TASK DEFINITION: In this task, you need to answer the given multiple-choice question on the gain. Gain is the value by which to multiply the input. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
PROBLEM: Problem: in a certain math department , students are required to enroll in either calculus or trigonometry , each of which is offered in beginner and advanced courses . the number of students enrolled in trigonometry is 50 % greater than the number of students enrolled in calculus , and 80 % of calculus students are enrolled in the beginner course . if 4 / 5 of students are in the beginner courses , and one student is selected at random , what is the probability that an advanced trigonometry student is selected ? 
Options: a ) 8 % , b ) 12 % , c ) 16 % , d ) 20 % , e ) 24 %

SOLUTION: b

PROBLEM: Problem: in a certain city , 70 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 80 percent of the registered voters who are democrats and 30 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ? 
Options: a ) 65 % , b ) 52 % , c ) 85 % , d ) 69 % , e ) 75 %

SOLUTION: a

PROBLEM: Problem: if 45 % of z is 120 % of y and y is 75 % of x , what percent of x is z ? 
Options: a ) 200 , b ) 160 , c ) 100 , d ) 65 , e ) 50

SOLUTION:
a