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Difficulty:
95%
(hard)
Question Stats:
17% (02:47) correct
83%
(01:52)
wrong
based on 23
sessions
History
Date
Time
Result
Not Attempted Yet
On a two-dimensional plane surface, ten straight lines are drawn in the following ways. No two of the lines are parallel and no three of the lines pass through any common point. What is the total number of regions into which the plane surface is divided by the lines? Consider both finite and infinite regions.
(A) 56
(B) 160
(C) 255
(D) 630
(E) 1024
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(A) 56
(B) 160
(C) 255
(D) 630
(E) 1024
Are You Up For the Challenge: 700 Level Questions
_________________
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Posts: 3
if there are m parallel lines , max no of regions it can divide a plane = m(m+1)/2+1
=> 10(11)/2+1 =56
=> 10(11)/2+1 =56
All non parallel lines eventually intersect each other.
Start with simplified questions
Draw 2 nonparallel lines.
4 infinite regions can be
counted.
Draw 3 non parallel lines
6 infinite regions plus 1
enclosed region = 7 regions
Draw 4 nonparallel lines
8 infinite regions plus 3
enclosed regions = 11
regions observed
Determine the pattern
2 lines 4 regions
3 lines 7 regions
4 lines 11 regions
The pattern is likely 3,4,5 etc of increase in regions with increasing lines
So 5 lines has 16 regions, 6 lines 22, 7 lines 29, 8 lines 37, 9 lines 46 and
10 lines 56 regions
Posted from my mobile device
Start with simplified questions
Draw 2 nonparallel lines.
4 infinite regions can be
counted.
Draw 3 non parallel lines
6 infinite regions plus 1
enclosed region = 7 regions
Draw 4 nonparallel lines
8 infinite regions plus 3
enclosed regions = 11
regions observed
Determine the pattern
2 lines 4 regions
3 lines 7 regions
4 lines 11 regions
The pattern is likely 3,4,5 etc of increase in regions with increasing lines
So 5 lines has 16 regions, 6 lines 22, 7 lines 29, 8 lines 37, 9 lines 46 and
10 lines 56 regions
Posted from my mobile device
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