2003 AMC 8 Problem 12
Attempt Problem 12 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).
12.
When a fair six-sided die is tossed on a table top, the bottom face cannot be seen. What is the probability that the product of the numbers on the five faces that can be seen is divisible by
Answer: E
Small hint:
Check the only case where the face numbered is hidden.
Big hint:
If is hidden, the visible faces still include and
Solution:
If the face numbered is visible, then the visible product is divisible by
If the face numbered is on the bottom, then the visible faces include both and so their product is still divisible by
Every possible toss works, so the probability is
Thus, E is the correct answer.
Problem 12 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
- 1990 AMC 8
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