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If x and y are positive integers, is x an even integer?

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If x and y are positive integers, is x an even integer? [#permalink] New post 08 Mar 2011, 12:18
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If x and y are positive integers, is x an even integer?

(1) x(y + 5) is an even integer.
(2) 6y^2 + 41y + 25 is an even integer.
[Reveal] Spoiler: OA

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Re: If x and y are positive integers, is x an even integer? [#permalink] New post 08 Mar 2011, 12:38
Expert's post
Question moved to DS subforum.

If x and y are positive integers, is x an even integer ?

(1) x(y+5) is an even integer --> if y is an odd integer then y+5=even and x can be even or odd. Not sufficient.

(2) 6y^2 + 41y + 25 is an even integer --> 6y^2 + 41y + 25=even+41y+odd=even --> odd+41y=even --> 41y=odd --> y=odd, still insufficient as no info about x.

(1)+(2) As from (2) y=odd then from (1) x can be even as well as odd. Not sufficient.

Answer: E.

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Re: If x and y are positive integers, is x an even integer? [#permalink] New post 08 Mar 2011, 17:29
My answer is E.

1. is not sufficient , as the expression is satisfied for both o and e values of x.

2. no info about x. not sufficient

together y is odd, x can still be odd or even . so not enough
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Re: If x and y are positive integers, is x an even integer? [#permalink] New post 08 Mar 2011, 18:13
(1) x(y+5) is an even integer --> x can be odd, y can be odd too, not sufficient

(2) 6y^2 + 41y + 25 is an even integer --> y(6y + 41) + 25 => y (even + odd) + odd , no info about x though, so not enough


Combining (1) and (2), from (2) we only know that y (even + odd) is odd, so y is odd, but even this can't make x odd necessarily in (1)


x * even = even, so again x can be odd or even
So the answer is E.
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Re: If x and y are positive integers, is x an even integer? [#permalink] New post 14 Mar 2011, 14:43
I got this wrong this the first time around when pressed for time but it's pretty clear where I went wrong.

1) and 2) were easy to rule out as insufficient on their own.

x could be even or odd from the situation given in 1). 2) doesn't give us any information at all about x.

The answer must be C or E.

When looking at 1) + 2) I got confused how to pry information for 2). I kept seeing a quadratic equation, although factoring it would obviously do no good in this case.

When reviewing and having more time, I saw that:

6y^2 + 41y + 25 = even
6y^2 + 41y + odd = even
6y^2 + 41y = odd

Therefore, in 6y^2 and 41y must be one odd and one even. Y must be odd, otherwise you would have two evens.

Looking back at 1), if Y is odd, this all we know:

x(even) = even

We know nothing. :-D Answer is E.
Re: If x and y are positive integers, is x an even integer?   [#permalink] 14 Mar 2011, 14:43
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