2012 AMC 12B Problems/Problem 11
Problem
In the equation below, and are consecutive positive integers, and , , and represent number bases: What is ?
Solution 1
Change the equation to base 10:
Either or , so either or . The second case has no integer roots, and the first can be re-expressed as . Since A must be positive, and
Solution 2 (Answer Choices)
We can eliminate answer choice because you can't have a in base . Now we know that A and B are consecutive, so we can just test answers. You will only have to test at most cases. Eventually, after testing a few cases, you will find that and . The solution is .
~kempwood
See Also
2012 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 10 |
Followed by Problem 12 |
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 |
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