King School has an enrollment of 900 students. The school day

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Fri May 29, 2020 6:46 am

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King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

A. 25
B. 30
C. 36
D. 60
E. 150

Answer: C
Source: Official guide

Source: Beat The GMAT — Problem Solving | Fri May 29, 2020 6:46 am

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Re: King School has an enrollment of 900 students. The school day

by Brent@GMATPrepNow » Fri May 29, 2020 8:52 am

BTGModeratorVI wrote: ↑
Fri May 29, 2020 6:46 am
King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

A. 25
B. 30
C. 36
D. 60
E. 150

Answer: C
Source: Official guide

There are 900 students, and there are 30 students per class.
900/30 = 30
So, at any given time during the school day, there are 30 class periods happening.

Since there are 6 class periods per day, the TOTAL number of classes each day = (6)(30) = 180

Each teacher teaches 5 classes per day
If there are 180 classes per day, then the number of teachers = 180/5 = 36

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

ezmodest: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Sat May 30, 2020 9:02 am

Re: King School has an enrollment of 900 students. The school day

by ezmodest » Sat May 30, 2020 9:30 am

My solution:

At any point in time, only 5/6 of the teachers are teaching a class, but every student is in class. Therefore we know the following:

Total Student Body / Students per Class = # of teachers currently teaching
900 / 30 = 30 teachers currently teaching

If we know that only 5/6 of teachers are every teaching at one time then the total # of teachers must be:
30/(5/6) = 30*6/5 = 36

Answer C

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