Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 09:00 AM PDT  10:00 AM PDT Watch & learn the Do's and Don’ts for your upcoming interview Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes. Oct 27 07:00 AM EDT  09:00 AM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE. Oct 27 08:00 PM EDT  09:00 PM EDT Strategies and techniques for approaching featured GMAT topics. One hour of live, online instruction
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 07 Apr 2007
Posts: 9

If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
Updated on: 08 Oct 2019, 02:30
Question Stats:
75% (01:23) correct 25% (01:46) wrong based on 782 sessions
HideShow timer Statistics
If r and s are integers and rs + r is odd, which of the following must be even ? A. r B. s C. r + s D. rs  r E. r^2 + s
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by nxrfelix on 02 Jun 2007, 00:57.
Last edited by Bunuel on 08 Oct 2019, 02:30, edited 2 times in total.
Renamed the topic, edited the question and added the OA.




Math Expert
Joined: 02 Sep 2009
Posts: 58434

Re: If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
04 Oct 2014, 15:18
minakshigurani wrote: bsd_lover wrote: RS+R = R(S+1) > which is ODD Now this implies that R is odd AND S+1 is odd. which means S is even
Ans B. I am not sure if i got this one .. i mean if r is odd what is the possibility of s being odd or even ?? If r and s are integers and rs + r is odd, which of the following must be even ? A. r B. s C. r + s D. rs  r E. r^2 + s Given that rs + r is odd > \(rs + r =r*(s+1)=odd\). For the product of two integers, r and s+1, to be odd both must be odd. Theretofore, r and s+1 are odd, which means that r is odd and s is even. Answer: B.
_________________




Director
Joined: 08 Jun 2005
Posts: 911

Re: If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
02 Jun 2007, 12:55
Himalayan is right !
according to OG , zero is even
R*S+R =
e=even
o=odd
we have two options:
(1) e*o+e = e
(2) o*e+o = o
since the stem states that R*S+R =odd then we will choose (2) and S must be even.



CEO
Joined: 17 May 2007
Posts: 2705

Re: If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
02 Jun 2007, 16:43
RS+R = R(S+1) > which is ODD
Now this implies that R is odd AND S+1 is odd. which means S is even
Ans B.



Intern
Status: Open
Joined: 30 Aug 2014
Posts: 1
Location: India
Minakshi: Gurani
Concentration: Marketing, General Management
GPA: 4
WE: Brand Management (Other)

Re: If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
04 Oct 2014, 14:02
bsd_lover wrote: RS+R = R(S+1) > which is ODD Now this implies that R is odd AND S+1 is odd. which means S is even
Ans B. I am not sure if i got this one .. i mean if r is odd what is the possibility of s being odd or even ??



Intern
Joined: 21 Dec 2014
Posts: 9

Re: If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
04 Jun 2015, 06:02
Great explanation, Bunuel. Love your approach in every answer you put in the threads.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15294
Location: United States (CA)

Re: If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
04 Jun 2015, 17:46
Hi All, This question is perfect for TESTing VALUES. We're told that R and S are integers and that (R)(S)+R = ODD. We're asked which of the 5 answers MUST be even... IF.... R = 1 S = 2 (1)(2)+1 = 3 Answer A: R = 1 NOT even Answer B: S = 2 This IS EVEN Answer C: R+S = 3 NOT even Answer D: RSR = 21 = 1 NOT even Answer E: R^2+S = 1+2 = 3 NOT even Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



SVP
Joined: 06 Nov 2014
Posts: 1873

Re: If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
10 Jun 2015, 23:41
If r and s are integers and rs + r is odd, which of the following must be even ?
If r is factored out to rewrite this as r (s + 1), we can see it as a product of two parts, r and s + 1. For their product to be odd, r must be odd and s + 1 must be odd. We also know that even + odd = odd. For s+1 to be odd, s must be even since 1 is odd. A. R B. s C. r + s D. rs  r E. r^2 + s



