Question

At a "university mixer", there is a room full of either first-year students or returning students. Currently, 1/2 that is 50% of them are first-year students, and the rest are returning students. How many more returning students would need to enter the room so that first-year students make up only 2/5, that is 40% of the resulting mixture.

A) 6

B) 24

C) 36

D) 30

E) 15

Answer 1

Let 2x be the total number of the first year and returning students. Now, (1/2) of 2x i.e. x are first-year students, and the rest i.e. 2x-x = x are returning students.

let the l number of returning students in=crease by y for the first-year students to make up only 2/5 of the resulting mixture. Then x/(2x+y) = 2/5 or, 2(2x+y) = 5x or, 2y =5x-4x = x so that y = x/2.

Hence the number of returning students would need to increase by 50 % , while the number of the first year students remain the same, if the first-year students are to make up only 2/5, that is 40% of the resulting mixture.