Each of the 39 points is placed either inside or on the surface of a perfect sphere. If 72% 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? Choose the correct choice
A) 7
B) 11
C) 13
D) 14
E) 38
Maximum number of points on the surface is 72%*39 = 28.08 ... or 28 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 28 points, so at best we can form 14 pairs (28).   So, answer is (14)
<result>D</result>
Each of the 39 points is placed either inside or on the surface of a perfect sphere. If 72% 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?