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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
A. r
B. s
C. r + s
D. rs - r
E. r^2 + s
Solving this question helps.
Taking a timed set of similar questions in
GMAT Club Forum Quiz →
is even better.
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.
_________________
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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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.
Now this implies that R is odd AND S+1 is odd. which means S is even
Ans B.
General Discussion
Great explanation, Bunuel.
Love your approach in every answer you put in the threads.
Love your approach in every answer you put in the threads.
EMPOWERgmatRichC
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Expert reply
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:
GMAT assassins aren't born, they're made,
Rich
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:
GMAT assassins aren't born, they're made,
Rich
narendran1990
Joined: 24 May 2014
Last visit: 09 Jun 2024
Posts: 77
Location: India
Schools: Kelley '19 McCombs '19
GMAT 1: 640 Q42 V35 (Online)
GRE 1: Q159 V151
GRE 2: Q159 V153
GPA: 2.9
Schools: Kelley '19 McCombs '19
GMAT 1: 640 Q42 V35 (Online)
GRE 1: Q159 V151
GRE 2: Q159 V153
Posts: 77
Elegant explanation Bunuel. I was plugging in various values and ended up taking long time to solve the question.
narendran1990
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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nxrfelix
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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