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

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There are 8 different circles. What is the greatest number of the poss  [#permalink]

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New post 17 Jul 2017, 02:53
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  65% (hard)

Question Stats:

54% (00:56) correct 46% (01:33) wrong based on 76 sessions

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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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Re: There are 8 different circles. What is the greatest number of the poss  [#permalink]

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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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Re: There are 8 different circles. What is the greatest number of the poss  [#permalink]

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New post 17 Jul 2017, 03:23
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Re: There are 8 different circles. What is the greatest number of the poss  [#permalink]

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New post 29 Jul 2018, 06:00
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 &nbs [#permalink] 29 Jul 2018, 06:00
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