1985 AMC 8 Problem 7
Attempt Problem 7 of the 1985 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 1985 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
7.
A “stair-step” figure is made up of alternating shaded and unshaded squares in each row. Rows through are shown. All rows begin and end with an unshaded square. The number of shaded squares in the th row is
Answer: C
Small hint:
Row has squares, and they alternate starting and ending with an unshaded square
Big hint:
Since the ends are unshaded and the squares alternate, there is one more unshaded square than shaded square in each row
Solution:
Row contains squares. Because both ends are unshaded and the squares alternate, each row has one more unshaded square than shaded square, so the number of shaded squares is
For the th row, this is
Thus, the correct answer is C .
Problem 7 in other years
- 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
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