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What is the maximum number of nonoverlapping regions into which 3 line

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What is the maximum number of nonoverlapping regions into which 3 line  [#permalink]

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New post 16 Nov 2017, 08:31
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A
B
C
D
E

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Re: What is the maximum number of nonoverlapping regions into which 3 line  [#permalink]

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New post 16 Nov 2017, 08:51
Not sure but I can't see it being anything other than D

Make an X in the circle that's two lines draw a line in the middle of the "X" that makes 8 parts.
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Re: What is the maximum number of nonoverlapping regions into which 3 line  [#permalink]

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New post 16 Nov 2017, 09:46
Please refer to the attached image.
As per this maximum 7 non overlapping regions are possible. Ans (c)
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Re: What is the maximum number of nonoverlapping regions into which 3 line  [#permalink]

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New post 16 Nov 2017, 09:52
SoulSurfer wrote:
Please refer to the attached image.
As per this maximum 7 non overlapping regions are possible. Ans (c)


What defines a overlapping region ?
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What is the maximum number of nonoverlapping regions into which 3 line  [#permalink]

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New post 16 Nov 2017, 09:54
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Bunuel wrote:
What is the maximum number of nonoverlapping regions into which 3 lines can divide the interior of a circle?

(A) 4
(B) 6
(C) 7
(D) 8
(E) 9

Attachment:
regionscirc.png
regionscirc.png [ 7.94 KiB | Viewed 1315 times ]

In the diagram, one line makes two regions in the circle. 1 line adds one more region to the region already there (1 + 1 =2).

Two lines add two more regions (to the 2 regions already there, 2 + 2 = 4)); 2 lines create 4 regions.

Three line add three more regions (to the 4 regions already there, 4 + 3 = 7); 3 lines create 7 regions.

The pattern: Each Lth line adds L regions to the number of regions that already existed:

Line (+ line) --- Regions

1 (+ 1st line = adds 1 more region, 1+ 1 = 2) --> 2 regions
2 (+ 2nd line = adds 2 more regions, 2 + 2 = 4) --> 4 regions
3 ( + 3rd line = adds 3 more regions, 4 + 3 + 7) --> 7 regions

I cannot figure out a way to make 8 regions with three lines; and given the pattern, I think it is not possible.

Answer C

Navski , when I drew what you described, I counted six regions.
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Re: What is the maximum number of nonoverlapping regions into which 3 line  [#permalink]

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New post 17 Nov 2017, 04:31
genxer123 wrote:
Bunuel wrote:
What is the maximum number of nonoverlapping regions into which 3 lines can divide the interior of a circle?

(A) 4
(B) 6
(C) 7
(D) 8
(E) 9

Attachment:
regionscirc.png

In the diagram, one line makes two regions in the circle. 1 line adds one more region to the region already there (1 + 1 =2).

Two lines add two more regions (to the 2 regions already there, 2 + 2 = 4)); 2 lines create 4 regions.

Three line add three more regions (to the 4 regions already there, 4 + 3 = 7); 3 lines create 7 regions.

The pattern: Each Lth line adds L regions to the number of regions that already existed:

Line (+ line) --- Regions

1 (+ 1st line = adds 1 more region, 1+ 1 = 2) --> 2 regions
2 (+ 2nd line = adds 2 more regions, 2 + 2 = 4) --> 4 regions
3 ( + 3rd line = adds 3 more regions, 4 + 3 + 7) --> 7 regions

I cannot figure out a way to make 8 regions with three lines; and given the pattern, I think it is not possible.

Answer C

Navski , when I drew what you described, I counted six regions.


Looked over it again and it's my fault. You were right, thought I saw 8 for some reason.
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Re: What is the maximum number of nonoverlapping regions into which 3 line &nbs [#permalink] 17 Nov 2017, 04:31
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