Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.1 Junior Find the answer

Sreshtha needs to estimate the quantity $\frac{a}{b} - c$ , where $a, b,$ and $c$ are large positive integers. She rounds each of the integers so that the calculation will be easier to do mentally. In which of these situations will her answer necessarily be greater than the exact value of $\frac{a}{b} - c$ ?

Pick one

Solution

To maximize our estimate, we want to maximize $\frac{a}{b}$ and minimize $c$ , because both terms are positive values. Therefore we round $c$ down. To maximize $\frac{a}{b}$ , round $a$ up and $b$ down. $\Rightarrow \boxed{\textbf{(D)}}$

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