This is a Yes/No question with variables in the question stem and in the statements, so you can Plug In values for p and q.VJesus12 wrote:p>q, Is q negative?
(1) pq + q^2 is positive
(2) (p^2)(q) + (p)(q^2) is positive
The OA is E.
How can I determine that the correct answer is the option E? May someone help me?
Statement (1) states that pq + q^2 > 0
Plug In p=2 and q=3, so that (2)(3) + (3)^2 > 0, and 6 + 9 > 0.
Since the inequality is true when q=3, q can be positive.
Try to prove the statement insufficient by showing that q can also be negative.
Plug In p=2 and q=-3, so that (2)(-3) + (-3)^2 > 0, and -6 + 9 > 0.
Since the inequality is true when q=-3, q can be negative.
Statement (1) is insufficient, so write down BCE.
Statement (2) states that (p^2)(q) + (p)(q^2) > 0
Factor p out of the expression on the left of the inequality sign, so that p(pq + q^2) > 0.
We know from Statement (1) that pq + q^2 > 0 can be true whether q is positive or negative.
Therefore, p(pq + q^2) > 0 can be true whether q is positive or negative.
Statement (2) is insufficient, so eliminate choice B.
The expression in Statement (2) is simply p times the expression in Statement (1), so the combination of the statements provides no additional information.
The correct answer is choice E.
