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

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

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New post 04 Oct 2010, 05:45
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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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Re: Each of the 39 points is placed either inside or on the surface of a  [#permalink]

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New post 04 Oct 2010, 07:39
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eladshush wrote:
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).

So, answer is (B)
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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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Re: Each of the 39 points is placed either inside or on the surface of a &nbs [#permalink] 29 Oct 2018, 09:00
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