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# If x and y are integers and x^2 + y^2 is odd, which of the following m

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Senior Manager
Joined: 18 Jun 2018
Posts: 263
If x and y are integers and x^2 + y^2 is odd, which of the following m  [#permalink]

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17 Oct 2018, 08:47
1
00:00

Difficulty:

35% (medium)

Question Stats:

64% (00:47) correct 36% (01:01) wrong based on 37 sessions

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If $$x$$ and $$y$$ are integers and $$x^2 + y^2$$ is odd, which of the following must be even?

(A) $$x$$
(B) $$y$$
(C) $$x + y$$
(D) $$xy + y$$
(E) $$xy$$
Director
Joined: 19 Oct 2013
Posts: 520
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
Re: If x and y are integers and x^2 + y^2 is odd, which of the following m  [#permalink]

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17 Oct 2018, 10:12
1
Bismarck wrote:
If $$x$$ and $$y$$ are integers and $$x^2 + y^2$$ is odd, which of the following must be even?

(A) $$x$$
(B) $$y$$
(C) $$x + y$$
(D) $$xy + y$$
(E) $$xy$$

The powers does not effect odd or even.

even + odd = odd.

Even * odd = even.

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Director
Joined: 09 Mar 2018
Posts: 997
Location: India
Re: If x and y are integers and x^2 + y^2 is odd, which of the following m  [#permalink]

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17 Oct 2018, 10:29
1
For x^2 + y^2 to be odd, there are two cases possible
Case 1: x is Odd and y is Even
Case 2: x is Even and y is Odd

Need to find which one of the following will be even

Take a magic number like x=4 and y=5

Once you realize this, question is quite simple
(A) x, Can be true if you take Case 2
(B) y, Can be true if you take Case 1
(C) x+y, Not true
(D) xy+y Not true
(E) xy

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Re: If x and y are integers and x^2 + y^2 is odd, which of the following m   [#permalink] 17 Oct 2018, 10:29
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