2003 AMC 8 Problem 14
Attempt Problem 14 of the 2003 AMC 8 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 2003 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
14.
In this addition problem, each letter stands for a different digit. If and the letter represents an even number, what is the only possible value for
Answer: D
Small hint:
Use the hundreds column after
Big hint:
The ones column and the fact that is even force
Solution:
Since both ’s are we get that is either or Since is even, we get that
Then, we get that We also know that doesn’t carry over, since otherwise would be
Therefore, is less than and cannot be or If then which gives two letters the same digit. If then which is also not allowed.
This makes
Thus, D is the correct answer.
Problem 14 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
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
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