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# For x and y integers, is xy even? (1) x2 + y2 is odd. (2) x

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For x and y integers, is xy even? (1) x2 + y2 is odd. (2) x [#permalink]  29 Oct 2004, 07:34
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For x and y integers, is xy even?

(1) x2 + y2 is odd.
(2) x + y is even.

Pls explain
Senior Manager
Joined: 06 Dec 2003
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Location: India
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Re: DS - XY [#permalink]  29 Oct 2004, 07:59
ninomoi wrote:
For x and y integers, is xy even?

(1) x2 + y2 is odd.
(2) x + y is even.

Pls explain

ODD + EVEN = ODD, otherwise EVEN

ODD * ODD = ODD, otherwise EVEN

So, xy to be even atleast one of them should be EVEN.

(A) X^2 + y^2 = ODD then one of them must be ODD and the other should be EVEN (as you know square of even is even and square of odd is odd)
clearly says, xy must be EVEN

(B) says X + Y = EVEN, so either both X and Y are ODD or both X and Y are EVEN.
If both are ODD - then XY = ODD and
if both are EVEN then XY = EVEN so, B can not answer the Question.

Dharmin
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Perseverance, Hard Work and self confidence

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Yep, the ans is A. Thanks for your help!
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