smc

Question

Sreshtha needs to estimate the quantity ab - 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 ab - c?

Accepted Answer

To maximize our estimate, we want to maximize ab and minimize c, because both terms are positive values. Therefore we round c down. To maximize ab, round a up and b down. She rounds a up, and she rounds b and c down.