VP
Joined: 09 Mar 2016
Posts: 1230

Re: If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
02 Apr 2018, 12:27
Bunuel wrote: minakshigurani wrote: bsd_lover wrote: RS+R = R(S+1) > which is ODD Now this implies that R is odd AND S+1 is odd. which means S is even
Ans B. I am not sure if i got this one .. i mean if r is odd what is the possibility of s being odd or even ?? If r and s are integers and rs + r is odd, which of the following must be even ? A. r B. s C. r + s D. rs  r E. r^2 + s Given that rs + r is odd > \(rs + r =r*(s+1)=odd\). For the product of two integers, r and s+1, to be odd both must be odd. Theretofore, r and s+1 are odd, which means that r is odd and s is even. Answer: B. Hi Bunuel are you using some formula ? i just plugged in different values and it was time consuming please Xplain why did you use only 1



Math Expert
Joined: 02 Sep 2009
Posts: 58434

Re: If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
02 Apr 2018, 21:00
dave13 wrote: Bunuel wrote: If r and s are integers and rs + r is odd, which of the following must be even ?
A. r B. s C. r + s D. rs  r E. r^2 + s
Given that rs + r is odd > \(rs + r =r*(s+1)=odd\). For the product of two integers, r and s+1, to be odd both must be odd. Theretofore, r and s+1 are odd, which means that r is odd and s is even.
Answer: B. Hi Bunuel are you using some formula ? i just plugged in different values and it was time consuming please Xplain why did you use only 1 Your question is not clear. What do you mean by "are you using some formula" or by "why did you use only 1"? I factored out r from rs + r, which we are given to be odd, to get r*(s + 1), thus r*(s + 1) = odd.
_________________



VP
Joined: 31 Oct 2013
Posts: 1465
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)

Re: If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
02 Apr 2018, 21:48
nxrfelix wrote: If r and s are integers and rs + r is odd, which of the following must be even ?
A. R B. s C. r + s D. rs  r E. r^2 + s rs +r =r(s+1) it is given that rs+r is odd. so r(s+1) is also odd. now we know that odd*odd is odd. Example: 3*5=15 thus, r is odd and we have to put a even integer to make s+1 is odd . so, s is even. thus correct answer is B.



Intern
Joined: 15 Apr 2014
Posts: 2

Re: If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
02 Apr 2018, 22:59
Hi,
Best approach for MUSTBE/COULDBE would be trying out the numbers (Plugin your own values).
Remember:
MUST–BE means “always” (For all values according to the given condition).
COULDBE means “One possible value” (which satisfy the given condition).
Here try out numbers such a way that,
r*s + r is odd,
let’s take r = 3 and s = 2, then r*s + r is 9. So, its odd.
Then let’s try it out in the answer choices and check whether the result is even.
A. R – 3 – odd – Strike off
B. s – 2 – even. Hold it. Don’t stop here. Since we trying out numbers its important to check all answer choices.
C. r + s – 3+2 = 5 – odd. Strike off.
D. rs – r  63 = 3 – Odd. Strike off.
E. r^2 + s – 9+2 = 11 – Odd. Strike off.
So only B holds true for r =3 and s = 2. So B is our answer.
Hope this helps.



Manager
Joined: 24 May 2014
Posts: 86
Location: India
GRE 1: Q159 V151 GRE 2: Q159 V153
GPA: 2.9

Re: If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
08 Apr 2018, 00:58
Elegant explanation Bunuel. I was plugging in various values and ended up taking long time to solve the question.



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
08 Apr 2018, 01:15
narendran1990 wrote: Elegant explanation Bunuel. I was plugging in various values and ended up taking long time to solve the question. The heirarchy of the two methods is as follows 1) Understand the algebraic expression 2) Substitute the values if you are stuck or have no idea what the algebraic expression means here the question was If r and s are integers and rs + r is odd, which of the following must be even ? A. R B. s C. r + s D. rs  r E. r^2 + s rs + r = r(s+1) = odd . (Only product of two odd numbers can be odd given that the two numbers are integersi.e. r = Odd and s+1 = Odd i.e. r = Odd and s = Even (Hence answer Option B)
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



NonHuman User
Joined: 09 Sep 2013
Posts: 13317

Re: Here is another one from GMATPREP that i thought i got
[#permalink]
Show Tags
08 Oct 2019, 02:30
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: Here is another one from GMATPREP that i thought i got
[#permalink]
08 Oct 2019, 02:30






