Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 1/3 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?	Choices
A) 7 / 15  B) 1 / 5  C) 4 / 15  D) 1 / 3  E) 2 / 5

Rationale: tot students = x 1 st year student = x / 2 - - - - > non majaor = 4 / 5 ( x / 2 ) - - - - - > maj = 1 / 5 ( x / 2 ) 2 nd year student = x / 2 - - - - > maj = 1 / 3 ( 1 / 5 ( x / 2 ) ) = 1 / 30 ( x ) - - - > non major = x / 2 - 1 / 30 ( x ) = 7 / 15 ( x ) hence 7 / 15 a
Answer: A