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Factor out \(a\): \(a(x^4 + |y|) < 0\). Since \(x^4 + |y| = nonnegative + nonnegative = nonnegative\), then for \(a*nonnegative\) to be negative, a must be negative. We know nothing about \(x\) and \(y\). Not sufficient.

(2) \(a*x^3 > a*y^3\).

If \(a\) is positive, then when reducing by it, we'll get \(x^3 > y^3\), or which is the same \(x > y\) BUT if \(a\) is negative, then when reducing by negative value and flipping the sign, we'd get \(x^3 < y^3\), or which is the same \(x < y\). Not sufficient.

(1)+(2) Since from (1) \(a < 0\), then from (2) \(x < y\). Sufficient.

For statement 1 to be true, cant all three be fractions ?

From (1) all we can deduce is that a is negative (and that not both from x and y are 0). Other than that, the variables could be integers, fractions, or irrational numbers, we don't know that.
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