mojorising800 wrote:
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 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. 151
B. 51
C. 154
D. 31
E. 52
Say there are in all 100 students. Use a matrix:
50 are first year and 50 are second year students.
........................Major Dec................Major not dec..............Total
First Year............................................................................50
Second Yr...........................................................................50
Total
4/5 * 50 = 40 not declared major first year students.
........................Major Dec................Major not dec..............Total
First Year................10..................................40....................50
Second Yr...........................................................................50
Total
second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major
........................Major Dec................Major not dec..............Total
First Year................10..................................40.....................50
Second Yr...............30..................................20......................50
Total
So second year students who've not declared a major is 20/100 = 1/5
Answer (B)