The fact that xyz < 0 does not give enough information about the unknowns to be able to compare the two quantities. We just know that two of them should be positive and the other negative but nothing more. Given that we can't compare the quantities answer is D!

Let's test some possible values of x, y and z

case i: Since \(xyz < 0\), it could be the case that \(x=1\), \(y=1\) and \(z=-1\)
We get:
Quantity A: \(x + y + z = 1 + 1 + (-1) = 1\)
Quantity B: \(2(1) + 2(1) + 2(-1) = 2\)
In this case, Quantity B is greater

case -i: Since \(xyz < 0\), it could be the case that \(x=-1\), \(y=-1\) and \(z=-1\)
We get:
Quantity A: \(x + y + z = (-1) + (-1) + (-1) = -3\)
Quantity B: \(2(-1) + 2(-1) + 2(-1) = -6\)
In this case, Quantity A is greater

Answer: D


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