This question seems to work best by testing a few numbers.

For (1), I started out by testing two options: when both numbers are positive and when both numbers are negative. Here, if we take a = 2 and b = 1, then f = 2^2 - 1^2 = 4 - 1 = 3, and thus > 0. However, if we take a = -1 and b = -2, then we get f = (-1)^2 - (-2)^2 = 1 - 4 = -3, and thus < 0. So (1) is not sufficient.

For (2), what a/b > 0 means is that a and b shares a sign, and are non-zero. We just need to test two positive and two negative values for a and b. Hey... didn't we already do that for (1)? Yeah we did. (2) is not sufficient.

Even when we put (1) and (2) together, those examples still work. So E is our answer.

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Not a professional entity or a quant/verbal expert or anything. So take my answers with a grain of salt.