| 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.
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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.
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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.
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Since $$y$$ is a positive integer, $$x-y$$ is necessarily less than $$x$$.

Incorrect.
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Finance

Accounting

Economics

Commerce

Business Studies