2018 AMC 12B Problems/Problem 17
Problem
Let and be positive integers such that and isi as small as possible. What is ?
Solution
We claim that, between any two fractions and , if , the fraction with smallest denominator between them is . To prove this, we see that
which reduces to . We can easily find that , giving an answer of . (pieater314159)
See Also
2018 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 16 |
Followed by Problem 18 |
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All AMC 12 Problems and Solutions |
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