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# 1/4 of all the juniors and 2/3 of all the seniors are going on a trip.

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Manager
Joined: 18 Feb 2015
Posts: 87
1/4 of all the juniors and 2/3 of all the seniors are going on a trip. [#permalink]

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18 Sep 2016, 09:48
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Difficulty:

35% (medium)

Question Stats:

69% (01:18) correct 31% (01:49) wrong based on 85 sessions

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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
[Reveal] Spoiler: OA
Manager
Joined: 05 Jun 2015
Posts: 84
Location: United States
WE: Engineering (Transportation)
Re: 1/4 of all the juniors and 2/3 of all the seniors are going on a trip. [#permalink]

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18 Sep 2016, 19:31
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J be the number of Juniors and S be the number of Seniors.
there are 2/3 as many juniors as seniors
$$\frac{2}{3}*S = J$$
$$\frac{J}{S}= \frac{2}{3}$$

Going on Trip = $$\frac{J}{4} +\frac{2}{3} *S$$
Fraction = $$(\frac{J}{4} +\frac{2}{3}S) / (J +S)$$
= (2/3*1/4 + 2/3 )/ (2/3 +1 )
= $$\frac{1}{2}$$

Fraction not on trip = 1/2
Option B
VP
Joined: 22 May 2016
Posts: 1431
1/4 of all the juniors and 2/3 of all the seniors are going on a trip. [#permalink]

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27 Nov 2017, 10:03
HarveyKlaus 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

Pick a number of seniors that is a multiple of 2, 3, and 4.

Let seniors = 12
Juniors = 2/3 of seniors = 8
Total students: 20

Seniors going on trip:
2/3 * 12 = 8

Juniors going on trip:
1/4 * 8 = 2

Total going: (8 + 2) = 10
Total not going: (20 - 10) = 10

Fraction of students not going:
$$\frac{10}{20} = \frac{1}{2}$$

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Re: 1/4 of all the juniors and 2/3 of all the seniors are going on a trip. [#permalink]

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29 Nov 2017, 10:51
HarveyKlaus 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.

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Intern
Joined: 08 Dec 2017
Posts: 17
Re: 1/4 of all the juniors and 2/3 of all the seniors are going on a trip. [#permalink]

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08 Dec 2017, 23:34
Basically a weighted average problem. Juniors =2x and seniors =3x so the ratio is 2 to 3.
[(1/4)(2)+(2/3)(3)]\(3+2)
=1/2
So 1/2 are going 1/2 aren't.

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Re: 1/4 of all the juniors and 2/3 of all the seniors are going on a trip.   [#permalink] 08 Dec 2017, 23:34
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