1985 AMC 8 Problem 20
Below is the professionally curated solution for Problem 20 of the 1985 AMC 8, 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.
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Difficulty rating: 1090
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
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
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