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

Input: Consider 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

Output: d

Input: Consider Input: Problem: a wooden cube whose edge length is 8 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ?
Options: a ) 46.3 % , b ) 50.4 % , c ) 54.2 % , d ) 57.8 % , e ) 61.3 %

Output: d

Input: Consider Input: Problem: what is the max number of rectangular boxes , each measuring 4 inches by 6 inches by 10 inches , that can be packed into a rectangular packing box measuring 16 inches by 18 inches by 30 inches , if all boxes are aligned in the same direction ?
Options: ['a ) 36', 'b ) 14', 'c ) 12', 'd ) 15', 'e ) 11']
Output: a