Difference between revisions of "2015 AMC 12A Problems/Problem 5"
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==Problem== | ==Problem== | ||
| − | + | Sreshtha needs to estimate the quantity <math>\frac{a}{b} - c</math>, where <math>a, b,</math> and <math>c</math> 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 <math>\frac{a}{b} - c</math>? | |
<math> \textbf{(A)}\ \text{She rounds all three numbers up.}\\ | <math> \textbf{(A)}\ \text{She rounds all three numbers up.}\\ | ||
Latest revision as of 05:00, 15 February 2021
Problem
Sreshtha needs to estimate the quantity 
, where 
and 
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 ?
Solution
To maximize our estimate, we want to maximize 
and minimize , because both terms are positive values. Therefore we round down. To maximize , round 
up and 
down. 
See Also
| 2015 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 4 |
Followed by Problem 6 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
