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

Example Input: Problem: village p ’ s population is 1200 greater than village q ' s population . if village q ’ s population were reduced by 800 people , then village p ’ s population would be 6 times as large as village q ' s population . what is village q ' s current population ? 
Options: a ) 1050 , b ) 1100 , c ) 1150 , d ) 1200 , e ) 1250
Example Output: d

Example Input: Problem: if x is a positive integer , then the least value of x for which x ! is divisible by 100000 is ? can someone please explain intuitively what the question is asking ? 
Options: a ) 5 , b ) 9 , c ) 12 , d ) 20 , e ) 30
Example Output: d

Example Input: Problem: if a ^ 2 + b ^ 2 = 25 and ab = 10 , what is the value of the expression ( a - b ) ^ 2 + ( a + b ) ^ 2 ? 
Options: a ) 10 , b ) 20 , c ) 30 , d ) 50 , e ) 70
Example Output:
d