Critically reasoning about the relevant number property concepts is often the best approach to these kinds of questions. If you have to, or if you want to, you can also pick numbers to facilitate your reasoning. You should also spend adequate time analyzing the question stem before proceeding to the statements.
Looking at the question:
Is xy > x^2 + y^2?
Squares are always positive. Therefore, the right hand side is positive. Therefore, in order for the left hand side to be larger than the right hand side, the product xy will also have to be positive. Therefore, x and y would have to share the same sign (because if one were negative and the other positive, then the left hand side would be negative, and certainly smaller than the positive right hand side). So, in order to be sufficient, the statements would have to tell us whether x and y share the same sign.
(1) 14x^2 = 3
So, x^2 = 3/14
Because x^2 is a fraction, (1) tells us that x itself is also a fraction (ie, a noninteger whose absolute value is less than 1). But we don't have any info about x's sign. And, obviously, there is no info about y's sign. Thus, (1) is insufficient.
(2) y^2 = 1
So, y can be +1 or -1 (and no info about x). Thus, (2) is insufficient.
Together, you still don't know about either of x or y's sign.
Choose E.
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