2012 AMC 12A Problem 9
Attempt Problem 9 of the 2012 AMC 12A 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 2012 AMC 12A solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
9.
A year is a leap year if and only if the year number is divisible by (such as ) or is divisible by but not by (such as ). The th anniversary of the birth of novelist Charles Dickens was celebrated on February a Tuesday. On what day of the week was Dickens born?
Friday
Saturday
Sunday
Monday
Tuesday
Answer: A
Small hint:
Count the total number of days between the two February th dates, working modulo
Big hint:
In years there are ordinary days plus one extra for each leap year; is not a leap year
Solution:
From February to February there are ordinary days plus one for each leap day.
One quarter of the years contain a leap day, except giving leap days. So the span is days.
Since the birth day was days before a Tuesday, which is a Friday.
Thus, the correct answer is A.
Problem 9 in other years
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