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Intern  Joined: 07 Apr 2007
Posts: 9
If r and s are integers and rs + r is odd, which of the following must  [#permalink]

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Question Stats: 75% (01:23) correct 25% (01:46) wrong based on 782 sessions

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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 08 Oct 2019, 02:30, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: If r and s are integers and rs + r is odd, which of the following must  [#permalink]

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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.

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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]

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1
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.
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Re: If r and s are integers and rs + r is odd, which of the following must  [#permalink]

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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.
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Re: If r and s are integers and rs + r is odd, which of the following must  [#permalink]

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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]

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Great explanation, Bunuel.
Love your approach in every answer you put in the threads.
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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]

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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

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Posts: 1873
Re: If r and s are integers and rs + r is odd, which of the following must  [#permalink]

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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
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Re: If r and s are integers and rs + r is odd, which of the following must  [#permalink]

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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 V
Joined: 02 Sep 2009
Posts: 58434
Re: If r and s are integers and rs + r is odd, which of the following must  [#permalink]

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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.
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Re: If r and s are integers and rs + r is odd, which of the following must  [#permalink]

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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]

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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.
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Re: If r and s are integers and rs + r is odd, which of the following must  [#permalink]

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

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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)
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Re: Here is another one from GMATPREP that i thought i got  [#permalink]

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