Question:
In a business school, only three specializations are offered: marketing, finance, and operations. A student can opt for either one, or two, or no specializations. In the current batch of 120 students, 60 are specializing in marketing, 50 are specializing in finance and 30 are specializing in operations. During the placement process, all students specializing either in marketing or in finance are shortlisted for consulting job interviews.
In a business school, only three specializations are offered: marketing, finance, and operations. A student can opt for either one, or two, or no specializations. In the current batch of 120 students, 60 are specializing in marketing, 50 are specializing in finance and 30 are specializing in operations. During the placement process, all students specializing either in marketing or in finance are shortlisted for consulting job interviews.
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When calculating the number of students in overlapping categories, always account for double-counting students in both categories using the principle of inclusion-exclusion.
Updated On: Jan 7, 2026
- 40
- 35
- 50
- 60
- 45
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The Correct Option is D
Solution and Explanation
Step 1: Understand the total number of students in each specialization.
There are 120 students in total. - 60 students are specializing in marketing. - 50 students are specializing in finance. - 30 students are specializing in operations.
Step 2: Calculate the number of students not specializing in marketing or finance.
Since students specializing in either marketing or finance are shortlisted, we need to find how many students are specializing in both marketing and finance. Let’s assume this number is \( x \). The total number of students specializing in marketing or finance is \( 60 + 50 - x \), since those specializing in both marketing and finance have been counted twice. The number of students not specializing in either marketing or finance will be: \[ 120 - (60 + 50 - x) = 120 - 110 + x = 10 + x \] Since 45 students are not shortlisted, we can equate: \[ 10 + x = 45 \] Thus, \( x = 35 \), so the minimum number of students specializing in both marketing and finance is 35.
Step 3: Conclusion.
The minimum number of students specializing in both marketing and finance is 35, and the total number of students specializing in marketing or finance (including both) is 60. Thus, the correct answer is (D) 60.
There are 120 students in total. - 60 students are specializing in marketing. - 50 students are specializing in finance. - 30 students are specializing in operations.
Step 2: Calculate the number of students not specializing in marketing or finance.
Since students specializing in either marketing or finance are shortlisted, we need to find how many students are specializing in both marketing and finance. Let’s assume this number is \( x \). The total number of students specializing in marketing or finance is \( 60 + 50 - x \), since those specializing in both marketing and finance have been counted twice. The number of students not specializing in either marketing or finance will be: \[ 120 - (60 + 50 - x) = 120 - 110 + x = 10 + x \] Since 45 students are not shortlisted, we can equate: \[ 10 + x = 45 \] Thus, \( x = 35 \), so the minimum number of students specializing in both marketing and finance is 35.
Step 3: Conclusion.
The minimum number of students specializing in both marketing and finance is 35, and the total number of students specializing in marketing or finance (including both) is 60. Thus, the correct answer is (D) 60.
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