If x and y are integers, is xy even?

Statement 1 : x= y+1
y is odd, x= even (vice-versa)hence xy=even
y is even, x=odd(vice-versa) again hence xy=even
Sufficient
Options left A,D

Statement 2: x/y=even= lets say 2n
x=2ny
xy=2ny*y=even
sufficient

Answer D)

"Correct answer is D. I understand the explanation for 1) that the formula suggests that x and y are consecutive integers in which case on is even and one is off and odd x even is even.

BUT...I divided x by y ie x/y = 1. This indicates that x=y as 1/1 = 1 and 3/3 = 1 as there is no knowing if the numbers or odd or even I had this point 1 a NS. This is wrong but was hoping someone could explain why my own method/thinking is inaccurate.

Thanks!"

The question is asking is xy even. Therefore what you really want to understand is, is at least one of the xy pair even? Since xy will be even if one or or both are even. Statement 2 tells you that x/y is even. 1 is not even so this wouldn't be applicable to this problem. Try odd and even values for x and y to see if you always get an even answer when you divide them. 4/2=even. 36/18=even. 20/10=even. 12/3=even. 18/3=even. As you see, in order to get an even result from x/y, x and y have to be even or x has to be even in order to get an even integer. If x alone is even, or if x and y are even, xy is even. (sufficient).

If x and Y are integers, is xy even?

In order the product of two integers to be even either (or both) of them must be even. So, the question basically asks whether either x or y is even.

(1) x = y + 1. If x is odd then y is even and vise-versa. Sufficient.
(2) x/y is an even integer --> \(\frac{x}{y}=even\) --> \(x=y*even=even\). Sufficient.

Answer: D.

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