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Seventeen different points are to be located on the circumference of a

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Seventeen different points are to be located on the circumference of a [#permalink]

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New post 14 Nov 2017, 22:45
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Seventeen different points are to be located on the circumference of a circle and each point is to be connected to all other points by line segments. At most, how many of the segments thus formed can be diameters of a circle?

(A) 8
(B) 9
(C) 16
(D) 17
(E) 34
[Reveal] Spoiler: OA

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Kudos [?]: 135771 [0], given: 12708

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Joined: 05 Dec 2016
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Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
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Re: Seventeen different points are to be located on the circumference of a [#permalink]

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New post 15 Nov 2017, 00:09
Each pair forms up only one possible diameter when points are located at strictly opposite sides.
If we are considering "at most" extreme case then all ponts should be evenly distributed on the circumference of the circle, and since we have 17 points, only 16 out of 17 can be placed opposite each other and 17th one would not have a pair.
So there should be 8 possible diameteres at most however if we assume that there could be an overlap, then 17th point can overlap to any other and form up another 9th diameter.
OR maybe some more tricker logic lies behind the correct reasoning of subject problem :)

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Re: Seventeen different points are to be located on the circumference of a [#permalink]

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New post 15 Nov 2017, 08:18
Bunuel wrote:
Seventeen different points are to be located on the circumference of a circle and each point is to be connected to all other points by line segments. At most, how many of the segments thus formed can be diameters of a circle?

(A) 8
(B) 9
(C) 16
(D) 17
(E) 34


imo A - 8
only if two points are exactly opposite to each other,the line joining them would be diameter. 17 points have such 16 points and hence 8 pairs. One point has no point to be connected to as diameter.
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Kudos [?]: 91 [0], given: 467

Re: Seventeen different points are to be located on the circumference of a   [#permalink] 15 Nov 2017, 08:18
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