TASK DEFINITION: In this task, you need to provide the correct option for a given problem from the provided options.
PROBLEM: Problem: among 300 students , 56 % study sociology , 44 % study mathematics and 40 % study biology . if 30 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ? 
Options: a ) 30 , b ) 90 , c ) 120 , d ) 172 , e ) 188

SOLUTION: b

PROBLEM: Problem: a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 80 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ? 
Options: a ) 3 / 16,000 , b ) 1 / 8,100 , c ) 1 / 600 , d ) 1 / 90 , e ) 2 / 45

SOLUTION: c

PROBLEM: Problem: the hcf of two numbers is 62 and the other two factors of their lcm are 11 and 12 . what is the largest number . 
Options: a ) 462 , b ) 744 , c ) 480 , d ) 504 , e ) 555

SOLUTION:
b