# GMAT Data Sufficiency Practice Question 25

###### Geometry | Coordinate Geometry | Data Sufficiency

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.

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### Explanatory Answer | GMAT Geometry DS Practice Question

#### Step 1: Evaluate Statement 1 ALONE

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.

##### Possibility 1: Negative sloping Line L with a positive x-intercept

In this possibility, answer to the question is YES

##### Possibility 2: Negative sloping Line L with a negative x-intercept

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.

#### Step 2: Evaluate Statement 2 ALONE

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

##### Possibility 1: Line L passes through IV quadrant. Has a positive x-intercept.

In this possibility, answer to the question is YES

##### Possibility 2: Line L passes through IV quadrant. Has a negative x-intercept

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.

#### Step 3: Evaluate Statements TOGETHER

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.

##### Possibility 1: Negative Sloping Line L passes through IV quadrant. Has a positive x-intercept.

In this possibility, answer to the question is YES

##### Possibility 2: Negative Sloping Line L passes through IV quadrant. Has a negative x-intercept

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.

##### Choice E is the correct answer.

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