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

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

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

by swerve » Fri Dec 20, 2019 1:42 pm

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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

The OA is D

Source: Princeton Review

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Source: Beat The GMAT — Problem Solving | Fri Dec 20, 2019 1:42 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Mon Dec 23, 2019 3:30 am

swerve 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

The OA is D

Source: Princeton Review

Say there are 6 desks; there the fifth-graders sit on 1/2 of 6 = 3; remaining no of desks = 6 - 3 = 3. Thus, the sixth-graders sit on 2/3 of 3 = 2 desks

Total no of seats occupied = 3 + 2 = 5. Thus, the fraction of seats occupied by the sixth-graders of the desks in use = 2/5.

The correct answer: D

Hope this helps!

-Jay
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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

by deloitte247 » Sat Dec 28, 2019 2:06 am

5th grades are seated in 1/2 of the total desk.
6th grades are seated in 2/3 of the remaining desk.
i.e 6th graders = 2/3 of 1/2 = 2/3 * 1/2 = 1/3
Note: This is because if 5th grades are already using half of the desks available, that means that 6th grades are using only two-third of the remaining half/
Therefore, let the total number of desks = x
Hence, 5th grades = 1/2 * x = x/2
6th grades = 1/3 * x = x/3
Total number of desks in use = x/2 + x/3
$$=\frac{3x+2x}{6}=\frac{5}{6}\left(x\right)$$
The fraction of desk in use for 6th grades =
$$=\frac{6th\ grades}{desk\ in\ use}=\frac{\frac{1}{3}x}{\frac{5}{6}x}=\frac{1}{3}x\cdot\frac{6}{5}x$$
$$=\frac{2}{5}x^2$$
No matter what thevalue of x might be, 6th grades will always use 2/5 of the total number of disks.

Answer = option D

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sat Dec 28, 2019 8:12 pm

swerve 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

The OA is D

Source: Princeton Review

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 30 desks and sixth graders sit at 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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