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Lines and planes

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by winnerhere » Thu Oct 14, 2010 5:45 pm
Twelve straight lines are drawn i a plane such that no two of them are parallel and no three of them are concurrent. A circle is now drawn in the same plane such that all points of intersection of all the lines lie inside the circle.What is the number of non overlapping regions into which the circle is divided?


1) 25

2) 69

3) 79

4) 83

5)60
Last edited by winnerhere on Sun Oct 17, 2010 7:55 am, edited 1 time in total.
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by GMATGuruNY » Thu Oct 14, 2010 7:35 pm
winnerhere wrote:Twelve straight lines are drawn i a plane such that no two of them are parallel and no three of them are concurrent. A circle is now drawn in the same plane such that all points of intersection of all the lines lie inside the circle.What is the number of non overlapping regions into which the circle is divided?


1) 25

2) 69

3) 75

4) 83

5)60
The question seems to be asking for the maximum number of non-overlapping regions that can be formed by 12 lines intersecting inside a circle. Here's the rule:

The nth line drawn will add n more regions to the circle.

1st line adds 1 region to the circle for a total of 2 regions.
2nd line adds 2 more regions to the circle, bringing the total number of regions to 2+2=4.
3nd line adds 3 more regions to the circle, bringing the total number of regions to 4+3=7.
4th line adds 4 more regions to the circle, bringing the total number of regions to 7+4=11.
5th line adds 5 more regions to the circle, bringing the total number of regions to 11+5=16.
6th line adds 6 more regions to the circle, bringing the total number of regions to 16+6=22.
7th line adds 7 more regions to the circle, bringing the total number of regions to 22+7=29.
8th line adds 8 more regions to the circle, bringing the total number of regions to 29+8=37.
9th line adds 9 more regions to the circle, bringing the total number of regions to 37+9=46.
10th line adds 10 more regions to the circle, bringing the total number of regions to 46+10=56.
11th line adds 11 more regions to the circle, bringing the total number of regions to 56+11=67.
12th line adds 12 more regions to the circle, bringing the total number of regions to 67+12=79.

The correct answer should be 79. Are you certain that the answer choices have been transcribed correctly?
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by winnerhere » Sun Oct 17, 2010 7:50 am
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by winnerhere » Sun Oct 17, 2010 7:58 am
@gmatguru..yes the answer is 79 ..great ..thanks for the logic that you have provided.
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