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There are different 10 circles. What is the number of the greatest pos

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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There are different 10 circles. What is the number of the greatest pos [#permalink]

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29 Apr 2016, 19:16
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There are different 10 circles. What is the number of the greatest possible points with which the circles intersect?

A. 90
B. 100
C. 110
D. 180
E. 200

* A solution will be posted in two days.
[Reveal] Spoiler: OA

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Re: There are different 10 circles. What is the number of the greatest pos [#permalink]

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29 Apr 2016, 19:38
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Maximum points of intersection between n different circles = n*(n - 1) = 10*9 = 90

Similar question from Math Revolution: what-is-the-greatest-possible-number-of-points-at-which-11-circles-210362.html
Math Expert
Joined: 02 Aug 2009
Posts: 5649
Re: There are different 10 circles. What is the number of the greatest pos [#permalink]

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29 Apr 2016, 19:49
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MathRevolution wrote:
There are different 10 circles. What is the number of the greatest possible points with which the circles intersect?

A. 90
B. 100
C. 110
D. 180
E. 200

* A solution will be posted in two days.

Hi,
if someone is not aware of the formula, you can easily do the Q through systematic approach..

VISUALIZATION can help us in these type of Qs,
first circle - no intersection
second circle - 2-points
third circle- two existing circles s0 2*2 - 4..
and so on till 10th - 9 existing circle and 2-points on each = 2*9=18..

$$TOTAL = 0+2+4+...16+18 = 2(1+2+3+...8+9) = 2*9*\frac{10}{2} = 90$$
A
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Re: There are different 10 circles. What is the number of the greatest pos [#permalink]

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04 May 2016, 06:24
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2+2*2+…+2*9=2(1+2+…+9)=2(9)(10)/2=90
Hence, the correct answer is A.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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Re: There are different 10 circles. What is the number of the greatest pos [#permalink]

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11 May 2017, 08:36
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Bunuel: Please untag probability
MathRevolution wrote:
There are different 10 circles. What is the number of the greatest possible points with which the circles intersect?

A. 90
B. 100
C. 110
D. 180
E. 200

* A solution will be posted in two days.

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Joined: 02 Sep 2009
Posts: 43804
Re: There are different 10 circles. What is the number of the greatest pos [#permalink]

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11 May 2017, 08:38
BrushMyQuant wrote:
Bunuel: Please untag probability
MathRevolution wrote:
There are different 10 circles. What is the number of the greatest possible points with which the circles intersect?

A. 90
B. 100
C. 110
D. 180
E. 200

* A solution will be posted in two days.

_______________
Done. Thank you.
_________________
Re: There are different 10 circles. What is the number of the greatest pos   [#permalink] 11 May 2017, 08:38
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