1979 AMC 12 Problem 5
Attempt Problem 5 of the 1979 AMC 12 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 1979 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
5.
Find the sum of the digits of the largest even three digit number (in base ten representation) which is not changed when its units and hundreds digits are interchanged.
Answer: D
Small hint:
The hundreds and units digits must be equal
Big hint:
Maximize the equal outer digits subject to the number being even, then maximize the tens digit
Solution:
The equal hundreds and units digit must be even. The largest possible nonzero such digit is and the tens digit can be Thus the largest number is whose digit sum is
Therefore, the correct answer is D.
Problem 5 in other years
- 1950 AMC 12
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