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

Q: Problem: if m = 3 ^ n , what is the greatest value of n for which m is a factor of 25 ! 
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16

A: b
****
Q: Problem: teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 157 per kg , the price of the third variety per kg will be ? 
Options: a ) rs . 147.50 , b ) rs . 785.50 , c ) rs . 179.50 , d ) rs . 258.50 , e ) none of these

A: c
****
Q: Problem: set a consists of the integers from 4 to 15 , inclusive , while set b consists of the integers from 7 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ? 
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10

A:
d
****