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# For a set of four distinct lines in a plane, there are exactly N disti

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Math Expert
Joined: 02 Sep 2009
Posts: 59573
For a set of four distinct lines in a plane, there are exactly N disti  [#permalink]

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14 May 2019, 00:24
00:00

Difficulty:

85% (hard)

Question Stats:

19% (01:32) correct 81% (01:58) wrong based on 32 sessions

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For a set of four distinct lines in a plane, there are exactly N distinct points that lie on two or more of the lines. What is the sum of all possible values of N?

A. 14
B. 16
C. 18
D. 19
E. 21

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Intern
Joined: 08 Apr 2019
Posts: 25
Location: India
GMAT 1: 700 Q50 V34
Re: For a set of four distinct lines in a plane, there are exactly N disti  [#permalink]

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14 May 2019, 01:11
Maximum value of N can be 6. Hence sum of all possible values of N is 21. 6*7/2

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Intern
Joined: 01 Dec 2018
Posts: 43
Re: For a set of four distinct lines in a plane, there are exactly N disti  [#permalink]

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14 May 2019, 08:46
rupam : can you please explain much more?

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Intern
Joined: 08 Apr 2019
Posts: 25
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GMAT 1: 700 Q50 V34
Re: For a set of four distinct lines in a plane, there are exactly N disti  [#permalink]

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14 May 2019, 09:31
1
kunalbean The maximum no of intersecting points for N different lines on a plane is (N^2-N)/2. In this case N=4; So maximum no of intersecting points is (16-4)/2=6. And the least no of intersecting points is 0(Considering all 4 parallel). So summation is 6+5+4+3+2+1+0=21
Intern
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Re: For a set of four distinct lines in a plane, there are exactly N disti  [#permalink]

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15 May 2019, 09:36
1
@rupampaul : thank you for the response!
Manager
Status: Don't Give Up!
Joined: 15 Aug 2014
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Re: For a set of four distinct lines in a plane, there are exactly N disti  [#permalink]

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16 May 2019, 09:59
RupamPaul13 wrote:
kunalbean The maximum no of intersecting points for N different lines on a plane is (N^2-N)/2. In this case N=4; So maximum no of intersecting points is (16-4)/2=6. And the least no of intersecting points is 0(Considering all 4 parallel). So summation is 6+5+4+3+2+1+0=21

From where this formula originates...Do you have any details to refer and understand?
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Re: For a set of four distinct lines in a plane, there are exactly N disti  [#permalink]

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29 Nov 2019, 09:36

Thank you!
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Re: For a set of four distinct lines in a plane, there are exactly N disti  [#permalink]

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29 Nov 2019, 09:53
Case 1 all lines meet at the same point. =1
Case 1a try to make 2 not possible
Case 2 3 parallel = 3
Case 3 2 sets o parallels = 4
Case 4 parallel 2 not with independent intersection = 5
Case 5 all independent = 6
Case 6 all parallel 0
0+1+3+4+5+6=19

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Re: For a set of four distinct lines in a plane, there are exactly N disti   [#permalink] 29 Nov 2019, 09:53
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