If xy 0, is x < y ? (1) x^4 < y^4 (2) x^(-3) < x^(-3)

In other words, "Is x smaller than y?", but remember that you can also rewrite the question to Is \(y-x>0\)? which is equivalent to "Is y to the right of x on the number line?".

\(xy\neq{0}\) gives us that neither of the variables are zero.

Statement 1:
Any non-zero number with an even exponent is positive.
If you take the 4th root of both sides of the inequality \(x^{4}<y^{4}\), you get \(|x|<|y|\).
\(x\) could be \(-2\) and \(y\) could be \(3\), giving us a YES to the question.
\(x\) could be \(3\) and \(y\) could be \(-10\), giving us a NO to the question.
INSUFFICIENT

Statement 2:
We can rewrite the inequality as \(\frac{1}{x^{3}}<\frac{1}{y^{3}}\).
The signs (positive or negative) are the same for \(x\) and \(y\) as \(x^{3}\) and \(y^{3}\), respectively.
But since the variables are in the denominator, we do not have enough information to answer the question.
\(x\) could be negative and \(y\) could be positive, giving us a YES to the question.
\(x\) could be \(-2\) and \(y\) could be \(-5\), giving us a NO to the question.
INSUFFICIENT

Statement 1 and 2 together:
Still not enough information.
\(x\) could be \(-2\) and \(y\) could be \(3\), giving us a YES to the question.
\(x\) could be \(-2\) and \(y\) could be \(-5\), giving us a NO to the question.
INSUFFICIENT