2005 AMC 12A Problem 19
Attempt Problem 19 of the 2005 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2005 AMC 12A solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
A faulty car odometer proceeds from digit to digit always skipping the digit regardless of position. For example, after traveling one mile the odometer changed from to If the odometer now reads how many miles has the car actually traveled?
Answer: B
Small hint:
The odometer only ever shows distinct digits, so it is really counting in base
Big hint:
Map each shown digit to its base- value: stand for
Solution:
Because the odometer never displays a it uses only symbols and counts in base where its digits represent the base- digits
The reading therefore corresponds to in base which equals
Thus, the correct answer is B.
Problem 19 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
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