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Re: If x and y are integers and x^2 + y^2 is odd, which of the following
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16 Oct 2019, 21:27
If x and y are integers and x2+y2 is odd, which of the following must be even?
If x2 + y2 is odd, this can be inferred that one of x2 and y2 is odd, and another is even.
So, we'll get either x is odd, y is even OR x is even, y is odd.
Now, let's see each answer choice on which choice yield EVEN
(A) x - can be both even/odd
(B) y - can be both even/odd
(C) x+y - definitely odd: since if x is even, y is odd and x+y = odd OR if y is even, x is odd, x+y = odd
(D) xy+y can be both even/odd, if x is even, y is odd; xy+y = odd OR if y is even, x is odd; xy+y = even
(E) xy - one of x and y needs to be even, which even * any number = even - CORRECT answer choice