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Counting... Lines

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Counting... Lines

by knight247 » Mon Oct 17, 2011 10:03 am
If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then on how many points do they intersect?
(A)250
(B)276
(C)300
(D)600
(E)2300

OA is C. Detailed explanations would be appreciated. Thanks
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by GmatKiss » Mon Oct 17, 2011 10:20 am
Great question! :)
I am unable to understand the stem.
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by shankar.ashwin » Mon Oct 17, 2011 10:22 am
We know any set of 2 lines intersect at only 1 point.
Here we have 25 lines. Each set of 2 lines would have a distinct intersecting point.

Considering all 25, we have 25C2. C
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by GmatMathPro » Mon Oct 17, 2011 11:23 am
Agreed.

To clarify the stem...

All of the lines are in the same plane and none of them are parallel. This guarantees that each pair of lines intersects. No three lines are concurrent. Lines are said to be concurrent when they intersect at a single point. For example, if you had three lines all going through the origin of the xy-coordinate plane they would be concurrent, and the point of concurrency would be the origin. The point of this statement is to guarantee that each point of intersection is unique to each pair of lines. Without it, it could be the case that all 25 lines intersect intersect at a single point, and the answer would be 1.

As shankar said, each pair of lines gives us exactly one point of intersection, so the number of points of intersection is the same as the number of ways to choose 2 lines out of 25.
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