Data Sufficiency

Hi,

Request help with the following question.Thanks..

In xy plane, a certain line L1 has how many intersections with y = x^2 +2?

1. Line L1 does not intersect the X- Axis
2. The point Q (2,1) lies on line L1

Shivani,

The answer would be C

y = x2+2 means that the line of the symmetry is at x=0 and parabola intersects the y axis at 2.

Statement 1 tells me that line l1 does not intersect the x axis which means that line l1 is parallel to the x axis. Therefore the line l1 could intersect the parabola at 2 points (in quadrant 1 or 2) or not at all. If it had any slope then the line l1 would intersect the x-axis at some point. InSufficient.

Statement 2 - With point (2,1) intersecting the line l1, the line l1 could be parallel to the x-axis or could be at a slope intersecting the parabola at quadrant I or II. Insufficient.

Statement 1 and 2 combined: It states that the line is parallel but intersects the Y axis at 1 which means that line L1 does not intersect the parabola.


Regards
Anup