2002 AMC 12B Problem 8
Attempt Problem 8 of the 2002 AMC 12B 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 2002 AMC 12B solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
8.
Suppose July of year has five Mondays. Which of the following must occur five times in August of year (Note: Both months have days.)
Monday
Tuesday
Wednesday
Thursday
Friday
Answer: D
Small hint:
With days, the weekday of July is the one that repeats five times, so Monday is July or
Big hint:
August falls three weekdays after July ; test the three cases and find the August weekday common to all
Solution:
Since July has days, the weekday of July occurs five times, so Monday falls on July or The days that occur five times in August are those of August and August is three weekdays after July
Testing the three cases, the August weekdays occurring five times are Thursday through Saturday, Wednesday through Friday, and Tuesday through Thursday. Thursday appears in every case.
Thus, the correct answer is D.
Problem 8 in other years
- 1950 AMC 12
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