Dblooos wrote:I was wondering what should be the correct answer to this data sufficiency question. Can anyone please explain with the reasoning? Thank you in advance.

106. If x and y are integers, is xy even?
(1) x = y + 1
(2)x/y is an even integer.

Hi Dblooos,
This question test the properties of Numbers.

The product of two Integers can be Even if either of them(or both) are Even.
So Question ask whether X or Y Even or not?

Statement1 : x = y + 1
if X is Odd Y will be even or Vise-versa. Hence Sufficient.

Statement 2: x/y is an even integer.
X/Y = Even
X = Y* Even
So X = Even
hence Sufficient.

Answer is [spoiler]D[/spoiler]

Hope it helps you.

Regards,
Uva

Hi,
In statement 1: x = y + 1
y could be 0, then x = 1
In this case xy is even. In other cases also xy is even. So statement 1 is sufficient.

Statement 2: x/y = even so x = y * even = even so X is even
Y could be even or odd but xy is always even. Sufficient,

So answer according is d.

Plug in some numbers -


(1) x = y + 1

X = 3 , Y = 2

xy = 6 ( According to the condition )

Sufficient....


(2)x/y is an even integer.

X = 6 , Y = 1

XY = 6


xy = 6 ( According to the condition )

Sufficient....

EACH statement ALONE is sufficient to answer the question asked ..

x & y are INTEGER.. can be "0" as well

To find: xy is even..

IMP: "0" is even

Statement 1:
x = y + 1
if y is EVEN or "0" then "x" is ODD
if y is ODD then "X" is EVEN
(EVEN)*(ODD) = EVEN
SUFFICIENT

Statement 2:
X/Y is EVEN
If, X/Y is even then either "X" is EVEN or "0"
Also, is "x" is "0" then also resultant xy is EVEN
SUFFICIENT

Answer [spoiler]{D}[/spoiler]

Thank you everyone. I think I was confused as I didn't consider "0" as even. I got it. Cheers!!