In this task, you need to answer the given multiple-choice question on the general math. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.

Problem: what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 50 ? 
Options: a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 120
d

Problem: if - 3 x + 2 y = 28 and 3 x + 6 y = 84 , what is the product of x and y ? 
Options: a ) 264 . , b ) 428 , c ) 0 , d ) 462 , e ) 642
c

Problem: 115 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ? 
Options: a ) 12 liters , b ) 32 liters , c ) 46 liters , d ) 50 liters , e ) 34 liters

c