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King School has an enrollment of 900 students. The school

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King School has an enrollment of 900 students. The school

by BTGmoderatorDC » Wed Dec 11, 2019 6:13 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


OA C

Source: Official Guide
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by [email protected] » Wed Dec 11, 2019 9:16 pm
Hi All,

We're told that 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 and there are 30 students per class. However, each teacher teaches a class during 5 of the 6 class periods and has one class period free (but NO students have a free class period). We're asked for the number of teachers that the school has. This question provides us with all of the 'numbers' that we need to answer the question, but you can still perform the necessary calculations in a number of different ways. As such, how you organize your information will impact how quickly you can answer the question.

To start, since each class consists of 30 students, we know that 900/30 = 30 classes run each period.

Since the School runs 6 class periods a day, we will need (6)(30) = 180 teacher-periods to be covered by the teachers.

Each teacher covers 5 teacher-periods a day though (NOT 6), so we need 180/5 =36 teachers to cover all of the classes.

Final Answer: C

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by Brent@GMATPrepNow » Thu Dec 12, 2019 6:06 am
BTGmoderatorDC wrote: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
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

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by Scott@TargetTestPrep » Thu Dec 12, 2019 6:35 pm
BTGmoderatorDC wrote: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


OA C

Source: Official Guide
Since there are 900 students in the school and each student has to attend 6 classes, there are 900 x 6 = 5400 student-class units.

Since each teacher has to teach 5 classes and each class has 30 students, one teacher can manage 5 x 30 = 150 student-class units.

Therefore, we need 5400/150 = 36 teachers.

Answer: C

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by deloitte247 » Fri Dec 20, 2019 9:52 pm
Total enrollment = 900 students
If there are 30 students in 1 class, then there will be 900 students in $$\frac{900\cdot1}{30}classes\ =\ 30\ classes$$
So, 900 students in 30 classes, hence at any given time in the school, 3- class periods will take place.
Since there are 6 class periods per day, this means;
1 class = 6 class periods
30 classes = 6 * 30 = 180 class periods per day

If each teacher teaches 5 classes per day;
1 teacher = 5 class periods
x teacher = 180 class periods
$$x=\frac{180\cdot1}{5}=36\ teachers$$
In conclusion, King School has 36 teachers.
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