Hi folks,

Could someone walk me through this problem? Thanks!

official answer is (E)

Abramson, whenever you are given a visual description of a problem on the Quant section, be sure to draw the problem on you scratch board. Sometimes, simply by visualizing the possibilities (Data Sufficiency) or ballparking (Problem Solving), you can arrive at the correct response without doing any math.

In this problem, the only information given is that circle C is centered at (0,0) and has a radius of 1.

Statement (1) alone is insufficient since we have no idea where line k actually crosses the x axis or what the line's slope actually is. For example, line k could cross the x axis at (2,0) and have a small (relatively horizontal) slope, thus creating an intersection with circle C. However, line k could cross the x axis at (1 million,0) and have a steep (relatively vertical) slope, thus never intersecting with circle C. Eliminate AD from your AD/BCE grid.

Statement (2) alone is insufficient as we have no idea where in the plane line k is located. Eliminate B from your BCE grid.

Together, we still suffer from the same lack of information that plagued us with Statement (1). Though we know from Statement (2) that the slope of line k is relatively horizontal, we have no idea where the line crosses the x axis - it could be at (2,0), which yields an intersection with the circle, or it could be at (1 million, 0), which yields no intersection.

Due to this lack of information, the credited response is E.

-dan