In this task, you need to provide the correct option for a given problem from the provided options.

[Q]: Problem: what is the greatest positive integer e such that 3 ^ e is a factor of 9 ^ 10 ? 
Options: a ) e = 5 , b ) e = 9 , c ) e = 10 , d ) e = 20 , e ) 30
[A]: d


[Q]: Problem: what number has a 150 : 1 ratio to the number 2 ? 
Options: a ) 130 , b ) 300 , c ) 200 , d ) 30 , e ) 75
[A]: b


[Q]: Problem: the h . c . f . of two numbers is 40 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is : 
Options: a ) 276 , b ) 600 , c ) 699 , d ) 722 , e ) 745
[A]:
b