1990 AMC 8 Problem 3
Attempt Problem 3 of the 1990 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 1990 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
3.
What fraction of the square is shaded?
Small hint:
Reflect the figure across the main diagonal that runs corner to corner
Big hint:
Each shaded piece on one side of the diagonal matches an unshaded piece of equal area on the other side
Solution:
The diagonal from one corner to the opposite corner splits the square into two equal halves. Every shaded piece on one side of the diagonal is the mirror image of an equal unshaded piece on the other side.
So the shaded and unshaded areas are equal, and exactly of the square is shaded.
Thus, the correct answer is E .
Problem 3 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 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
- 2001 AMC 8
- 2002 AMC 8
- 2003 AMC 8
- 2004 AMC 8
- 2005 AMC 8
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- 2007 AMC 8
- 2008 AMC 8
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