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Every student of a certain school must take one and only

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by Gmat_mission » Sat Apr 14, 2018 3:32 am

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Difficulty—

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

[spoiler]OA=A[/spoiler].

I don't know how to solve this PS question. Can anyone give me some help? Please.
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by [email protected] » Sat Apr 14, 2018 4:20 pm
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

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by Scott@TargetTestPrep » Mon May 14, 2018 4:07 pm
Gmat_mission 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
We can let the number of students = 120.

Thus, 60 took biology, 40 took chemistry, and 20 took physics.

This year 1/3 x 60 = 20 left school, and 1/4 x 40 = 10 left school, thus 30 students left but we still have a total of 40 + 30 = 70 students who took biology and chemistry and 90 students in the school. So the fraction is 70/90 = 7/9.

Answer: A

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