1985 AMC 8 Problem 20
Attempt Problem 20 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).
20.
In a certain year, January had exactly four Tuesdays and four Saturdays. On what day did January fall that year?
Monday
Tuesday
Wednesday
Friday
Saturday
Answer: C
Small hint:
January has days, which is full weeks plus extra days
Big hint:
The three weekdays that occur five times are the days of January and Tuesday and Saturday must not be among them
Solution:
Since the weekdays falling on January and each occur five times that month, and every other weekday occurs four times.
For Tuesday and Saturday to occur only four times, neither may be January or The only starting day that works is Wednesday: then Wednesday, Thursday, and Friday occur five times, while Tuesday and Saturday each occur four times.
Thus, the correct answer is C .
Problem 20 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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