TASK DEFINITION: In this task, you need to provide the correct option for a given problem from the provided options.
PROBLEM: Problem: two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 1 : 1 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 5 : 2 , d ) 4 : 3 , e ) 7 : 9

SOLUTION: d

PROBLEM: Problem: what is the greatest positive integer n such that 3 ^ n is a factor of 36 ^ 150 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 600 , e ) 900

SOLUTION: c

PROBLEM: Problem: in a graduating class of 242 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 123

SOLUTION:
e