Each of the 55 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? Choices:
A) 7  B) 11  C) 13  D) 16  E) 38
Maximum number of points on the surface is 60%*55 = 33   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 33 points, so at best we can form 16 pairs (32).   So, answer is (16)
<result>D</result>
Each of the 55 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?