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When three parallel lines are intersected by three nonparallel lines

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When three parallel lines are intersected by three nonparallel lines [#permalink]

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New post 08 Aug 2017, 01:43
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When three parallel lines are intersected by three nonparallel lines, what is the maximum number of intersections possible?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 16
[Reveal] Spoiler: OA

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Re: When three parallel lines are intersected by three nonparallel lines [#permalink]

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New post 08 Aug 2017, 01:51
Bunuel wrote:
When three parallel lines are intersected by three nonparallel lines, what is the maximum number of intersections possible?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 16


We can start with 9 (minimum maximum) 3 lines intersecting 3 lines) = 9
Now two non parallel lines can intersect only at one point = 1
but the third line can intersect both of them = 2

12
D
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Re: When three parallel lines are intersected by three nonparallel lines [#permalink]

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New post 09 Aug 2017, 01:46
I was just guessing 3!*2! =6*2=12
Is it somehow correct?

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Re: When three parallel lines are intersected by three nonparallel lines [#permalink]

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New post 09 Aug 2017, 04:15
Parallel lines don't intersect each other

3 non-parallel lines intersect 3 parallel lines at different points = 3* 3 =9
3 non-parallel lines intersect each other at 3 different points (creating a triangle) = 3

total 12 (Choice D)

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Re: When three parallel lines are intersected by three nonparallel lines   [#permalink] 09 Aug 2017, 04:15
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