I think the answer should be B not C

[email protected] wrote:In the xy-plane , line l intersects a circle with center at origin. Is the slope of line l equal to zero?

1) line l passes through second quadrant.

2) line l is perpendicular to the tangent of the circle.

But I don't think either way, because I can visualize the tangent to this circle may or may not be parallel to y-axis. My answer under the given constraints is E.

i think it should be E

the line with zero slope means its horizontal where the value of y remains zero. the first statement says that its in II quadrant...its insufficient
statement II says its perpendicular to the tangent of the circle. u can draw tangent anywhere and thus wont be sufficient to prove.
together still i cant find the two statements sufficient. u can pass a line with negative slope that passes from II quadrant perpendicular to tangent drawn in quadrant III

Brent@GMATPrepNow wrote:

[email protected] wrote:In the xy-plane , line l intersects a circle with center at origin. Is the slope of line l equal to zero?

1) line l passes through second quadrant.

2) line l is perpendicular to the tangent of the circle.

Target question: Is the slope of line l equal to zero?

IMPORTANT: Since a circle can have an infinite number of tangent lines, the answer here is E.
To prove this, let's jump straight to . . .

Statements 1 and 2 combined
Here are two possible scenarios that meet the two given conditions:
Case a:


Case b:


In once case, the slope of line l equals 0, and in the other case, the slope of line l does not equal 0.
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

Hi Brent,

I wonder where and how do you do these drawings, this really makes great sense while explaining Geometry problems. Would you please PM or tell me the same under this thread only.


Warm Regards

If the diagram is there,it will be easy to understand the question.

[email protected] wrote:In the xy-plane , line l intersects a circle with center at origin. Is the slope of line l equal to zero?

1) line l passes through second quadrant.

2) line l is perpendicular to the tangent of the circle.