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10 straight lines, no two of which are parallel and no three

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Intern
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Joined: 13 May 2014
Posts: 32
Concentration: General Management, Strategy
10 straight lines, no two of which are parallel and no three  [#permalink]

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New post Updated on: 01 Aug 2018, 23:20
3
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

43% (01:56) correct 57% (02:01) wrong based on 37 sessions

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10 straight lines, no two of which are parallel and no three of which pass through any common point, are drawn on a plane. The total number of regions into which the plane would be divided by the lines is

A) 44
B) 46
C) 52
D) 56
E) 64

Source :MBA Entrance CAT exam

Originally posted by gmatacequants on 20 May 2014, 13:14.
Last edited by Bunuel on 01 Aug 2018, 23:20, edited 2 times in total.
Intern
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Joined: 13 May 2014
Posts: 32
Concentration: General Management, Strategy
Re: 10 straight lines, no two of which are parallel and no three  [#permalink]

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New post 20 May 2014, 14:10
2
[quote="gmatacequants"]10 straight lines, no two of which are parallel and no three of which pass through any common point, are drawn on a plane. The total number of regions into which the plane would be divided by the lines is
A) 44
B) 46
C) 52
D) 56
E) 64

Source :MBA Entrance CAT exam


We can solve it stepwise increasing the no. of lines (n) :
Attachment:
g1.JPG
g1.JPG [ 11.99 KiB | Viewed 8984 times ]


..............................................
.............................................. so on
R = regions created on plane by these lines
D = difference in no. of regions created by n lines w.r.t (n-1) lines

One can derive the no of regions for by using the D and R columns :
No. of regions by n lines = no. of regions by (n-1) lines + n = 2+ [2+3+...+(n-1)] + n
= n*(n+1)/2 + 1

So, for n= 10, no. of regions = 10* 11/2 +1 = 56

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Re: 10 straight lines, no two of which are parallel and no three  [#permalink]

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New post 07 Apr 2019, 20:18
Triangles.
Triangle numbers. 1 3 6...
10 lines. 10*11/2 triangles = 55 + 1 for outside 56 | D

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Re: 10 straight lines, no two of which are parallel and no three   [#permalink] 07 Apr 2019, 20:18
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10 straight lines, no two of which are parallel and no three

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