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# If r and s are integers, is r^2+s even?

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Board of Directors
Joined: 01 Sep 2010
Posts: 3279
If r and s are integers, is r^2+s even?  [#permalink]

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02 Nov 2018, 02:46
Top Contributor
00:00

Difficulty:

15% (low)

Question Stats:

82% (01:12) correct 18% (00:45) wrong based on 28 sessions

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If r and s are integers, is $$r^2+s$$ even?

(1) The product of rs is odd.
(2) r is odd.

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examPAL Representative
Joined: 07 Dec 2017
Posts: 868
Re: If r and s are integers, is r^2+s even?  [#permalink]

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02 Nov 2018, 03:05
carcass wrote:
If r and s are integers, is $$r^2+s$$ even?

(1) The product of rs is odd.
(2) r is odd.

Questions involving number properties are usually based on logic, not explicit calculations.
We'll look for such an answer, a Logical approach.

(1) rs is odd implies that both r and s are odd. Then r^2 is odd and r^2 + s is odd + odd = even.
Sufficient.

(2) without information on s, this is insufficient.
Insufficient.

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Re: If r and s are integers, is r^2+s even? &nbs [#permalink] 02 Nov 2018, 03:05
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