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

(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.

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. Answer is E.

Another Quality Question from the GMAT prep
Here we are given that x,y are two integers
We need to examine x for its even/odd nature

Lets look at statement
Statement 1
Here if y is odd
x can be even or odd
hence not sufficient
Statement 2
This statement tells us that 41y=> even-even-odd=> odd so => y must be odd
No clue of x
hence not sufficient
Combing the two statements
as y is odd => y+5 will be even
hence x(y+5 will always be even irrespective of whether x is even or not
Hence we can't say whether x is even or not
Hence insufficient

Hence E

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