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Latest revision as of 11:20, 25 October 2024
Contents
[hide]Problem
Positive integers , , and , with , form a geometric sequence with an integer ratio. What is ?
Solution
The prime factorization of is . As , the ratio must be positive and larger than , hence there is only one possibility: the ratio must be , and then , and .
We know that this is important because the complete equation would be and the only possible outcome for is -Edited slightly by RealityWrites - minor edits by BS2012
See Also
2009 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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 |
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