If x and y are integers, is xy even?

Hi mpcostello,

The prompt tells us that X and Y are integers. Fact 2 tells us that X/Y is an EVEN INTEGER.

Neither of your examples fits the 'restriction' described by Fact 2.

1/1 = 1 which is NOT an EVEN integer
3/3 = 1 which is NOT an EVEN integer

Thus, you haven't proven anything yet. TESTing VALUES is a great way to prove what's going on in Fact 2, but you have to use values that fit what you're told.

GMAT assassins aren't born, they're made,
Rich

Dear Mpcostello

You were right in trying different values of x and y because as you said, at this point, we had no way of knowing whether x and y are odd or even. However, the point where you went wrong was that you considered such values of x and y that violated the information given in St. 2. Statement 2 clearly mentioned that x/y is an Even integer. However, both the sets of (x,y) values that you considered led to an odd value of x/y (1).

Actually, in this case, instead of going down the 'plugging different values of x and y' route, processing Statement 2 from the first principles would have been easier and would also have taken lesser time. Here's how I would have thought through this Statement:

x/y = Even Integer
=> x = (y)*(Even Integer)
=> x is an Even integer
=> Product xy = (Even integer x)*(y)
=> Product xy will definitely be Even.

Therefore, Statement 2 is sufficient.

So, the takeaway I hope you learn from your mistake in this question is:

- When taking the 'plugging in numbers' approach, be very careful that the chosen numbers do not violate the constraints given in the question.

Hope this helped.

- Japinder
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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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