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If 25 lines are drawn in a plane such that no two of them

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If 25 lines are drawn in a plane such that no two of them [#permalink] New post 06 Dec 2007, 06:04
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If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?

A 2300
B 600
C 250
D 300
E none of these

Please explaing for me to understand the concept

Amar
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 [#permalink] New post 06 Dec 2007, 06:19
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D.

let try draw lines one by one.

1st line - 0 points
2nd line - new 1 point
3td line - new 2 points + old 1 point
4th line - new 3 points + old 2+1 points
5th line - new 4 points + old 3+2+1 points
n-th line - (n-1) points + (n-2) .... 3+2+1

therefore, S=1+2+3...(n-1)

S=(n-1)n/2=24*25/2=300
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Re: Permutation & combination [#permalink] New post 06 Dec 2007, 06:27
It is very hard. I can only say that the answer must not be E, because "no two of them are parallel", so they must meet in some point.
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explanation [#permalink] New post 06 Dec 2007, 06:30
Can you explain me your reasoning step by step very slowly?
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Re: explanation [#permalink] New post 06 Dec 2007, 06:37
marcodonzelli wrote:
Can you explain me your reasoning step by step very slowly?


No. less than 2 min.

Another way, even easier and faster:

one line has 24 intersections. We have 25 line. Therefore the number of intersection points is 24*25/2 (2- because we count twice the same point)
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 [#permalink] New post 07 Dec 2007, 12:08
The question should state that the lines are of infinite length otherwise the answer could be anything.
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 [#permalink] New post 07 Dec 2007, 12:49
alexperi wrote:
The question should state that the lines are of infinite length otherwise the answer could be anything.


see difference between "line" and "line segment" in geometry
http://www.mathleague.com/help/geometry/basicterms.htm or
http://math.about.com/library/weekly/aa031503a.htm
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Re: Permutation & combination [#permalink] New post 08 Dec 2007, 04:39
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Amardeep Sharma wrote:
If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?

A 2300
B 600
C 250
D 300
E none of these

Please explaing for me to understand the concept

Amar


I got D:
since any 2 lines has 1 intersect with each other, we need to find the number of ways to choose 2 out of 25: 25C2=25*24/2=300.
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Re: Permutation & combination [#permalink] New post 25 Aug 2008, 13:26
Amardeep Sharma wrote:
If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?

A 2300
B 600
C 250
D 300
E none of these

Please explaing for me to understand the concept

Amar


2 lines form 1 intersect points =2C2
3 lines form 3 intersect points= 3C2
25 llines form 25C2 intersect points = 25*12=300.

D
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Re: Permutation & combination [#permalink] New post 27 Sep 2009, 21:12
If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?

A 2300
B 600
C 250
D 300
E none of these

Soln: Since no three are concurrent, hence any point that is formed by two different lines are distinct.
The first line intersects each of the other 24 lines at 24 points. => statement 1
The second line intersects each of the other 23 lines at 23 points. The point with first line has already been counted in the statement no.1.
The third line intersects each of the other 22 lines at 22 points
and so on.

Thus total number of points is
= 24 + 23 + 22 + ... + 1
= 24 * 25/2
= 300

Ans is D
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Re: Permutation & combination [#permalink] New post 16 Feb 2010, 08:41
Amardeep Sharma wrote:
If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?

A 2300
B 600
C 250
D 300
E none of these

Please explaing for me to understand the concept

Amar


No three lines are concurrent and no two lines are parallel gives us the info that every line intersects the other and no intersection point is common. Hence no of intersection points = 25c2 = 300 = D
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Re: Permutation & combination   [#permalink] 16 Feb 2010, 08:41
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