GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Jul 2018, 05:55

### 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

# If r and s are integers and rs + r is odd, which of the following must

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: 04 Oct 2014, 15:08
4
13
00:00

Difficulty:

25% (medium)

Question Stats:

73% (00:54) correct 27% (01:09) wrong based on 816 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

Originally posted by nxrfelix on 02 Jun 2007, 00:57.
Last edited by Bunuel on 04 Oct 2014, 15:08, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 47077
If r and s are integers and rs + r is odd, which of the following must [#permalink]

### Show Tags

04 Oct 2014, 15:18
9
5
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.

_________________
##### General Discussion
VP
Joined: 08 Jun 2005
Posts: 1139
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: 2896
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
4
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, 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: 11
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.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11984
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
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
1
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: RS-R = 2-1 = 1 NOT even
Answer E: R^2+S = 1+2 = 3 NOT even

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

Co-Founder & 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: 1888
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
1
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
Director
Joined: 09 Mar 2016
Posts: 653
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.

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: 47077
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.

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.
_________________
Senior Manager
Joined: 31 Oct 2013
Posts: 368
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 MUST-BE/COULD-BE would be trying out the numbers (Plug-in your own values).

Remember:

MUST–BE means “always” (For all values according to the given condition).

COULD-BE 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 --- 6-3 = 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: 95
Location: India
GMAT 1: 590 Q39 V32
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.
SVP
Joined: 08 Jul 2010
Posts: 2119
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 integers

i.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
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

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   [#permalink] 08 Apr 2018, 01:15
Display posts from previous: Sort by

# Events & Promotions

 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®.