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

[Q]: Problem: if both 5 ^ 3 and 3 ^ 4 are factors of n x ( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) x ( 10 ^ 2 ) , what is the smallest possible positive value of n ? 
Options: a ) 15 , b ) 45 , c ) 75 , d ) 125 , e ) 150
[A]: b


[Q]: Problem: the present ratio of students to teachers at a certain school is 30 to 1 . if the student enrollment were to increase by 50 students and the number of teachers were to increase by 5 , the ratio of students to teachers would then be 25 to 1 . what is the present number of teachers ? 
Options: a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 15
[A]: e


[Q]: Problem: if the ratio of two number is 3 : 4 and lcm of the number is 180 then what is the number . 
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
[A]:
a