TASK DEFINITION: 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'.
PROBLEM: 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

SOLUTION: d

PROBLEM: Problem: find the smallest positive integer n such that 11 n - 1 is divisible by 105 . 
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7

SOLUTION: d

PROBLEM: Problem: if p ( a ) = 2 / 5 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events . 
Options: a ) 7 / 25 , b ) 4 / 25 , c ) 8 / 25 , d ) 2 / 13 , e ) 3 / 17

SOLUTION:
b