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The figure above shows that 4 straight lines can have 6 points of

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The figure above shows that 4 straight lines can have 6 points of  [#permalink]

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New post 15 Aug 2017, 23:08
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

80% (01:09) correct 20% (01:29) wrong based on 56 sessions

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The figure above shows that 4 straight lines can have 6 points of  [#permalink]

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New post 16 Aug 2017, 07:07
5
Bunuel wrote:
Image
The figure above shows that 4 straight lines can have 6 points of intersection. The greatest number of points of intersection of 5 straight lines is

(A) 9
(B) 10
(C) 12
(D) 15
(E) 20

Attachment:
The attachment 2017-08-16_1006.png is no longer available

Attachment:
5lines.png
5lines.png [ 8.7 KiB | Viewed 760 times ]

(Count the black dots and the red ones I added to get the total # of intersections.)

Formula for maximum number of intersections made by n lines, which writing out the pattern helped me remember, is

\(\frac{n(n-1)}{2}\)

\(\frac{5(4)}{2}\) = 10

Answer B

Here's the pattern:

# of lines|(# of intersections) -->

1(0)
2(1)
3(3)
4(6)
5(10)

1 + 0 = 1 (for two lines)
2 + 1 = 3 (for three lines)
3 + 3 = 6 (for four lines)
4 + 6 = 10 (for five lines)

Answer B
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Re: The figure above shows that 4 straight lines can have 6 points of  [#permalink]

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New post 27 Aug 2018, 18:26
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Re: The figure above shows that 4 straight lines can have 6 points of   [#permalink] 27 Aug 2018, 18:26
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