# Solutions

Get detailed explanations to advanced GMAT questions.

### Question

In the xy-plane, does the line L intersect the graph of y = x^2

I. Line L passes through (4, -8)

II. Line L passes through (-4, 16)

Option A:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Option B:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Option C:

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Option D:

Option E:

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Hard

### Solution

Option B is the correct answer.

### Option Analysis

y=x^2 is a parabola with vertex at (0,0) and upward……

Statement I is insufficient: Line passes through (4,-8); if the line is parallel to X-axis it can never intersect the parabola…. if the line is parallel to Y-axis it will… Not Sufficient

Statement II is sufficient: Line passes through (-4,16); observe that this point is on y=x^2 which means the line is intersecting parabola at the point…. It may or may not intersect y=x^2 at some other point, we don’t bother about it…. because the question asks for if the line is intersecting y=x^2 or not… so just a yes or no question…. in this case it is intersecting the graph… so sufficient…. 