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# Each of the 39 points is placed either inside or on the surface of a

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Intern
Joined: 01 Sep 2010
Posts: 20
Each of the 39 points is placed either inside or on the surface of a  [#permalink]

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04 Oct 2010, 06:45
5
4
00:00

Difficulty:

45% (medium)

Question Stats:

68% (01:43) correct 32% (01:52) wrong based on 67 sessions

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Each of the 39 points is placed either inside or on the surface of a perfect sphere. If 60% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere?

A. 7
B. 11
C. 13
D. 23
E. 38
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Joined: 02 Sep 2010
Posts: 726
Location: London
Re: Each of the 39 points is placed either inside or on the surface of a  [#permalink]

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04 Oct 2010, 08:39
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Each of the 39 points is placed either inside or on the surface of a perfect sphere. If 60% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere?

A. 7
B. 11
C. 13
D. 23
E. 38

Maximum number of points on the surface is 60%*39 = 23.4 ... or 23 since it has to be an integer

Now note that if two points form a diameter, they cannot be part of any other diameter.
So in the best case we can pair up the points

We have 23 points, so at best we can form 11 pairs (22).

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Re: Each of the 39 points is placed either inside or on the surface of a  [#permalink]

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29 Oct 2018, 10:00
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Re: Each of the 39 points is placed either inside or on the surface of a   [#permalink] 29 Oct 2018, 10:00
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