IMPORTANT: From the given inequalities, we can conclude that x ≠ 0 and y ≠ 0
This mean that x² is POSITIVE and y² is POSITIVE

If x² is POSITIVE, we safely take x²y > 0 and divide both sides by x² to get: y > 0
In other words, y is some positive number

Likewise, since y² is POSITIVE, we safely take xy² < 0 and divide both sides by y² to get: x < 0
In other words, x is some negative number

So, we get:
Quantity A: some negative number
Quantity B: some positive number

Answer: B