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# Maximum number of points that 10 circles of different radii intersect

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Intern
Joined: 25 Oct 2016
Posts: 5
Maximum number of points that 10 circles of different radii intersect  [#permalink]

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25 Oct 2016, 13:22
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6
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Difficulty:

55% (hard)

Question Stats:

54% (01:40) correct 46% (01:43) wrong based on 97 sessions

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What is the maximum number of points that 10 circles of different radii intersect?

(A) 24
(B) 26
(C) 33
(D) 90
(E) 100
Intern
Joined: 18 Sep 2016
Posts: 49
Re: Maximum number of points that 10 circles of different radii intersect  [#permalink]

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25 Oct 2016, 13:39
1
sitagupta385 wrote:
What is the maximum number of points that 10 circles of different radii intersect?

A: 24
B: 26
C: 33
D: 90
E: 100

the maximum number of points that two circles intersect is two.

therefore, each of these 10 circles intersect two point with each of the other 9 circles.

as a consequence, the number of these points is equal to two times the number of combination of the 10 circles.

$$2*\frac{(10!)}{(2!*10!)}= 90$$

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Intern
Joined: 22 Jan 2015
Posts: 23
Re: Maximum number of points that 10 circles of different radii intersect  [#permalink]

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01 Feb 2017, 01:22
sitagupta385 wrote:
What is the maximum number of points that 10 circles of different radii intersect?

A: 24
B: 26
C: 33
D: 90
E: 100

=n(n-1)
=10*9
=90 (D)
Intern
Joined: 29 Dec 2015
Posts: 4
GMAT 1: 600 Q41 V32
Re: Maximum number of points that 10 circles of different radii intersect  [#permalink]

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26 Feb 2017, 16:25
Every circle intersects with another circle at max 2 points. Every circle interacts with a total of 9 circles. So, every circle has a max of 18 intersections (2*9). There are 10 circles, so 2*9*10 intersections. However, every intersection in counted twice. therefore we must divide by 2. this gets us to 9*10=90.
Re: Maximum number of points that 10 circles of different radii intersect &nbs [#permalink] 26 Feb 2017, 16:25
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