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# Plugging In: Basic Technique

| Subject | Number of students | |------------------|---------------------------------------------| | Finance | $$x$$ | | Accounting | $$y$$ | | Economics | $$x + y$$ | | Commerce | $$x - y$$ | | Business Studies | $$\displaystyle \frac{x}{2} + \frac{y}{2}$$ | In the table given, $$x$$ and $$y$$ are positive integers. What subject is the mode among the set of students?
Incorrect. [[snippet]] Since $$x$$ and $$y$$ are both positive integers, $$x$$ is necessarily less than $$x+y$$.
Incorrect. [[snippet]] Since $$x$$ and $$y$$ are both positive integers, $$y$$ is necessarily less than $$x+y$$.
Correct. [[snippet]] Given that $$x$$ and $$y$$ are positive integers, $$x + y$$ is the greatest frequency in the given table. Hence, Economics is the mode. If you're not sure, __Plug In__ numbers such as $$x=4$$ and $$y=2$$, and see which of the five categories has the greatest number of students and thus is the most frequent category. | Subject | Number of students | |------------------|-----------------------------------------------------| | Finance | 4 | | Accounting | 2 | | Economics | $$4 + 2=6$$ | | Commerce | $$4 - 2=2$$ | | Business Studies | $$\displaystyle \frac{4}{2} + \frac{2}{2} = 2+1=3$$ | Economics has 6 students, which is more than any of the other subjects. Thus, the economics students are the mode of the group.
Incorrect. [[snippet]] Since $$y$$ is a positive integer, $$x-y$$ is necessarily less than $$x$$.
Incorrect. [[snippet]]
Finance
Accounting
Economics
Commerce