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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Brent Hanneson – GMATPrepNow.com