More math

Discus: SAT/ACT Tests and Test Preparation: October 2003 Archive: More math
 By Nop86 (Nop86) on Tuesday, October 07, 2003 - 12:23 pm: Edit

Three lines are drawn in a plane so that there are exactly three different intersection points. Into how many nonoverlapping regions do these lines divide the plane?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7
(can someone explain what the question means?)

Quantative Comparison:
Point O is the center of a circle. Point P is inside the circle and point M is outside the circle.
A: The length of OP
B: The length of PM
(for this, I thought B but was wrong?)

Thanks!

 By Kevinkleinz (Kevinkleinz) on Tuesday, October 07, 2003 - 12:37 pm: Edit

1. E
2. I would say D

If you imagine three lines with three DIFFERENT intersection points, they will form a triangle between them and then the lines will continue outwards, cutting the plane into six pieces. These six pieces plus the triangle in between them divide the plane into 7 total regions.

The length of OP may or may not be larger than PM. For example, P could be just inside the circle and M could be just outside the circle, yielding a small PM value that is less than OP. (It also depends on the radius). However, M could go off to infinity, in which case PM is most certainly larger than OP.

Perhaps I'm wrong, but thats how I interpreted those questions.

 By Nop86 (Nop86) on Tuesday, October 07, 2003 - 12:41 pm: Edit

Those are the right answers. For the second I was just being really dumb..despite typing it out, I was reading PM as OM! OMG