2001 AMC 8 Problem 24
Attempt Problem 24 of the 2001 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 2001 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
24.
Each half of this figure is composed of red triangles, blue triangles and white triangles. When the upper half is folded down over the centerline, pairs of red triangles coincide, as do pairs of blue triangles. There are red-white pairs. How many white pairs coincide?
Answer: B
Small hint:
Account for all red triangles first
Big hint:
Then track how the unmatched blue triangles must pair
Solution:
Each half has red, blue, and white triangles.
The red-red pairs use red triangles from each half, so the remaining red triangle from each half is used in the red-white pairs. Thus all red triangles are accounted for.
The blue-blue pairs use blue triangles from each half, leaving blue triangles from each half. Since no more blue-blue pairs occur, those blue triangles must pair with white triangles.
So on each half, white is used with red and whites are used with blue, leaving white triangles to pair with white triangles.
Thus, B is the correct answer.
Problem 24 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
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- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
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