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

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nxrfelix
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If r and s are integers and rs + r is odd, which of the following must [#permalink] New post   Updated on: 08 Oct 2019, 02:30
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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
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B

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.
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If r and s are integers and rs + r is odd, which of the following must [#permalink] New post   04 Oct 2014, 15:18
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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

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.
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Re: If r and s are integers and rs + r is odd, which of the following must [#permalink] New post   02 Jun 2007, 16:43
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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] New post   04 Jun 2015, 17:46
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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

Final Answer:
Show Spoiler
B


GMAT assassins aren't born, they're made,
Rich
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Re: If r and s are integers and rs + r is odd, which of the following must [#permalink] New post   08 Apr 2018, 01:15
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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: If r and s are integers and rs + r is odd, which of the following must [#permalink] New post   04 Jun 2015, 06:02
Great explanation, Bunuel.
Love your approach in every answer you put in the threads.
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Re: If r and s are integers and rs + r is odd, which of the following must [#permalink] New post   08 Apr 2018, 00:58
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] New post   17 Aug 2020, 12:20
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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


Some important rules:
#1. ODD +/- ODD = EVEN
#2. ODD +/- EVEN = ODD
#3. EVEN +/- EVEN = EVEN

#4. (ODD)(ODD) = ODD
#5. (ODD)(EVEN) = EVEN
#6. (EVEN)(EVEN) = EVEN

Take: rs + r is odd
Factor: r(s + 1) is odd

If (r)(s + 1) = ODD, then from rule #4, we know that r is ODD and (s+1) is ODD
If s+1 is ODD, then it must be the case that s is even

Answer: B

Cheers,
Brent
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Re: If r and s are integers and rs + r is odd, which of the following must [#permalink] New post   02 Dec 2023, 20:32
Hello from the GMAT Club BumpBot!

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Re: If r and s are integers and rs + r is odd, which of the following must [#permalink]
02 Dec 2023, 20:32
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