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605-655 (Medium)|   Geometry|      
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Bunuel
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What is the maximum number of nonoverlapping regions into which 3 line 16 Nov 2017, 08:31
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C
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45% (medium)

Question Stats:

51% (01:06) correct 49% (01:04) wrong based on 104 sessions

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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
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C
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Navski
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What is the maximum number of nonoverlapping regions into which 3 line 16 Nov 2017, 08:51
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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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What is the maximum number of nonoverlapping regions into which 3 line 16 Nov 2017, 09:46
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Please refer to the attached image.
As per this maximum 7 non overlapping regions are possible. Ans (c)
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Capture.PNG [ 7.05 KiB | Viewed 16687 times ]

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Navski
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What is the maximum number of nonoverlapping regions into which 3 line 16 Nov 2017, 09:52
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SoulSurfer
Please refer to the attached image.
As per this maximum 7 non overlapping regions are possible. Ans (c)
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What defines a overlapping region ?
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What is the maximum number of nonoverlapping regions into which 3 line 16 Nov 2017, 09:54
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Bunuel
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
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Attachment:
regionscirc.png
regionscirc.png [ 7.94 KiB | Viewed 15993 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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What is the maximum number of nonoverlapping regions into which 3 line 17 Nov 2017, 04:31
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Bunuel
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.
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Looked over it again and it's my fault. You were right, thought I saw 8 for some reason.
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What is the maximum number of nonoverlapping regions into which 3 line 20 Oct 2019, 10:36
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SoulSurfer
Please refer to the attached image.
As per this maximum 7 non overlapping regions are possible. Ans (c)
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Why the third line cannot go through the center of the circle?
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What is the maximum number of nonoverlapping regions into which 3 line 14 Nov 2019, 16:59
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ShahadatHJ
SoulSurfer
Please refer to the attached image.
As per this maximum 7 non overlapping regions are possible. Ans (c)
Why the third line cannot go through the center of the circle?
Show more

Because if it does, it would be 6 regions. We want to look for the maximum, so by not going through the middle, we created a 7th region.
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What is the maximum number of nonoverlapping regions into which 3 line 15 Nov 2019, 08:45
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Jayshoot
ShahadatHJ
SoulSurfer
Please refer to the attached image.
As per this maximum 7 non overlapping regions are possible. Ans (c)
Why the third line cannot go through the center of the circle?

Because if it does, it would be 6 regions. We want to look for the maximum, so by not going through the middle, we created a 7th region.
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Thank you very much... I did not notice in this way.
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What is the maximum number of nonoverlapping regions into which 3 line 01 Sep 2021, 12:30
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