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If x and y are integers, and x² + xy + y + x is even,

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Re: If x and y are integers, and x² + xy + y + x is even, [#permalink]
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BrentGMATPrepNow wrote:
If x and y are integers, and x² + xy + 2y + x is even, which of the following MUST be true?

I. xy is even
II. x is even
III. x + y is odd

A) I only
B) III only
C) I and II
D) I and III
E) II and III

With this question type, I find it useful to first test all 4 possible cases, by plugging in 0 for even numbers, and 1 for odd numbers.

When we do so, we get:

Since we're told x² + xy + y + x is EVEN, we can see that cases i, ii and iii are all possible.

Now let's examine the three statements...

I. xy is even
For all three possible cases (i.e., cases i, ii and iii), xy will be even.
So, statement I must be true.

II. x is even
x is even for cases i and ii, but x is ODD for case iii.
Therefore, statement II need not be true.

III. x + y is odd
x + y is odd for cases ii and iii, but x + y is EVEN for case i.
Therefore, statement III need not be true.

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Re: If x and y are integers, and x² + xy + y + x is even, [#permalink]
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Re: If x and y are integers, and x² + xy + y + x is even, [#permalink]
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