Max@Math Revolution wrote:
Is xy > 0?
1) x³y > 0
2) x²y > 0
Target question: Is xy > 0?
Statement 1: x³y > 0
Since x² is POSITIVE, we can safely divide both sides of the inequality by x²
When we do this, we get xy > 0
So, the answer to the target question is
YES, xy IS greater than 0
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: x²y > 0
Once again, we can safely divide both sides of the inequality by x²
However, this time we get y > 0
So, we now know that y is POSITIVE, but we don't know whether x is positive or negative.
As such statement 2 is NOT SUFFICIENT
If you're not convinced, we can always
test some values
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 1 and y = 1. In this case, xy = (1)(1) = 1. So, the answer to the target question is
YES, xy IS greater than 0
Case b: x = -1 and y = 1. In this case, xy = (-1)(1) = -1. So, the answer to the target question is
NO, xy is NOT greater than 0
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
