When DS questions involve algebra in the question stem, always try to simplify the algebra before looking at the statements.
With xy > (x^2)(y^2), it's tempting to want to divide both sides by xy. But what if one of the variables is 0? Or if xy is negative, we'd have to flip the sign. Instead, think conceptually: When would a product of two numbers be greater than the product of the squares? xy would have to be non-negative, since the squares will always be non-negative. It would also have to be between 0 and 1, because only numbers in that range get smaller when they are squared.
Target question: is xy between 0 and 1?
(1) 4x^2 = 19
This tells us that x^2 = 4.75, so x is the positive or negative square root of 4.75 (something close to 2 or -2). This doesn't tell us about y, so it's insufficient.
(2) y^2 = 1
This tells us that y = 1 or -1, but tells us nothing about x. Insufficient.
1 & 2 together
It seems like we don't have enough information, because we don't know whether x and y are positive or negative. But - it doesn't matter. The product xy will equal (approximately) 2 or -2. Either way, (xy)^2 will be larger than xy. Sufficient.
The answer is C.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
