January 26, 2019 January 26, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions. January 27, 2019 January 27, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 06 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: 04 Oct 2014, 14:08
Question Stats:
73% (01:23) correct 27% (01:51) wrong based on 884 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 01 Jun 2007, 23:57.
Last edited by Bunuel on 04 Oct 2014, 14:08, edited 1 time in total.
Renamed the topic, edited the question and added the OA.




Math Expert
Joined: 02 Sep 2009
Posts: 52431

If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
04 Oct 2014, 14:18




VP
Joined: 08 Jun 2005
Posts: 1133

Re: If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
02 Jun 2007, 11:55
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: 2838

Re: If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
02 Jun 2007, 15:43
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: 2
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, 13:02
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, 05:02
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: 13375
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, 16:46
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
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



SVP
Joined: 06 Nov 2014
Posts: 1877

Re: If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
10 Jun 2015, 22:41
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: 1287

Re: If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
02 Apr 2018, 11:27
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: 52431

Re: If r and s are integers and rs + r is odd, which of the following must
[#permalink]
Show Tags
02 Apr 2018, 20:00
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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



VP
Joined: 31 Oct 2013
Posts: 1014
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, 20:48
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, 21:59
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: 89
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
07 Apr 2018, 23:58
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: 2726
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, 00:15
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!!! GMATinsight Bhoopendra 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 Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION




Re: If r and s are integers and rs + r is odd, which of the following must &nbs
[#permalink]
08 Apr 2018, 00:15






