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 hub proposal.png

Official Solutions: Q1.Select True/ False for each of the statements below. Plan A: Total area : 400,000 sq. ft. Free area : 160,000 sq. ft. The percentage of free area = (160,000 ÷ 400,000) × 100 = 40% Plan A meets the minimum threshold for open area. Plan B: Total area : 500,000 sq. ft. Free area : 200,000 sq. ft. The percentage of free area = (200,000 ÷ 500,000) × 100 = 40% Plan B meets the minimum threshold for open area. Plan C: Total area : 550,000 sq. ft. Free area : 220,000 sq. ft. The percentage of free area = (220,000 ÷ 550,000) × 100 = 40% Plan C meets the minimum threshold for open area. Plan A meets the minimum threshold for open area → Yes Plan B meets the minimum threshold for open area → Yes Plan C meets the minimum threshold for open area → Yes Q2. Select True/ False for each of the statements below. Statement 1: Plan A can accommodate 100 students per classroom Student capacity for Plan A : 1,800 students Number of classrooms in Plan A : 18 classrooms Students per classroom = 1,800 ÷ 18 = 100 students per classroom This statement is True . Statement 2: Plan B has the minimum required number of study rooms Student capacity for Plan B : 2,000 students The requirement is one study room per 50 students. Required study rooms = 2,000 ÷ 50 = 40 study rooms Number of study rooms in Plan B : 50 study rooms Since 50 study rooms exceed the required 40, this statement is True . Statement 3: Plan C has the minimum required number of study rooms Student capacity for Plan C : 2,000 students The requirement is one study room per 50 students. Required study rooms = 2,000 ÷ 50 = 40 study rooms Number of study rooms in Plan C : 38 study rooms Since Plan C has only 38 study rooms (fewer than the required 40), this statement is False . True – Plan A can accommodate 100 students per classroom. True – Plan B has the minimum required number of study rooms. False – Plan C does not have the minimum required number of study rooms. Q3. Disregarding the budget constraints, which among the three plans satisfy all the guidelines laid down by the school administration? Evaluating each of the guidelines: Capacity of at least 1,800 students : Plan A: 1,800 students (Meets the requirement) Plan B: 2,000 students (Meets the requirement) Plan C: 2,000 students (Meets the requirement) At least one study room for every 50 students : Plan A: 1,800 students, requires 1,800 ÷ 50 = 36 study rooms . Plan A has 36 study rooms (Meets the requirement). Plan B: 2,000 students, requires 2,000 ÷ 50 = 40 study rooms . Plan B has 50 study rooms (Exceeds the requirement). Plan C: 2,000 students, requires 2,000 ÷ 50 = 40 study rooms . Plan C has 38 study rooms (Does not meet the requirement). At least 80 faculty offices : Plan A: 80 faculty offices (Meets the requirement) Plan B: 85 faculty offices (Meets the requirement) Plan C: 90 faculty offices (Meets the requirement) At least 40% of the total area must be designated as open space : Plan A: 40% open area (Meets the requirement) Plan B: 40% open area (Meets the requirement) Plan C: 40% open area (Meets the requirement) Plan A : Meets all the guidelines. Plan B : Meets all the guidelines. Plan C : Fails to meet the study room requirement (does not have 40 study rooms). Thus, the plans that satisfy all the guidelines are Plan A and Plan B .

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A business school located by Lake Michigan is planning to construct a

catinabox

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Updated on: 30 Oct 2025, 09:22

Originally posted by catinabox on 31 Aug 2024, 20:30.
Last edited by Bunuel on 30 Oct 2025, 09:22, edited 8 times in total.

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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.

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

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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

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For each of the following statements, select Yes if it can be deduced from the information provided. Otherwise, select No.

Yes	No
		Plan A meets the minimum required percentage of open area.
		Plan B meets the minimum required percentage of open area.
		Plan C meets the minimum required percentage of open area.

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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

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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

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For each of the following statements, select True if the statement is supported by the information provided. Otherwise, select False.

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		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.

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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

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Plan A and Plan B

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Disregarding the budget constraint, which of the plans meet all of the school’s building requirements?

	Only Plan A
	Plan A and Plan B
	Plan A, Plan B, and Plan C
	Only Plan B
	None of the plans

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Plan A and Plan B

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Bunuel

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Official Solution:

Bunuel

For each of the following statements, select True if the statement is supported by the information provided. Otherwise, select False.

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.

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"

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Bunuel

For each of the following statements, select Yes if it can be deduced from the information provided. Otherwise, select No.

Yes	No
		Plan A meets the minimum required percentage of open area.
		Plan B meets the minimum required percentage of open area.
		Plan C meets the minimum required percentage of open area.

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"

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Bunuel

Disregarding the budget constraint, which of the plans meet all of the school’s building requirements?

The school’s requirements are:

• Capacity for at least 1,800 students

• At least one study room for every 50 students

• At least 80 faculty offices

• At least 40% open area on each floor

Plan A has capacity for 1,800 students, 36 study rooms (required = 1,800 ÷ 50 = 36), 80 faculty offices, and 40% open area. Plan A meets all requirements.

Plan B has capacity for 2,000 students, 50 study rooms (required = 2,000 ÷ 50 = 40), 85 faculty offices, and 40% open area. Plan B meets all requirements.

Plan C has capacity for 2,000 students, 38 study rooms (required = 2,000 ÷ 50 = 40), 90 faculty offices, and 40% open area. Plan C does not meet the study room requirement.

Correct answer:

Disregarding the budget constraint, which of the plans meet all of the school’s building requirements? "Plan A and Plan B"

General Discussion

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31 Aug 2024, 21:39

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This is a very straightforward Q.

