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805+ (Hard)|   Geometry|      
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Bunuel
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For a set of four distinct lines in a plane, there are exactly N disti 14 May 2019, 00:24
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95% (hard)

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30% (01:51) correct 70% (02:04) wrong based on 64 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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D
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RupamPaul13
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For a set of four distinct lines in a plane, there are exactly N disti 14 May 2019, 01:11
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Maximum value of N can be 6. Hence sum of all possible values of N is 21. 6*7/2

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kunalbean
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For a set of four distinct lines in a plane, there are exactly N disti 14 May 2019, 08:46
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rupam : can you please explain much more?

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RupamPaul13
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For a set of four distinct lines in a plane, there are exactly N disti 14 May 2019, 09:31
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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
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For a set of four distinct lines in a plane, there are exactly N disti 15 May 2019, 09:36
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@rupampaul : thank you for the response!
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For a set of four distinct lines in a plane, there are exactly N disti 16 May 2019, 09:59
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RupamPaul13
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
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From where this formula originates...Do you have any details to refer and understand?
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For a set of four distinct lines in a plane, there are exactly N disti 29 Nov 2019, 09:36
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Someone please solve and share your approach to this question.

Thank you!
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Stonely
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For a set of four distinct lines in a plane, there are exactly N disti 29 Nov 2019, 09:53
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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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For a set of four distinct lines in a plane, there are exactly N disti 14 Dec 2022, 14:19
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