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

Question

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

Bunuel · Accepted Answer

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.

bsd_lover · Answer

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.

Viver · Answer

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

EMPOWERgmatRichC · Answer

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:  B

GMAT assassins aren't born, they're made,
Rich

narendran1990 · Answer

Elegant explanation  Bunuel . I was plugging in various values and ended up taking long time to solve the question.

GMATinsight · Answer

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)

BrentGMATPrepNow · Answer

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

bumpbot · Answer

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

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My Rewards