2012 AMC 8 Problem 16
Attempt Problem 16 of the 2012 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
16.
Each of the digits and is used only once to make two five-digit numbers so that they have the largest possible sum. Which of the following could be one of the numbers?
Answer: C
Small hint:
Put the largest digits in the largest place values.
Big hint:
The ten-thousands digits should be and , then continue in pairs.
Video solution:
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Written solution:
To construct two five-digit numbers, the digits in the largest place values must be as great as possible. Therefore, the leftmost digits must be the greatest two digits. This means the first digit must be either or the second digit must be either or the third digit must be either or the fourth digit must be either or and the last digit must be either or
The only one of the given numbers that satisfy this is
Thus, the answer is C .
Problem 16 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
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- 1998 AMC 8
- 1999 AMC 8
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