Each of the 42 points is placed either inside or on the surface of a perfect sphere. If 65% 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 from the following
A) 7
B) 11
C) 13
D) 23
E) 38

Rationale: "maximum number of points on the surface is 65 % * 42 = 27.3 . . . or 27 since it has to be an integer now note that if two points form a diameter , they can not be part of any other diameter . so in the best case we can pair up the points we have 27 points , so at best we can form 13 pairs ( 26 ) . so , answer is ( c )"
Answer: C