I30-13

Question

The business school is planning to construct a new Infinity Hub on its Lake Michigan campus to accommodate students enrolled in its MBA program. The school administration has provided the following guidelines for the building design:
 
1. The Hub must have capacity for at least 1,800 students at any given time.
 
2. There must be at least one study room for every 50 students.
 
3. A separate floor must include individual offices for at least 80 faculty members and administrators.
 
4. At least 40% of the total area of the building must be designated as open space.
 
5. The total construction budget must not exceed $200 million.An architectural firm has submitted three design plans for the new Infinity Hub. Each plan differs in size, layout, and budget. In all plans, the top floor is reserved for faculty and administrative offices.
 
The table below summarizes the details of each proposed plan.
      Specification   Plan A   Plan B   Plan C       Student Capacity   1800   2000   2000       Floors   4   5   5       Classrooms   18   20   25       Study Rooms   36   50   38       Faculty Offices   80   85   90       Area utilized (ft squared)   240,000   300,000   330,000       Open area (ft squared)   160,000   200,000   220,000       Total area (ft squared)   400,000   500,000   550,000       Total Budget ($ millions)   $200   $215   $230

Bunuel · Answer

Official Solution:

Plan A can accommodate on average 100 students per classroom 
 
• Plan A has capacity for 1,800 students and 18 classrooms. On average, students per classroom = 1,800 ÷ 18 = 100. This meets the condition.
 
 Plan B meets the minimum required number of study rooms. 
 
• The school requires at least one study room for every 50 students.
 
Plan B has capacity for 2,000 students. Required study rooms = 2,000 ÷ 50 = 40. Plan B has 50 study rooms. This meets the minimum requirement.
 
 Plan C meets the minimum required number of study rooms.  
 
• Plan C has capacity for 2,000 students. Required study rooms = 2,000 ÷ 50 = 40. Plan C has 38 study rooms. This does not meet the minimum requirement.

Correct answer:

Plan A can accommodate on average 100 students per classroom  "True"

Plan B meets the minimum required number of study rooms.  "True"

Plan C meets the minimum required number of study rooms.  "False"

ankitjain2201 · Answer

I don’t quite agree with the solution. In the first statement where it is asked that Plan A can accommodate 100 students per classroom on average. This statement can't be inferred from the given data as there is no specific information on how much capacity an individual classroom has.

Suppose, according to plan A there are only 10 seats per classroom to accommodate 10 students - in that case average would come out to be 10. I believe there should be more information in tabs to be able to prove this as until that happens we are just assuming things by dividing 1800/18.

Bunuel · Answer

You are overcomplicating.

“Can accommodate on average 100 students per classroom” is not claiming anything about the physical seating capacity of each room. It is just an arithmetic implication of the plan totals: capacity 1800 and 18 classrooms means 1800 divided by 18 = 100 students per classroom on average, by definition of average.

“10 seats per classroom” objection would matter only if the statement said something like “each classroom can seat 100 students” or “classrooms have capacity for 100 students.” It does not.

I30-13

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Specification	Plan A	Plan B	Plan C
Student Capacity	1800	2000	2000
Floors	4	5	5
Classrooms	18	20	25
Study Rooms	36	50	38
Faculty Offices	80	85	90
Area utilized (ft squared)	240,000	300,000	330,000
Open area (ft squared)	160,000	200,000	220,000
Total area (ft squared)	400,000	500,000	550,000
Total Budget ($ millions)	$200	$215	$230

True	False
		Plan A can accommodate on average 100 students per classroom
		Plan B meets the minimum required number of study rooms.
		Plan C meets the minimum required number of study rooms.