The best way to save time is never read the data points before reading the Q/s just read what all info variables are given such as student capacity constraint, budget, offices, study rooms, open space etc. No calculations or insights needed as of now - because we dont know what the Q may end up asking.

Q1 - Read the Q carefully - Do we have to compute one variable or multiple depending on options? Great just 1! Open space so look for info pertaining to only that and ignore the rest.

Prompt tells us atleast 40% of total space on each floor has to be allocated as open space.

Atleast 40% mean 40 or more

SO just take 40% of total space for each plan, compare it with free space allocated under each plan and we see the condition is met for all!7

Q2 Again read how many variables are asked in the Q - Students per classroom and Open study rooms
Zero down info from prompt basis this
Statement 1 is fairly easy = Number of students/No of classrom = Students per classroom Option A is correct

There must be at least one study room for every 50 students.
So for Classroom B there are 2000/50 = 40 min room they have 50 great
Classroom C there are 2000/50 = 40 min rooms, they ave 38 Not good

Q3 This will again require you to use only relevant info so as to not waste lot of time.
We already know C is out because it doesnt fulfill Min study room criteria
Lets review the constraints, besides budget constraints quickly for A & B

1. The Hub must have a capacity to hold at least 1,800 students at any given time. Yes clearly
2. There must be at least one study room for every 50 students. Calculated for B, Calculate for A
3. A separate floor must include individual offices for at least 80 faculty members and administrators. Can see from Data yes for both
4. At least 40% of the area on each floor must be designated as open space. Already calculated in Q1 yes both
5. The total construction budget must not exceed $200 million. Have to be ignored

Ans is A& B

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01 Sep 2024, 04:13

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Kavicogsci

Yes, this is the correct solution!

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Kavicogsci

In Question 3. I Think the Answer should be only 'Plan B' as In 'Plan A' The total number of students are 1800 and the Number of Study Rooms is 36 i.e., 1800/36 = 50 but the minimum they only have is 36 so why are we considering it as YES??

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karan_vasudeva20

Kavicogsci

I think you're mixing two things here. If for 1800 students the plan accounts for 36 study rooms, that meets the criteria that there should be a study room for every 50 students. Since 1800/50= 36, that criteria is fulfilled.

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Official Solutions:

Q1.Select True/ False for each of the statements below.
Plan A:

Total area: 400,000 sq. ft.
Free area: 160,000 sq. ft.
The percentage of free area = (160,000 ÷ 400,000) × 100 = 40%

Plan A meets the minimum threshold for open area.

Plan B:

Total area: 500,000 sq. ft.
Free area: 200,000 sq. ft.
The percentage of free area = (200,000 ÷ 500,000) × 100 = 40%

Plan B meets the minimum threshold for open area.

Plan C:

Total area: 550,000 sq. ft.
Free area: 220,000 sq. ft.
The percentage of free area = (220,000 ÷ 550,000) × 100 = 40%

Plan C meets the minimum threshold for open area.

Plan A meets the minimum threshold for open area → Yes
Plan B meets the minimum threshold for open area → Yes
Plan C meets the minimum threshold for open area → Yes

Q2. Select True/ False for each of the statements below.

Statement 1: Plan A can accommodate 100 students per classroom

Student capacity for Plan A: 1,800 students
Number of classrooms in Plan A: 18 classrooms
Students per classroom = 1,800 ÷ 18 = 100 students per classroom

This statement is True.

Statement 2: Plan B has the minimum required number of study rooms

Student capacity for Plan B: 2,000 students
The requirement is one study room per 50 students.
Required study rooms = 2,000 ÷ 50 = 40 study rooms
Number of study rooms in Plan B: 50 study rooms

Since 50 study rooms exceed the required 40, this statement is True.

Statement 3: Plan C has the minimum required number of study rooms

Student capacity for Plan C: 2,000 students
The requirement is one study room per 50 students.
Required study rooms = 2,000 ÷ 50 = 40 study rooms
Number of study rooms in Plan C: 38 study rooms

Since Plan C has only 38 study rooms (fewer than the required 40), this statement is False.

True – Plan A can accommodate 100 students per classroom.
True – Plan B has the minimum required number of study rooms.
False – Plan C does not have the minimum required number of study rooms.

Q3. Disregarding the budget constraints, which among the three plans satisfy all the guidelines laid down by the school administration?

Evaluating each of the guidelines:

Capacity of at least 1,800 students:
- Plan A: 1,800 students (Meets the requirement)
- Plan B: 2,000 students (Meets the requirement)
- Plan C: 2,000 students (Meets the requirement)
At least one study room for every 50 students:
- Plan A: 1,800 students, requires 1,800 ÷ 50 = 36 study rooms. Plan A has 36 study rooms (Meets the requirement).
- Plan B: 2,000 students, requires 2,000 ÷ 50 = 40 study rooms. Plan B has 50 study rooms (Exceeds the requirement).
- Plan C: 2,000 students, requires 2,000 ÷ 50 = 40 study rooms. Plan C has 38 study rooms (Does not meet the requirement).
At least 80 faculty offices:
- Plan A: 80 faculty offices (Meets the requirement)
- Plan B: 85 faculty offices (Meets the requirement)
- Plan C: 90 faculty offices (Meets the requirement)
At least 40% of the total area must be designated as open space:
- Plan A: 40% open area (Meets the requirement)
- Plan B: 40% open area (Meets the requirement)
- Plan C: 40% open area (Meets the requirement)

Plan A: Meets all the guidelines.
Plan B: Meets all the guidelines.
Plan C: Fails to meet the study room requirement (does not have 40 study rooms).

Thus, the plans that satisfy all the guidelines are Plan A and Plan B.