If x3 + yz 0, is xy3z2 0? (1) y 0 z (2) x 0

Question

If  x^3 + yz > 0 , is  xy^3z^2 > 0 ?

(1) y > 0 > z
(2) x > 0

IanStewart · Answer

Since y^2 z^2 is positive, we can divide the question on both sides by y^2 z^2 without needing to worry about whether we should reverse the inequality. So the question is just asking "is xy > 0?"

Statement 1 tells us y is positive. It also tells us yz is negative. Since x^3 + yz > 0, then x^3 > -yz, and if yz itself is negative, -yz is positive, so this tells us "x^3 is greater than some positive number", and x^3 must be positive. That means x is positive, so x and y are both positive, and xy > 0, and Statement 1 is sufficient.

Statement 2 is not sufficient since y can be positive or negative, so the answer is A.

MHIKER · Answer

(1) y is positive but z is negative. So from  x^3 + yz > 0  we can deduce x is positive.  xy^3z^2 > 0  holds true. Sufficient.

(2) No information about y. INSUFFICIENT.

The Answer is A

MHIKER · Answer

Your reasoning is Y and Z are non-zero. Right? Because if x is negative and either y or z is zero then  x^3 +yz will not be greater than "0"

IanStewart · Answer

Statement 1 tells us y and z are nonzero.

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If x3 + yz > 0, is xy3z2 > 0? (1) y > 0 > z (2) x > 0

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