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

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Math Expert
Joined: 02 Sep 2009
Posts: 51121
The figure above shows that 4 straight lines can have 6 points of  [#permalink]

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15 Aug 2017, 22:08
00:00

Difficulty:

25% (medium)

Question Stats:

80% (01:08) correct 20% (01:29) wrong based on 55 sessions

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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:

2017-08-16_1006.png [ 5.31 KiB | Viewed 805 times ]

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Posts: 2204
The figure above shows that 4 straight lines can have 6 points of  [#permalink]

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16 Aug 2017, 06:07
5
Bunuel wrote:

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 [ 8.7 KiB | Viewed 668 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

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)

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

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27 Aug 2018, 17:26
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Re: The figure above shows that 4 straight lines can have 6 points of &nbs [#permalink] 27 Aug 2018, 17:26
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