Difference between revisions of "2018 AMC 10A Problems/Problem 5"
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From Alice and Bob, we know that <math>5 < d < 6.</math> | From Alice and Bob, we know that <math>5 < d < 6.</math> | ||
From Charlie, we know that <math>4 < d.</math> | From Charlie, we know that <math>4 < d.</math> | ||
| − | We take the | + | We take the intersection of these two intervals to yield <math>\boxed{\textbf{(D) } (5,6)}</math>, because the nearest town is between 5 and 6 miles away. |
== See Also == | == See Also == | ||
Revision as of 12:56, 14 October 2019
Alice, Bob, and Charlie were on a hike and were wondering how far away the nearest town was. When Alice said, "We are at least 6 miles away," Bob replied, "We are at most 5 miles away." Charlie then remarked, "Actually the nearest town is at most 4 miles away." It turned out that none of the three statements were true. Let 
be the distance in miles to the nearest town. Which of the following intervals is the set of all possible values of ?
Solution
From Alice and Bob, we know that 
From Charlie, we know that 
We take the intersection of these two intervals to yield 
, because the nearest town is between 5 and 6 miles away.
See Also
| 2018 AMC 10A (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 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
