Difficult Math Question #39 - Sets

800guy wrote:Every student of a certain school must take one and only one elective course. In 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. In 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 come in. What fraction of all students took biology and took chemistry?

A. 7/9 B .6/7 C.5/7 D.4/9 E.2/5

Initially there were Say X students

X/2 took biology
X/3 took Chemistry
X/6 took Physics

took initially

This year

People who Take biology = 2/3*1/2*X= X/3
People who take chemistry=3/4*1/3*X=X/4
People who took physics= X/6

People took Chemistry or biologt = 7/12X
Total No of students = 9/12 X

required ratio =7/9

Which turns out to be A

OA:

Soln: If total =1
Last year
B=1/2
C=1/3
P=1/6
This year
B= 1/2 * 2/3 = 1/3
C= 1/3 * 3/4= 1/4
Tot 1/3+1/4=7/12
student left this year
B = 1/2 * 1/3 = 1/6
C= 1/3 *1/4 = 1/12
tot= 1/6 +1/12 = 1/4
So the school has total student this year
= Last year student no - total no of student left this year
= 1- 1/4
=3/4
Answer = 7/12 / 3/4
= 7/9

Assume we have 120 students last year
Number of students last year Number of students left Number of students remain
Biology 60 (1/2) 20 (1/3 of 60) 40 (60-20)
Chemistry 40 (1/3) 10 (1/4 of 40) 30 (40-10)
Physics 20 0 20
Total 120 90
fraction of all students took biology and took chemistry = (40+30)/90 = 70/90 = 7/9