grandh01 wrote:If point P'S (x,y) coordinates in a rectangular
system are (a,b), is point P in the rectangular
system's II quadrant?

1) a= -b
2) a<0

OA IS C

Target question: Is point P in quadrant II?

For point P to lie in quadrant II, it must be the case that the point's x-coordinate is negative and the y-coordinate is positive. In other words, we need coordinate a to be negative and coordinate b to be positive.

So, let's rewrite the target question as: Is a<0 and b>0?

Statement 1: a = -b
This essentially tells us that a is the opposite sign as b (or they both equal zero). From this information, we can get two conflicting cases.
case a) a = 1 and b = -1, in which case the answer to our rephrased target question is no.
case b) a = -1 and b = 1, in which case the answer to our rephrased target question is yes.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT.

Statement 2: a < 0
This answers part of our rephrased target question, but we have no idea whether or not b>0.
We cannot answer the target question with certainty, so statement 2 is NOT SUFFICIENT.

Statements 1 & 2:
Statement 2 tells us that a is negative.
Statement 1 tells us that a is the opposite sign as b.
So, if a is negative, then b must be positive.
At this point, we can be certain that a<0 and b>0
So, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent