smushkas wrote:Hey there,

Can anyone explain this problem? I have the explanation, but I can't quite catch the logic behind the question.



Both x and y are integers. In all cases where x is even, y is also even. Is xy even?

[1] y - x is odd

[2] sqrt[xy] = 6


Thanks in advance!

OA [spoiler] D [/spoiler]

Is xy even?

Since x and y are integers, xy will be even if x OR y is even. So, the question is really asking:

is either x or y even?

(1) y - x is odd. Well, the only way to get an odd difference is an even - an odd or an odd - an even. Therefore, y is even and x is odd (since if x was even, y would have to be as well). Y is even, therefore xy is even: sufficient.

(2) sqrt(xy) = 6

If we square both sides, we get xy = 36, which is even: sufficient.

Each of (1) and (2) are sufficient alone: choose (d).

What's the purpose of this statement in the question : 'In all cases where x is even, y is also even' - doesn't it suggest that xy is even*even?

xilef wrote:What's the purpose of this statement in the question : 'In all cases where x is even, y is also even' - doesn't it suggest that xy is even*even?

It's a one-way conditional statement:

"if x is even, then y is even".

So, there are 3 possibilities:

x even, y even
x odd, y even
x odd, y odd