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

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If r and s are integers and rs + r is odd, which of the following must [#permalink]  01 Jun 2007, 23:57
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Oct 2014, 14:08, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: If r and s are integers and rs + r is odd, which of the following must [#permalink]  02 Jun 2007, 11:55
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.
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Re: If r and s are integers and rs + r is odd, which of the following must [#permalink]  02 Jun 2007, 15:43
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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]  04 Oct 2014, 13:02
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 ??
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Re: If r and s are integers and rs + r is odd, which of the following must [#permalink]  04 Oct 2014, 14:18
Expert's post
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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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Re: If r and s are integers and rs + r is odd, which of the following must   [#permalink] 04 Oct 2014, 14:18
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