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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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15 Sep 2021, 01:16
15 Sep 2021, 01:16
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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
(A) x
(B) y
(C) x + y
(D) xy + y
(E) xy
Re: If x and y are integers and x 2 + y 2 is odd, which of the following m
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15 Sep 2021, 09:35
15 Sep 2021, 09:35
1
\(x^2 + y^2\) is odd.
So we can say for sure that one of them will be even and the other will be odd. No other possibilities.
Hence, the multiplication of both will be even.
Answer E
So we can say for sure that one of them will be even and the other will be odd. No other possibilities.
Hence, the multiplication of both will be even.
Answer E
Re: If x and y are integers and x 2 + y 2 is odd, which of the following m
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15 Sep 2021, 11:14
15 Sep 2021, 11:14
1
Saying \(x^2+y^2\) is odd is same as \(x+y\) is odd. Since squaring keeps the parity.
if \(x+y\) is odd, then only one of them is odd, which means \(odd * even\) = even, so E)
if \(x+y\) is odd, then only one of them is odd, which means \(odd * even\) = even, so E)
