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What is the greatest number of intersection points between 6 straight

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What is the greatest number of intersection points between 6 straight [#permalink] New post   13 Oct 2020, 20:32
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What is the greatest number of intersection points between 6 straight lines, if they are arranged as three pairs of parallel lines?

A. 8
B. 9
C. 12
D. 18
E. 36
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C
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Re: What is the greatest number of intersection points between 6 straight [#permalink] New post   14 Oct 2020, 00:24
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What is the greatest number of intersection points between 6 straight lines, if they are arranged as three pairs of parallel lines?

Step 1: Understanding the question
Three pair of parallel lines can be arranged in a form of a triangle to find maximum intersection points (refer to the attachment)

C is correct
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Re: What is the greatest number of intersection points between 6 straight [#permalink] New post   14 Oct 2020, 08:06
There are 3 pairs of parallel lines say x, y, z

so 3x2x2 = 12 combinations

In other way
Intersection of x & y = 4 points
Intersection of y & z = 4 points
Intersection of x & Z = 4 points
Total = 12

Ans: C
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Re: What is the greatest number of intersection points between 6 straight [#permalink] New post   14 Oct 2020, 10:32
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DisciplinedPrep wrote:
What is the greatest number of intersection points between 6 straight lines, if they are arranged as three pairs of parallel lines?

A. 8
B. 9
C. 12
D. 18
E. 36


Remember the rule that the maximum number of intersection points that each additional line can create, is the same as the number of lines on the board before adding the additional line. We can envision two parallel lines crossing, there can be 4 intersections at most from that. Then we add in another set of parallel lines, there are currently 4 lines on the board so each line can only create 4 more intersection points. Thus we have 4 + 4 + 4 = 12 intersection points at most.

Ans: C
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Re: What is the greatest number of intersection points between 6 straight [#permalink]
14 Oct 2020, 10:32
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