Hi,
My approach to this problem is not the same as the approach described in the MGMAT solution, please let me know if my approach sounds right:
If pq ≠0, is (p^2)q > p(q^2)?
(1) pq < 0
(2) p < 0
I rephrased the question by dividing both sides by q^2, and then divide again by p^2 because it's ok to divide a variable if you're sure it's positive and the problem tells me that p or q cannot be 0. So the rephrased question is is (1/q)>(1/p)?
I need both statements in order to be sure that (1/q), which is a positive fraction must be greater than (1/p) which is a negative fraction.
Here's the MGMAT explanation:
The question can first be rewritten as "Is p(pq) > q(pq)?"
The temptation is to divide both sides by pq right away. However, you should always check yourself before dividing either an equation or an inequality by a variable expression, because you have to make sure you aren't dividing by zero. However, since pq does not equal zero, we know that we can divide by this expression (neither p nor q is zero). Secondly, if you divide (or multiply) both sides of an INEQUALITY by a variable expression, you have to track the positive and the negative cases separately, because the inequality sign changes direction in the negative case.
If pq is positive, we can divide both sides of the inequality by pq and the question then becomes: "Is p > q?"
If pq is negative, we can divide both sides of the inequality by pq and change the direction of the inequality sign and the question becomes: "Is p < q?" Notice that this question is now "Is p LESS THAN q?"
Since Statement 2 is less complex than Statement 1, begin with Statement 2 and a BD/ACE grid.
(1) INSUFFICIENT: Knowing that pq < 0 means that the question becomes "Is p < q?" We know that p and q have opposite signs, but we don't know which one is positive and which one is negative so we can't answer the question "Is p < q?"
(2) INSUFFICIENT: We know nothing about q or its sign.
(1) AND (2) SUFFICIENT: From statement (1), we know we are dealing with the question "Is p < q?," and that p and q have opposite signs. Statement (2) tells us that p is negative, which means that q is positive. Therefore p is in fact less than q.
The correct answer is C.
My approach to this problem is not the same as the approach described in the MGMAT solution, please let me know if my approach sounds right:
If pq ≠0, is (p^2)q > p(q^2)?
(1) pq < 0
(2) p < 0
I rephrased the question by dividing both sides by q^2, and then divide again by p^2 because it's ok to divide a variable if you're sure it's positive and the problem tells me that p or q cannot be 0. So the rephrased question is is (1/q)>(1/p)?
I need both statements in order to be sure that (1/q), which is a positive fraction must be greater than (1/p) which is a negative fraction.
Here's the MGMAT explanation:
The question can first be rewritten as "Is p(pq) > q(pq)?"
The temptation is to divide both sides by pq right away. However, you should always check yourself before dividing either an equation or an inequality by a variable expression, because you have to make sure you aren't dividing by zero. However, since pq does not equal zero, we know that we can divide by this expression (neither p nor q is zero). Secondly, if you divide (or multiply) both sides of an INEQUALITY by a variable expression, you have to track the positive and the negative cases separately, because the inequality sign changes direction in the negative case.
If pq is positive, we can divide both sides of the inequality by pq and the question then becomes: "Is p > q?"
If pq is negative, we can divide both sides of the inequality by pq and change the direction of the inequality sign and the question becomes: "Is p < q?" Notice that this question is now "Is p LESS THAN q?"
Since Statement 2 is less complex than Statement 1, begin with Statement 2 and a BD/ACE grid.
(1) INSUFFICIENT: Knowing that pq < 0 means that the question becomes "Is p < q?" We know that p and q have opposite signs, but we don't know which one is positive and which one is negative so we can't answer the question "Is p < q?"
(2) INSUFFICIENT: We know nothing about q or its sign.
(1) AND (2) SUFFICIENT: From statement (1), we know we are dealing with the question "Is p < q?," and that p and q have opposite signs. Statement (2) tells us that p is negative, which means that q is positive. Therefore p is in fact less than q.
The correct answer is C.
