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.

If $45$ students are not shortlisted for consulting job interviews, what is the MINIMUM possible number of students specializing in both marketing and finance?

Accepted Answer

A. Total students = $120$. Number of students not shortlisted = $45$. These students consist of those specializing only in operations ($c$) and those with no specialization ($h$). So $c + h = 45$. Number of shortlisted students = $120 - 45 = 75$. The shortlisted students are those in Marketing or Finance: $|M \cup F| = |M| + |F| - |M \cap F| = 75$ $60 + 50 - |M \cap F| = 75 \implies |M \cap F| = 35$. Thus, the number of students specializing in both marketing and finance is $35$.

Specializations in a business school

Explanation

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