Every student of a certain school must take one and only

Hi GMAT_mission,

We're told that every student of a certain school took ONLY ONE elective course and last year, 1/2 of the students took biology as an elective, 1/3 of the students took chemistry as an elective, and all of the other students took physics. Then this year, 1/3 of the students who took biology and 1/4 of the students who took chemistry left school, other students did not leave, and no fresh student came in. We're asked for the fraction of all students who took biology or chemistry.

While question is a bit awkwardly-worded, it can be solved by TESTing VALUES. To start, we should pick a TOTAL number of students that is a multiple of all of the fractions mentioned.

IF.... Total students LAST YEAR = 36
Last year, (1/2)(36) = 18 took biology
Last year, (1/3)(36) = 12 took chemistry
Last year, the rest = 36 - 30 = 6 took physics

THIS YEAR
(1/3)(18) = 6 biology students left, leaving 18 - 6 = 12 who took biology
(1/4)(12) = 3 chemistry students left, leaving 12 - 3 = 9 who took chemistry
The 6 who took physics were still there.

Thus, this year there are 12+9+6 = 27 students and the fraction that took biology or chemistry is (12+9)/27 = 21/27 = 7/9

Final Answer: A

GMAT assassins aren't born, they're made,
Rich