Question: Is x Even

Comment on Is x Even

For statement 2, I plugged in numbers. And every time it was an even number for x and an odd number for y, the = was odd. Every time I flipped it, the = was even. So I concluded that x = even. Why would plugging in numbers not work here?
gmat-admin's picture

Can you show me your calculations. I ask, because I think your calculations might be off.

Statement 2: 6x - 3y is odd

- case a: if x is even and y is odd, then 6x - 3y is ODD. In this case, x IS even

- case b: if x is odd and y is even, then 6x - 3y is ODD. In this case, x is NOT even

Both cases satisfy statement 2, but each case yields a different answer to the target question. This means statement 2 is not sufficient.

can statement 2 be solved this way: the difference btwn x and y means that x and y are not the same (one must be even, the other must be odd). Since we have no clue whether it's x or y that's even, since it works either way, statement 2 is not suff, so answer is A
gmat-admin's picture

Be careful. Statement 2 does talk about the difference between x and y; it talks about the difference between 6x and 3y. Since 6x must be EVEN, we can conclude that y is odd.

If the target question had asked "Is y odd?", your approach would have found statement 2 to be insufficient, when it would have been sufficient.

For statement 1, if I look at xy+y is odd then either of the two terms will have to be odd. If we assume that y= odd, then x will have to be even since first term xy = has to even. Alternatively, if y=even, then x will have to be odd since first term has to be odd. This statement 1 comes out as insufficient. What am I missing here.
gmat-admin's picture

Your first statement is true.

However, your second statement is not true: Alternatively, if y=even, then x will have to be odd since first term has to be odd.
If y is even, then the first term (xy) will be even, regardless of the value of x.

This tells us that, if xy+y is odd, then y must be odd.

Cheers,
Brent

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