I30-10

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 meets the minimum required percentage of open area. 
 
• The school requires that at least 40% of the total area of the building be designated as open space.
 
Plan A has a total area of 400,000 sq. ft. and an open area of 160,000 sq. ft. The percentage of open area is (160,000/400,000) * 100 = 40%. This meets the minimum requirement.
 
 Plan B meets the minimum required percentage of open area. 
 
• Plan B has a total area of 500,000 sq. ft. and an open area of 200,000 sq. ft. The percentage of open area is (200,000/500,000) * 100 = 40%. This meets the minimum requirement.
 
 Plan C meets the minimum required percentage of open area. 
 
• Plan C has a total area of 550,000 sq. ft. and an open area of 220,000 sq. ft. The percentage of open area is (220,000/550,000) * 100 = 40%. This meets the minimum requirement.

Correct answer:

Plan A meets the minimum required percentage of open area.  "Yes"

Plan B meets the minimum required percentage of open area.  "Yes"

Plan C meets the minimum required percentage of open area.  "Yes"

Shivang29 · Answer

how do we know that each floor has 40% when we are given the size and space of the entire building. Could it not be that some floors were left empty and some were filled to capacity?

Bunuel · Answer

Good point — but the key is the word  “designated”  open area.

It means the building plan itself reserves 40% of each floor’s area as open space — regardless of future occupancy or usage.

So it doesn’t matter if later someone leaves one floor empty and fills another — the  design  ensures that each floor meets the minimum 40% open area requirement.

That’s why using total area and total designated open area is enough to answer the question.

North23 · Answer

At least 40% of the area on  each floor  must be designated as open space

I think what the  Shivang29 meant was what if lets say as an example 2 floors with combined total area of 2000 sq ft (each floor being 1000 sq ft) have cobined open space area of 800 sq ft. 
But floor 1 has 600 sq ft of open space and floor 2 with 200 sq ft open space.
In this case, yes on an overall floor space, we have 40% open space, but this condition is not satisfied per floor.

So we cannot get a guarantee that the conditions   per floor   are being met from the overall open space data.

Bunuel · Answer

Thank you for pointing this out, you raised a valid concern.

We’ve updated the wording in the prompt and the statements to remove the ambiguity. The requirement now clearly refers to 40% of the total area of the building, not each individual floor. The statements and solution have also been revised accordingly to reflect this.

Appreciate you flagging this!

ljohar9899 · Answer

This is a great question that’s helpful for learning. as per tab 2, the area utilized and free areas for plans B and C do not add up to their respective total areas mentioned. is it a typo? if not then how are we to go about calculating the free area percentage as free area/total area would give us a different number from free area/(free area+area utilized).

Bunuel · Answer

Thanks for pointing that out, it's been fixed.

The area utilized and open area values for Plans B and C have been adjusted so they now correctly add up to the total area.

I30-10

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My Rewards

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