Is x an even integer?

[sahilk47]

From the GMATPREP test:

(I searched for this question in the folder but I could not find it. In case any of you can find an existing thread on the same, I would request you to share or else lets discuss this question here.)

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

1) x(y+5) even integer
2) 6y^2+41y+25 is even integer

My attempt:

So, Statement 1 says x(y+5) is an even integer. For this, either x is an even integer or (y+5) is an even integer or both are even integers.

Incase x is an even integer and (y+5) is not even integer, thus, (y+5) is odd and so, y is an even integer. >>> Yes case

Incase x is an odd integer and (y+5) is an even integer, thus, (y+5) is even and so, y is an odd integer. >>> No case

Thus, Insufficient.

Statement 2 says 6y^2+41y+25 is even integer.
Assume y to be even integer, then 6y^2+41y+25 can be restated as: even.(even)^2 + odd.even + odd >> This gives us even + even + odd >> This gives us odd integer. As this contradicts with statement 2, thus y is odd integer. But no information on x.

Thus, Insufficient.

Together,
y is odd integer and we saw in statement 1 when y is odd integer then x is odd integer. Thus satisfied. My analysis suggests answer (c). However answer is (e).

Where am I going wrong?

Thank you!

[RonPurewal]

So, Statement 1 says x(y+5) is an even integer. For this, either x is an even integer or (y+5) is an even integer or both are even integers.

Incase x is an even integer and (y+5) is not even integer, thus, (y+5) is odd and so, y is an even integer. >>> Yes case

Incase x is an odd integer and (y+5) is an even integer, thus, (y+5) is even and so, y is an odd integer. >>> No case

Thus, Insufficient.

you forgot about the pink thing. the pink thing is the reason why the answer is E and not C. (in the pink situation, x is even and y is odd.)

you didn't need the consider the pink thing for statement 1 (since the first two possibilities already established 'not sufficient'). but it is still a possibility!

[RonPurewal]

also, this...

and we saw in statement 1 when y is odd integer then x is odd integer.

when you reached this conclusion ^^ you should have realized there was a mistake.

if y is odd, then (y + 5) is already even. thus it doesn't matter whether x is even or odd, since x(y + 5) is going to be even no matter what.

[sahilk47]

also, this...

and we saw in statement 1 when y is odd integer then x is odd integer.

when you reached this conclusion ^^ you should have realized there was a mistake.

if y is odd, then (y + 5) is already even. thus it doesn't matter whether x is even or odd, since x(y + 5) is going to be even no matter what.

Gotcha! Thank you!

[RonPurewal]

sure.