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A premier B-school, which is in process of getting an AACSB accreditation, has 360 second year students. To incorporate sustainability into their curriculum, it has offered 3 new elective subjects in the second year namely Green Supply Chain, Global Climate Change & Business and Corporate Governance. Twelve students have taken all the three electives, and 120 students study Green Supply Chain. There are twice as many students who study Green Supply Chain and Corporate Governance but not Global Climate Change and Business, as those who study both Green Supply Chain and Global Climate Change & Business but not Corporate Governance, and 4 times as many who study all the three. 124 students study Corporate Governance. There are 72 students who could not muster up the courage to take up any of these subjects. The group of students who study both Green Supply Chain and Corporate Governance but not global Climate Change & Business is exactly the same as the group made up to the students who study both Global Climate Change & Business and Corporate Governance. How many students study Global Climate Change & Business only?
- a)176
- b)104
- c)152
- d)188
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A premier B-school, which is in process of getting an AACSB accreditat...
The number of students who study each combination of subjects (based on the direct data) given is as shown below:
It is given that: (GSC and CG but not GCCB) = 4 times (all three electives)
It is given that: (GSC and CG but not GCCB) = 4 times (all three electives)
∴ 2x = 4(12) i.e. x = 24
Also: (GSC and CG but not GCCB) = (all three electives) + (GCCB and CG but not GSC)
∴ (GCCB and CG but not GSC) = 2x − 12 = 2(24) − 12 = 36
So, the figure becomes:
Now, CG only = 124 − (48 + 12 + 36) = 28
Now, CG only = 124 − (48 + 12 + 36) = 28
∴ GCCB alone = 360 − 120 − 36 − 28 − 72 = 104
Hence, option (b).
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A premier B-school, which is in process of getting an AACSB accreditat...
Understanding the Problem
To solve the problem, we need to set up variables for the number of students in each category of elective subjects.
Given Data
- Total students = 360
- Students not taking any subject = 72
- Students taking Green Supply Chain (G) = 120
- Students taking Corporate Governance (C) = 124
- Students taking all three subjects = 12
- Let:
- x = Students taking G and C but not Global Climate Change (X)
- y = Students taking G and X but not C
- z = Students taking X and C but not G
Relationships between the groups
- According to the problem:
- \( x = 2y \)
- \( x = z \)
- \( y = 12 \) (since 12 students take all three subjects)
Calculating Students in Each Category
Using the relationships:
- \( y = 12 \) (students taking all three)
- \( x = 2y = 2 \times 12 = 24 \)
- \( z = x = 24 \)
Calculating Total Students Taking Each Subject
Using the inclusion-exclusion principle:
- Total taking G and C = \( 120 + 124 - (x + y + z + 12) \)
Set the equation:
- \( 120 + 124 - (24 + 12 + 24 + 12) = 360 - 72 \)
- Solve for students taking Global Climate Change only:
Final Calculation
Total students studying:
- \( G + C + X - G \cap C - G \cap X - C \cap X + G \cap C \cap X = 288 \)
Thus, the students studying Global Climate Change only = \( 360 - 72 - (students in G + C + both) = 104 \).
Conclusion
The number of students studying Global Climate Change & Business only is:
Answer: 104 (Option B).
To solve the problem, we need to set up variables for the number of students in each category of elective subjects.
Given Data
- Total students = 360
- Students not taking any subject = 72
- Students taking Green Supply Chain (G) = 120
- Students taking Corporate Governance (C) = 124
- Students taking all three subjects = 12
- Let:
- x = Students taking G and C but not Global Climate Change (X)
- y = Students taking G and X but not C
- z = Students taking X and C but not G
Relationships between the groups
- According to the problem:
- \( x = 2y \)
- \( x = z \)
- \( y = 12 \) (since 12 students take all three subjects)
Calculating Students in Each Category
Using the relationships:
- \( y = 12 \) (students taking all three)
- \( x = 2y = 2 \times 12 = 24 \)
- \( z = x = 24 \)
Calculating Total Students Taking Each Subject
Using the inclusion-exclusion principle:
- Total taking G and C = \( 120 + 124 - (x + y + z + 12) \)
Set the equation:
- \( 120 + 124 - (24 + 12 + 24 + 12) = 360 - 72 \)
- Solve for students taking Global Climate Change only:
Final Calculation
Total students studying:
- \( G + C + X - G \cap C - G \cap X - C \cap X + G \cap C \cap X = 288 \)
Thus, the students studying Global Climate Change only = \( 360 - 72 - (students in G + C + both) = 104 \).
Conclusion
The number of students studying Global Climate Change & Business only is:
Answer: 104 (Option B).
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A premier B-school, which is in process of getting an AACSB accreditation, has 360 second year students. To incorporate sustainability into their curriculum, it has offered 3 new elective subjects in the second year namely Green Supply Chain, Global Climate Change & Business and Corporate Governance. Twelve students have taken all the three electives, and 120 students study Green Supply Chain. There are twice as many students who study Green Supply Chain and Corporate Governance but not Global Climate Change and Business, as those who study both Green Supply Chain and Global Climate Change & Business but not Corporate Governance, and 4 times as many who study all the three. 124 students study Corporate Governance. There are 72 students who could not muster up the courage to take up any of these subjects. The group of students who study both Green Supply Chain and Corporate Governance but not global Climate Change & Business is exactly the same as the group made up to the students who study both Global Climate Change & Business and Corporate Governance. How many students study Global Climate Change & Business only?a)176b)104c)152d)188Correct answer is option 'B'. Can you explain this answer?
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