AAPL wrote:Manhattan Prep

At a certain high school, the junior class is twice the size of the senior class. If 1/3 of the seniors & 1/4 of the juniors study Japanese, what fraction of the students in both classes does not study Japanese?

A. 1/6
B. 5/18
C. 5/12
D. 7/12
E. 13/18

OA E

Say, the number of students in the senior class = S; thus, the number of students in the junior class = 2S; thus, the total number of students = S = 2S = 3S

Number of seniors who study Japanese = S/3;
Number of seniors who do not study Japanese = S - S/3 = 2S/3;

Number of juniors who study Japanese = 2S/4 = S/2;
Number of juniors who study Japanese = 2S - S/2 = 3S/2;

Thus, the total number of students who do not study Japanese = 2S/3 + 3S/2 = 13S/6

Thus, the fraction of the students in both classes who do not study Japanese = (13S/6) / 3S = 13/18

The correct answer: E

Hope this helps!

-Jay
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AAPL wrote:Manhattan Prep

At a certain high school, the junior class is twice the size of the senior class. If 1/3 of the seniors & 1/4 of the juniors study Japanese, what fraction of the students in both classes does not study Japanese?

A. 1/6
B. 5/18
C. 5/12
D. 7/12
E. 13/18

OA E

We can let the number of juniors = 240 and the number of seniors = 120.

Thus, 1/3 x 120 = 40 seniors study Japanese and 1/4 x 240 = 60 juniors study Japanese.

In other words, 80 seniors and 180 juniors do not study Japanese. Therefore, the fraction of the students in both classes not studying Japanese is:

(80 + 180)/360 = 260/360 = 26/36 = 13/18

Answer: E