GMAT Changed on April 16th - Read about the latest changes here

It is currently 24 May 2018, 08:35

Happening NOW:

INSEAD Rolling Out R1 Admission Decisions - Join CHAT Room2 to Get Latest Updates from Fellow Applicants


Close

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
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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

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

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 45368
If r and s are nonzero integers, is r/s an integer ? [#permalink]

Show Tags

New post 10 Oct 2017, 01:16
1
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

39% (01:57) correct 61% (01:51) wrong based on 45 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
User avatar
P
Joined: 02 Jul 2017
Posts: 292
GMAT 1: 730 Q50 V38
GMAT ToolKit User
If r and s are nonzero integers, is r/s an integer ? [#permalink]

Show Tags

New post 10 Oct 2017, 01:52
1
This post was
BOOKMARKED
If r and s are nonzero integers, is r/s an integer ?


(1) s – 4 = (r + 2)(r – 2)
=> \(s-4=r^2-4\)
=> \(s=r^2\)
if r =1 s=1 => \(\frac{r}{s}\) integer True
if r = 2 s = 4 => \(\frac{r}{s}\) not an integer
=> For \(r\neq{1}\) => \(s>r\) and \(\frac{r}{s}\) is not an integer
Insufficient

(2) \(r^2 – s^2 = -12\)
=> \(s^2 – r^2 = 12\)
=> That is r and s are not equal and |s| > |r|
=> \(\frac{r}{s}\) cannot be an integer
Sufficient

Answer: B
Senior Manager
Senior Manager
User avatar
S
Joined: 05 Dec 2016
Posts: 260
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
GMAT ToolKit User
Re: If r and s are nonzero integers, is r/s an integer ? [#permalink]

Show Tags

New post 10 Oct 2017, 02:14
We need to discover whether s is a factor of r

(1)s-4=(r-2)(r+2)
s-4=r^2-4
s=r^2

s=1; r=1 => r/s=1 YES-integer
s=4; r=2 r/s= 2/4=1/2 NO

Insufficient

(2) r^2-s^2= -12
This statement tells us that |r|<|s| hence r/s would not be an integer Sufficient.

Answer B.
Re: If r and s are nonzero integers, is r/s an integer ?   [#permalink] 10 Oct 2017, 02:14
Display posts from previous: Sort by

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

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


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.