1994 AMC 8 Problem 23
Attempt Problem 23 of the 1994 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 1994 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
23.
If and are different digits, then the largest possible -digit sum for
has the form
Answer: D
Small hint:
Write the addition in columns; if is too large the hundreds place carries and the answer gains a fourth digit.
Big hint:
Take the largest that keeps the sum to three digits, then choose to make the total as large as possible and see which letters the resulting digits match.
Solution:
The hundreds digit of the sum comes from plus any carry, so if the sum would spill over into four digits. The largest allowed value is
To make the sum as large as possible, take then Its digits are since and is a new digit the sum has the form
Thus, the correct answer is D .
Problem 23 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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