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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: 41908

Kudos [?]: 129394 [0], given: 12197

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

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15 Aug 2017, 23:08
00:00

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(N/A)

Question Stats:

100% (00:41) correct 0% (00:00) wrong based on 32 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

[Reveal] Spoiler:
Attachment:

2017-08-16_1006.png [ 5.31 KiB | Viewed 292 times ]
[Reveal] Spoiler: OA

_________________

Kudos [?]: 129394 [0], given: 12197

Director
Joined: 22 May 2016
Posts: 833

Kudos [?]: 268 [3], given: 556

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

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16 Aug 2017, 07:07
3
KUDOS
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

[Reveal] Spoiler:
Attachment:
The attachment 2017-08-16_1006.png is no longer available

Attachment:

5lines.png [ 8.7 KiB | Viewed 163 times ]

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)

Kudos [?]: 268 [3], given: 556

Re: The figure above shows that 4 straight lines can have 6 points of   [#permalink] 16 Aug 2017, 07:07
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