Is |xy|> (xy)^2 ?
The OA is C. I don't quite understand why its C and not D.
the left-hand side is the square root of the right-hand side. i.e., |xy| is the square root of (xy)^2.
so, a YES to this question means that, when |xy| is squared
, it gets smaller
.if |xy| is between 0 and 1, the answer to the question will be YES.
the individual statements aren't sufficient because they don't impose any constraints at all on the other
for instance, statement (1) limits x to between 0 and 1/2 (or between -1/2 and 0) -- but, under that statement, y can be literally any number in the world.
so, if x is, say, 1/4 and y is another fraction, you're going to get a YES to the question.
but, if x is 1/4 and y is 1,000,000,000, then you're going to get a NO to the question.
same logic applies to the other statement, with the roles of x and y reversed.
once you get the two statements together, though, you know for sure that both x and y are fractions. this way |xy| is definitely less than 1, and so it will definitely get smaller when you square it.