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In a classroom containing only fifth- and sixth-graders, fifth graders

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Bunuel
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In a classroom containing only fifth- and sixth-graders, fifth graders [#permalink] New post   05 Nov 2018, 01:04
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In a classroom containing only fifth- and sixth-graders, fifth graders are seated in 1/2 of the desks and sixth-graders are seated in 2/3 of the remainder. Sixth-graders are seated in what fraction of the desks in use?

A. 5/6
B. 2/3
C. 3/5
D. 2/5
E. 1/3
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D
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D
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Re: In a classroom containing only fifth- and sixth-graders, fifth graders [#permalink] New post   05 Nov 2018, 01:37
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Bunuel wrote:
In a classroom containing only fifth- and sixth-graders, fifth graders are seated in 1/2 of the desks and sixth-graders are seated in 2/3 of the remainder. Sixth-graders are seated in what fraction of the desks in use?

A. 5/6
B. 2/3
C. 3/5
D. 2/5
E. 1/3



Let the total no. of students be 60.

Seats for 5th grader = 30

Seats for 6 th grader = 20.

Question: Sixth-graders are seated in what fraction of the desks in use

In use = 50.

So required fraction : 20 /50 = 2/5.

The best answer is D.
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Re: In a classroom containing only fifth- and sixth-graders, fifth graders [#permalink] New post   05 Nov 2018, 11:45
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In a classroom containing only fifth- and sixth-graders, fifth graders are seated in 1/2 of the desks and sixth-graders are seated in 2/3 of the remainder. Sixth-graders are seated in what fraction of the desks in use?

A. 5/6
B. 2/3
C. 3/5
D. 2/5
E. 1/3

Let total desks b 6

5th graders would be: 1/2*6= 3
6th graders are seated 2/3 of remainder; 2/3*3=2

total desk in use ; 3+2=5
fraction of 6th graders would be 2/5; D
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Re: In a classroom containing only fifth- and sixth-graders, fifth graders [#permalink] New post   05 Jan 2020, 21:08
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Bunuel wrote:
In a classroom containing only fifth- and sixth-graders, fifth graders are seated in 1/2 of the desks and sixth-graders are seated in 2/3 of the remainder. Sixth-graders are seated in what fraction of the desks in use?

A. 5/6
B. 2/3
C. 3/5
D. 2/5
E. 1/3


First, make note that there is a number of unused desks in the classroom. If there are 60 desks in the classroom, fifth graders sit at 60 x 1/2 = 30 desks. With 30 desks remaining, sixth graders sit at 30 x 2/3 = 20 desks. We see that there are 50 desks in use in the classroom. Thus, sixth-graders sit at 20/50 = 2/5 of the desks that are in use.

Answer: D
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Re: In a classroom containing only fifth- and sixth-graders, fifth graders [#permalink] New post   05 Nov 2018, 13:38
Bunuel wrote:
In a classroom containing only fifth- and sixth-graders, fifth graders are seated in 1/2 of the desks and sixth-graders are seated in 2/3 of the remainder. Sixth-graders are seated in what fraction of the desks in use?

A. 5/6
B. 2/3
C. 3/5
D. 2/5
E. 1/3



let total # number be 60


Fifth graders \(60*\frac{1}{2} = 30\)

Sixth graders \(30*\frac{2}{3} = 20\)


\(\frac{20}{30}\)= \(\frac{2}{5}\)
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Re: In a classroom containing only fifth- and sixth-graders, fifth graders [#permalink] New post   07 Nov 2018, 05:53
assume total number be 60


Fifth graders 60∗12=3060∗12=30

Sixth graders 30∗23=2030∗23=20


20/30= 2/3
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Re: In a classroom containing only fifth- and sixth-graders, fifth graders [#permalink] New post   19 Apr 2019, 08:07
Watch out!

typical mistake is:
d=desks
1d/3 / 1d = 1/3 (but it's not as we should divide by the number of desks in use! and in this problem, desks in use differ from the total number of desks).

Thus, fifth graders use 1d/2 of the desks
sixth graders use d/3 of the desks.
From these two lines above we can calculate number of desks used: d/2 + d/3 = 2/5
therefore, coming to the main question which is desks used by 6th grades / desks used = 1/3 / 2/5 = 2/5

thus, IMO: d

cheers!
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Re: In a classroom containing only fifth- and sixth-graders, fifth graders [#permalink] New post   08 May 2019, 23:14
Total Students = 90

5 th Graders = 1/2(90) = 45

6 th Graders = 2/3(45) = 30

Total Desks in use should be 75

Hence, the answer is: 30/75 = 2/5.(D)
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Re: In a classroom containing only fifth- and sixth-graders, fifth graders [#permalink] New post   05 Jan 2020, 23:20
Let in the class room, there is 60 seats ( l.c.m. of 5 and 6)
The seats of fifth graders = ½*60 = 30
The seats of sixth graders = 2/3 * 30(Remaining =60-30=30)
= 20
Total seats in use = 30 +20 =50
Question: Sixth-graders are seated in what fraction of the desks in use?

Required seats in fraction = 20/50
=2/5(D)
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Re: In a classroom containing only fifth- and sixth-graders, fifth graders [#permalink]
05 Jan 2020, 23:20
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