1/4 of all the juniors and 2/3 of all the seniors are going on a trip. If there are 2/3 as many juniors as seniors, what fraction of the students are not going on the trip?
(A) 4/9
(B) 1/2
(C) 2/3
(D) 1/3
(E) 5/6
The OA is B.
I can understand this PS question. Can any expert explain it please? Thanks.
Hi LUANDATO,
Let's look at your question.
If there are a total of 'x' seniors, then the juniors will be (2/3)x.
Total students = seniors + juniors
Total students = $$=x+\frac{2}{3}x=\frac{5}{3}x$$
The students going on the trip are:
1/4 of all juniors =
$$\left(\frac{1}{4}\right)\left(\frac{2}{3}x\right)=\frac{1}{6}x$$
2/3 of all seniors = $$\frac{2}{3}x$$
Total students going on the trip are:
$$=\frac{1}{6}x +\frac{2}{3}x$$
$$=\left(\frac{1+4}{6\ }\right)x$$ $$=\left(\frac{5}{6\ }\right)x$$
Fraction of the students going on the trip = Students going on the trip / Total students
$$=\frac{\frac{5}{6}x}{\frac{5}{3}x}$$
$$=\frac{5x\times3}{6\times5x}$$
$$=\frac{3}{6}$$
$$=\frac{1}{2}$$
We are asked to find the fraction of the students not going on the trip which can be calculated as:
Fraction of the students not going on the trip = 1 - Fraction of the students going on the trip
Fraction of the students not going on the trip = 1 - 1/2 = 1/2
Therefore, Option
B is correct.
Hope this helps.
I am available if you'd like any follow up.
