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odd/even

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by Ramit88 » Tue Jan 25, 2011 10:23 pm
if r and s are integers and rs + r is always odd. which of the following must be even ?

a r
b s
c r+s
d rs-r
e r^2 +s

[spoiler]Ans B
[/spoiler]

how yo choose between r and r+s

both are always odd
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by Anurag@Gurome » Tue Jan 25, 2011 10:47 pm
Ramit88 wrote:if r and s are integers and rs + r is always odd. which of the following must be even ?

a r
b s
c r + s
d rs - r
e r² + s
(rs + r) = r(s + 1)
As product of r and (s + 1) is always odd, both r and (s + 1) will be always odd.

Hence, s is even and r is odd.
From this point we know that s is even and B is the correct answer as there will be only one correct answer. If you have doubt you can check the other option as follows...

Now,
  • (r + s) = odd + even = odd
    (rs - r) = r(s - 1) = odd*(even - 1) = odd*odd = odd
    (r² + s) = odd² + even = odd + even = odd
Hence, all of the answer choices except option B are odd.

The correct answer is B.
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by GMATGuruNY » Wed Jan 26, 2011 3:02 am
Ramit88 wrote:if r and s are integers and rs + r is always odd. which of the following must be even ?

a r
b s
c r+s
d rs-r
e r^2 +s

[spoiler]Ans B
[/spoiler]

how yo choose between r and r+s

both are always odd
Plug in r=3, s=2. This combination satisfies the condition given: rs + r = 3*2 + 3 = 9.

Eliminate any answer choice that does not yield an even result.

A) r=3. Eliminate A.
B) s=2. Hold onto B.
c) r+s = 3+2 = 5. Eliminate C.
d) rs-r = 3*2 - 3 = 3. Eliminate D.
e) r^2 + s = 3^2 + 2 = 11. Eliminate E.

The correct answer is B.
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