In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.

Example Input: Problem: points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction d of the area of triangle abc is the area of triangle xyz ?
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3
Example Output: a

Example Input: Problem: a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 100,000 and at the same time n is a perfect square and a perfect cube ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Example Output: d

Example Input: Problem: cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 23 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ?
Options: ['a ) 64', 'b ) 72', 'c ) 86', 'd ) 98', 'e ) 102']
Example Output:
e