2018 AMC 10A Problem 5
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 miles away,” Bob replied, “We are at most miles away.” Charlie then remarked, “Actually the nearest town is at most miles away.” It turned out that none of the three statements was true. Let be the distance in miles to the nearest town. Which of the following intervals is the set of all possible values of
Answer choices
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Solution
Alice’s statement tells us that Bob’s statement tells us that Charlie’s statement tells us that
Combining all of these tells us that and which means is in the interval
Thus, D is the correct answer.
Tagged: logical deduction · inequality