The given question is a challenging GMAT 650+ level quant data sufficiency question testing concepts in Geometry. Concepts covered: Coordinate Geometry - Properties of Straight Lines - x-intercept and y-intercept - quadrants in x-y plane.

Question 25: Does the line L whose equation is y = mx + c cut the x-axis in the positive direction of x-axis?

**Statement 1**: The intercepts of Line K, perpendicular to L, are of the opposite signs.

**Statement 2**: Line L passes through the 4th quadrant.

@ INR

**Statement 1**: The intercepts of Line K, perpendicular to L, are of the opposite signs.

__Inference 1__: If the intercepts of line K are of opposite signs, line K is a positive sloping line.

__Inference 2__: So, we can infer that line L is a negative sloping line.

In this possibility, answer to the question is YES

In this possibility, answer to the question is NO

Because both possibilities exist, we are not able to answer the question using statement 1.

Statement 1 alone is NOT sufficient.

__Eliminate answer options A and D__.

**Statement 2**: Line L passes through the 4th quadrant.

In this possibility, answer to the question is YES

In this possibility, answer to the question is NO

Because both possibilities exist, we are not able to answer the question using statement 2.

Statement 2 alone is NOT sufficient.

__Eliminate answer option B__.

**Statement 1**: The intercepts of Line K, perpendicular to L, are of the opposite signs.

**Statement 2**: Line L passes through the 4th quadrant.

**Key Inference from Statement 1**: Line L is a negative sloping line.

In this possibility, answer to the question is YES

In this possibility, answer to the question is NO

Because both possibilities exist, we are not able to answer the question despite combining the statements.

Statement TOGETHER are NOT sufficient.

__Eliminate answer option C__.

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