kilukilam
In the xy-plane, the line k passes through the origin and through the point (a,b), where ab does not equal 0. Is b positive?
(1) The slope of line k is negative
(2) a < b
Target question: Is b (the y-coordinate of the point on the line) positive? Given: Line k passes through the origin and through the point (a,b) Statement 1: The slope of line k is negative There are several lines and points that satisfy statement 1. Here are two:
Case a:
In this case, b (y-coordinate) is positive. So, the answer to the target question is
YES, b is positiveCase b:
In this case, b (y-coordinate) is negative. So, the answer to the target question is
NO, b is NOT positiveSince we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: a < bThere are several lines and points that satisfy statement 2. Here are two:
Case a:
In this case, b (y-coordinate) is positive. So, the answer to the target question is
YES, b is positiveCase b:
In this case, b (y-coordinate) is negative. So, the answer to the target question is
NO, b is NOT positiveSince we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that the slope of line k is negative. This means line k passes through quadrants II and IV.
In quadrant II, a (the x-coordinate) is always negative, and b (the y-coordinate) is always positive
In quadrant IV, a (the x-coordinate) is always positive, and b (the y-coordinate) is always negative
Statement 2 tells us that a < b
This means that the point (a,b) must be in quadrant II
(because, all points in quadrant IV are such that the x-coordinate (a) is greater than the y-coordinate (b) If point (a,b) is in quadrant II, we can be certain that
b (the y-coordinate) is positiveSince we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent