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

[Q]: Problem: two vessels a and b contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively . find the ratio in which these mixture be mixed to obtain a new mixture in vessel c containing spirit and water in the ration 8 : 5 ? 
Options: a ) 4 : 3 , b ) 3 : 4 , c ) 5 : 6 , d ) 7 : 9 , e ) none
[A]: d


[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: of the 70 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ? 
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
[A]:
b