: 35

If r and s are positive integers, is r/s an integer? [#permalink]

### Show Tags

27 Mar 2016, 19:06
For condition #1, remember that this is just a fancy way of indicating that r > s.
Senior Manager
Joined: 10 Jul 2015
Posts: 267
GMAT 1: 770 Q47 V48
WE: Education (Education)
Followers: 17

Kudos [?]: 149 [0], given: 35

Re: If r and s are positive integers, is r/s an integer? [#permalink]

### Show Tags

31 Mar 2016, 01:02
Attached is a visual that should help.
Attachments

Screen Shot 2016-03-31 at 1.01.50 AM.png [ 145.85 KiB | Viewed 2622 times ]

Re: If r and s are positive integers, is r/s an integer?   [#permalink] 31 Mar 2016, 01:02
Similar topics Replies Last post
Similar
Topics:
1 If r, s are positive integers, is r/s a terminating decimal? 4 04 Feb 2016, 18:25
10 Is r*s a multiple of 25? (r and s are positive integers) 5 13 Jan 2016, 23:34
if r and s are positive integers , is r/s an integer? 1 25 Jun 2011, 22:58
3 If r and s are positive integers, is r/s an integer? 1) 6 23 Apr 2011, 15:34
22 If r and s are positive integers, is r/s an integer? 18 10 Nov 2009, 15:24
Display posts from previous: Sort by