Balvinder wrote:

Of all the students in a certain dormitory, ½ 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 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?

A. 1/15

B. 1/5

C. 4/15

D. 1/3

E. 2/5

B.

used a double set matrix.

Column 1 = 1 st yr

Column 2 = 2 nd yr

Row 1 = Decl. Major

Row 2 = Not Decl.

Column 3 and Row 3 = Total.

If total = x; 1st yr = 1/2x; 2nd yr = 1/2x

1st yr not decl = 2/5 x

1 st yr decl = 1/2x - 2/5x = 1/10x

2nd yr decl = 3/10 x

2nd yr not decl = 1/2x - 3/10x = 1/5x