Bunuel wrote:

For integers x and y, is \(x + y\) even?

(1) \(x^2 − y^2\) is even

(2) \(x − y\) is even

Official solution from

Veritas Prep.

D. This question is a good example of the GMAT's classic "C trap", in which the statements are written to bait you toward selecting C. Yes, you can deconstruct statement 1 into:

\((x + y)(x - y)\) is even

But at this point you don't need to use statement 2 along with it. Your options now with statement 1 alone are:

\((Even + Even)(Even - Even) = Even\)

and

\((Odd + Odd)(Odd - Odd) = Even\)

It

cannot be \((Even + Odd)(Even - Odd)\) because then the two parentheticals would both be odd, making the product odd. So statement 1 guarantees that each of \((x + y)\) and \((x - y)\) are even.

Similarly, statement 2 guarantees that \(x + y\) is even. For \(x - y\) to be even, it's either Odd - Odd or Even - Even. Change that minus to a plus in either case and the result will still be even, so statement 2 is sufficient, also. The correct answer is D.

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