Bunuel wrote:
If line M passes through the coordinate system shown above, is the slope of line M greater than zero?
(1) Line M passes through Quadrant III.
(2) Line M passes through Quadrant I.
Target question: Does line M have a POSITIVE slope? Statement 1: Line M passes through Quadrant III Consider the two lines shown here:
Both lines satisfy the condition that line M passes through Quadrant III.
Case a: For the blue line, the answer to the target question is
YES, the slope is line M is IS positiveCase b: For the red line, the answer to the target question is
NO, the slope is line M is NOT positiveSince we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Line M passes through Quadrant I Consider the two lines shown here:
Both lines satisfy the condition that line M passes through Quadrant I.
Case a: For the blue line, the answer to the target question is
YES, the slope is line M is IS positiveCase b: For the red line, the answer to the target question is
NO, the slope is line M is NOT positiveSince we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statements 1 and 2 combined If line M passes through Quadrant III AND through Quadrant I, then the slope of line M must be positive.
For example:
So, the answer to the target question is
YES, the slope is line M is IS positiveSince we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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