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

[Q]: 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
[A]: d


[Q]: Problem: if y is the smallest positive integer such that 3,675 multiplied by y is the square of an integer , then y must be 
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 12
[A]: e


[Q]: Problem: danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 648 , what is the area of the side face of the box ? 
Options: ['a ) 32', 'b ) 78', 'c ) 84', 'd ) 90', 'e ) 72']
[A]:
e