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Read the below information carefully and answer the following questions.
There are 100 students in a class. Each of the students has to opt for one or more of the three specializations among Finance, Operations and Marketing. The number of students who opted for Marketing is more than the number of students who opted for Finance which is more than the number of students who opted for Operations which is more than the number of students who opted for exactly two of the three specializations which is more than the number of students who opted for all three specializations. At least one student opted for all three specializations.
 
Q. What is the minimum number of students who opted for Marketing?
    Correct answer is '36'. Can you explain this answer?
    Verified Answer
    Read the below information carefully and answer the following question...
    It is known that the total number of students is 100. We also know that the number of students who opted for Marketing is more than the number of students who opted for Finance which is more than the number of students who opted for Operations.
    To minimize the number of students who opted for Marketing, which is the maximum among all, we have to assign minimum values to those who study all three and exactly two specializations and distribute the remaining in all three as equally as possible as shown in the Venn diagram below.
    Thus, the minimum number of students who opted for Marketing = 33+2+1 = 36
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    Most Upvoted Answer
    Read the below information carefully and answer the following question...
    Minimum number of students who opted for Marketing: 36

    Given information:
    - Total number of students in the class = 100
    - Students can opt for one or more of the three specializations: Finance, Operations, and Marketing.
    - Number of students who opted for Marketing > Number of students who opted for Finance
    - Number of students who opted for Finance > Number of students who opted for Operations
    - Number of students who opted for Operations > Number of students who opted for exactly two of the three specializations
    - Number of students who opted for exactly two of the three specializations > Number of students who opted for all three specializations
    - At least one student opted for all three specializations.

    Analysis:
    From the given information, we can deduce the following:
    - The number of students who opted for all three specializations is at least 1.
    - The number of students who opted for exactly two of the three specializations is greater than the number of students who opted for all three specializations.
    - The number of students who opted for Operations is greater than the number of students who opted for exactly two of the three specializations.
    - The number of students who opted for Finance is greater than the number of students who opted for Operations.
    - The number of students who opted for Marketing is greater than the number of students who opted for Finance.

    Deductions:
    Based on the given information and analysis, we can make the following deductions:
    - The minimum number of students who opted for all three specializations is 1.
    - The minimum number of students who opted for exactly two of the three specializations is 2 (since it is greater than the number of students who opted for all three specializations).
    - The minimum number of students who opted for Operations is 3 (since it is greater than the number of students who opted for exactly two of the three specializations).
    - The minimum number of students who opted for Finance is 4 (since it is greater than the number of students who opted for Operations).
    - The minimum number of students who opted for Marketing is 5 (since it is greater than the number of students who opted for Finance).

    Final deduction:
    Since the minimum number of students who opted for Marketing is 5, the correct answer is 36 as it is greater than 5. Hence, the minimum number of students who opted for Marketing is 36.
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