Latest CAT Aptitude Question SOLUTION: A plane is divided into 79 regions by several number of straight lines. How many number of lines is required atleast for this division?

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A plane is divided into 79 regions by several number of straight lines. How many number of lines is required atleast for this division?

Asked In CAT Divya Srivastava (11 years ago)

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Bholanath   (11 years ago)

Ans. 12
explanation :
2 lines divide a plane in 4 region
3 lines divide a plane maximum of 7
4 lines divide in maximum of 11
similarly 5 lines 16
6 lines 22
...
difference b/w 3 lines and 2 lines =3
diffenece b/w 4 lines and 3 lines = 4
diference b/w 5 lines and 4 lines = 5
....
after analyse
....
for 2 lines=4 division
for 3 lines = 7 =4+3
for 4 lines = 11 =7+4
for 5 lines = 16=11+5
for 6 lines = 22=16+6
for 7 lines = 29=22+7
for 8 lines = 37=29+8
for 9 lines = 46=37+9
for 10 lines = 56=46+10
for 11 lines = 67=56+11
for 12 lines= 79=67+12

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Bholanath   (11 years ago)

@Divya g
12 is minimum no. of lines if there is no such option than answer will be the next no. after 12 i.e. according to your option answer will be 13.

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sreebhuvan  (11 years ago)

9*9=81 the least perfect square greater than 79
9+9=18 lines

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Divya Srivastava  (11 years ago)

the options for this question are:
a)10
b)9
c)13
d)15

@BHOLANATH : ur explanation is ryt but there is no such option.

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raushan kumar  (11 years ago)

n(n+1)/2 +n -(n-1) =79
n=12.
1 line divide = 2 regions
2 line divide = 4 regions
3 line divide = 7 regions (max)
4 line divide = 11 regions(max)
.
.
12 line divide =79 regions(max) :)

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yash modi  (11 years ago)

it is 78 lines because if i make 78 lines then 79 regions are possesed

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