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If x and y are positive integers, is x^2 + y^2 odd?

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Bunuel
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If x and y are positive integers, is x^2 + y^2 odd? [#permalink] New post   19 Jun 2018, 23:43
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If x and y are positive integers, is x^2 + y^2 odd?


(1) xy is even.

(2) (x + 2)(y + 4) is even.
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E
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If x and y are positive integers, is x^2 + y^2 odd? [#permalink] New post   20 Jun 2018, 00:06
1. \(xy\) is even.
Case 1: Both x and y are even. Here, \(x^2 + y^2\) is even.
Case 2: Either of x and y is odd, the other variable is even. Here,
\(x^2 + y^2\) is odd. We can't arrive at a unique solution. (Insufficient)

2. \((x + 2)(y + 4)\) is even.
This is pretty much the same thing as Statement 1. So, the same
cases apply here. Again, we can't arrive at a unique solution. (Insufficient)

When we combine the information in both the statements, we cannot
arrive at a unique solution for \(x^2 + y^2\), which can be both odd/even. (Insufficient - Option E)
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Re: If x and y are positive integers, is x^2 + y^2 odd? [#permalink] New post   20 Jun 2018, 00:37
Bunuel wrote:
If x and y are positive integers, is x^2 + y^2 odd?


(1) xy is even.

(2) (x + 2)(y + 4) is even.



we are asked to find out whether x^2+y^2 is odd or not.

Statement 1: xy is even. Not sufficient.

both x any could be even or x is even , y is odd, or vice versa. Thus we are failed to determine the ultimate result of the x^2+y^2

Statement 2: The same as statement 1. there is a multiplication relation between 2 properties. we are sure that either x+2 or y+4 is even. so, x or y both can be even or either x or y could be even.

Thus nit sufficient.

(1+2):

Still impossible to determine both x or y is even or odd. If and only if both x and y are even , x^2+y^2 will be even.

Thus the best answer is E.
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If x and y are positive integers, is x^2 + y^2 odd? [#permalink] New post   21 Jun 2018, 05:06
Given x ,y are +ve integers .

(1) xy is even.
Either X is even or Y is even or Both X and Y can be even ...So nothing can be said about x^2+y^2 ==> Insufficient

(2) (x + 2)(y + 4) is even.
(XY+ 4X +2Y +8) is Even->from this we can only say that XY is even which is a redundant information==> Insufficient .

Since Statement 1 and 2 gives the same info we need not go for option c , So Answer is Option E
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If x and y are positive integers, is x^2 + y^2 odd? [#permalink]
21 Jun 2018, 05:06
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Bunuel
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