GMAT Data Sufficiency (DS) | Re: If x and y are positive integers, what is the remainder when xy is div

I might not be thinking this through. Is using smart numbers a wrong approach?

1) x + y = xy. The only numbers that satisfy this equation are 2 + 2 = 4, 1 + 4 = 4, and 1 + 3 = 3 (xy). However, the remainder for 2 + 2 = 4 is 0 and for 1 + 3 = 3 is 3 when divided by 4. How is it sufficient?

2) For the second one, I get it (x - 1)(y - 1) is odd, IF we assume x and y to be 2 and 2, it would be (2 - 1) ( 2 -1) which is 1 and odd. Hence this is sufficent.

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