1989 AMC 8 Problem 20
Attempt Problem 20 of the 1989 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 1989 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
20.
The figure shown may be folded along the lines to form a number cube. Three faces come together at each corner of the cube. What is the largest sum of three numbers whose faces come together at a corner?
Answer: D
Small hint:
A corner uses three faces that are mutually adjacent, so no two of them can be opposite faces
Big hint:
Folding the net, the opposite face pairs are & & and & take the larger of each pair
Solution:
When the net is folded, the pairs of opposite faces are and and and and Three faces meeting at a corner must come one from each opposite pair.
To maximize the sum, take the larger number from each pair: and These three faces do meet at a corner, and their sum is
Thus, the correct answer is D .
Problem 20 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
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