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

SOLUTION: d

PROBLEM: Problem: a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 30 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ? 
Options: a ) 13 , b ) 30 , c ) 50 , d ) 51 , e ) 52

SOLUTION: b

PROBLEM: Problem: the area of a rectangular plot is 24 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ? 
Options: ['a ) 14 metres', 'b ) 5 metres', 'c ) 7.5 metres', 'd ) data inadequate', 'e ) none of these']

SOLUTION:
a