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There are 8 different circles. What is the greatest number of the poss

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Amby02
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There are 8 different circles. What is the greatest number of the poss [#permalink] New post   17 Jul 2017, 02:53
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There are 8 different circles. What is the greatest number of the possible points that the circles intersect?

A. 48
B. 56
C. 64
D. 70
E. 80
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amanvermagmat
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Re: There are 8 different circles. What is the greatest number of the poss [#permalink] New post   Updated on: 18 Jul 2017, 10:45
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Well, if we take 2 different circles - then the MAX possible points of their intersection are '2'.

In case of 'n' circles, the greatest number of points of intersection will be available in the case where Every 2 circles intersect in 2 distinct points. So first we will find out how many sets of two circles can be selected from 8:

8C2 = 8*7/2 = 28

So 28 distinct pairs of circles can be selected MAX from 8 distinct circles, and if every pair gives us 2 distinct points, then max points of intersection = 28*2 = 56

Hence B answer

Originally posted by amanvermagmat on 17 Jul 2017, 03:05.
Last edited by amanvermagmat on 18 Jul 2017, 10:45, edited 1 time in total.
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rahul16singh28
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Re: There are 8 different circles. What is the greatest number of the poss [#permalink] New post   29 Jul 2018, 06:00
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Amby02 wrote:
There are 8 different circles. What is the greatest number of the possible points that the circles intersect?

A. 48
B. 56
C. 64
D. 70
E. 80


Maximum point of Intersection between n different Circles. = 2 *nC2, where n >= 2.
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Re: There are 8 different circles. What is the greatest number of the poss [#permalink] New post   17 Jul 2017, 03:23
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Amby02 wrote:
There are 8 different circles. What is the greatest number of the possible points that the circles intersect?

A. 48 B. 56 C. 64 D. 70 E. 80


Similar question: https://gmatclub.com/forum/there-are-di ... 17589.html
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Re: There are 8 different circles. What is the greatest number of the poss [#permalink] New post   31 Aug 2021, 19:21
Given 2 identical circles (call them circle A and circle B) the MAX Intersection we can get with the 2 identical circles is ———> 2 points


The 3rd circle C: can get a maximum of 2 intersection points with circle A and a maximum of 2 intersection points with circle B ——-> + 4 more intersection points


The 4th circle D: can get a maximum of 2 intersection points with Each of the 3 prior circles ——> (2) (3) = + 6

5th circle: + 8 new points

6th circle: + 10 new points

7th circle: + 12 new points

8th circle: + 14 new points

Thus for 8 circles, the MAX intersection points we can get are:

(2) + (4) + (6) + (8) + (10) + (12) + (14) =

(7) * (8) =

56

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Re: There are 8 different circles. What is the greatest number of the poss [#permalink] New post   07 Sep 2021, 09:49
Amby02 wrote:
There are 8 different circles. What is the greatest number of the possible points that the circles intersect?

A. 48
B. 56
C. 64
D. 70
E. 80


Total ways of chosing first circle = 8

Total no of ways of selecting the second point without coinciding with the chosen point =7

Therefore total way of unique chosing = 8*7 = 56

Therefore IMO B
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Re: There are 8 different circles. What is the greatest number of the poss [#permalink] New post   27 Mar 2022, 20:16
Bunuel did not understand the problem! :/
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Re: There are 8 different circles. What is the greatest number of the poss [#permalink] New post   18 Sep 2023, 13:38
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Re: There are 8 different circles. What is the greatest number of the poss [#permalink]
18 Sep 2023, 13:38
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