DS: is Y an even integer?

Question

Please see below.

FN · Answer

E to for me...

can be odd and can be even both work..

gk3.14 · Answer

I think it is A

y(2+y) = (x)*(x+1)

If x is odd LHS is even; if x is even LHS is even (even * odd = even) which means y(2+y) is always even. This can only happen if y is even

govinam · Answer

Statement 2: 

we know that 2y is even on the left side of the equal side and that x is odd. This means that the left side of the equation must be odd.

left side:
e + o= odd

On the right side of the equation, we also know that x is odd but we don't know what y is. in order for the right side of the equation to be odd, y must be even.

right side:
O+E= Odd

Now the two side are both odd. Y must be even.

haas_mba07 · Answer

Answer: C

S1: 2y-x = x^2 -y^2
Simplifying:

y(y+2) = x(x+1)

Could have different values of y to satisfy integer or otherwise.

S2: x is odd integer.
Not sufficient.

S1 & S2:
x(x+1) = even
If y =odd, y+2= odd, y(y+2) = odd Not possible
If y = even, y = even, y(y+2) = even

Sufficient.

Answer: C

gmatornot · Answer

Got C also... exact same technique as haas_mba07 !

yezz · Answer

from one y(2+y) = (x)*(x+1) 
 since (x)*(x+1) will always be even

thus y(2+y) = even

2+y (ie even+??) could be even thus Y is even or could be odd and thus y is odd)

thus the only possible way that 2+y is even is when y is even

and thus the only way y(2+y) to be even is when Y is even.....suff

from b nothing of significance

thus my answer is A

Futuristic · Answer

good question....going with A.

x, y are I

From 1:

2y - x = x^2 -y^2
or
(2+y)y = x(x+1)

If x is an integer, then x is even or x is odd. If x is not even, then x+1 is even. Either ways, x(x+1) is even.

Then y(y+2) must be even.
This is only poss. if y is even....SUFF

From 2:

Insuff.

gmatornot · Answer

IF we take x = 1 or -1 we get y as a non-integer which is not possible since the stem says x & y are integers !

BG.. does this make sense ?

DS: is Y an even integer?

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