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1/4 of all the juniors and 2/3 of all the seniors are...

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1/4 of all the juniors and 2/3 of all the seniors are...

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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.

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LUANDATO wrote:
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
Let the total number of seniors = the LCM of the denominators in the prompt = 4*3 = 12.
Since there are 2/3 as many juniors as seniors, the total number of juniors = (2/3)(12) = 8.
Thus, the total number of students = 12+8 = 20.

Since 1/4 of the 8 juniors go on the trip, the number of juniors on the trip = (1/4)(8) = 2.
Since 2/3 of the 12 seniors go on the trip, the number of seniors on the trip = (2/3)(12) = 8.
Thus, the total number of students on the trip = 2+8 = 10.

Resulting fraction:
(total students on the trip)/(total number of students) = 10/20 = 1/2.

The correct answer is B.

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Quote:
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.

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LUANDATO wrote:
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
We can let the total number of seniors = 36. Since there are 2/3 as many juniors, there are 24 juniors.

Since 1/4 of the juniors are going on the trip, 1/4 x 24 = 6 juniors are going on the trip. Since 2/3 of the seniors are going on the trip, 2/3 x 36 = 24 seniors are going on the trip.

Since there are a total of 36 + 24 = 60 students, and 60 - 6 - 24 = 30 are not going on the trip, we see that 1/2 of the students are not going on the trip.

Answer: B

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scott@targettestprep.com



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