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 ?
"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 )"
divide(multiply(42, divide(65, const_100)), const_2)