Question

A year is a leap year if and only if the year number is divisible by $400$ (such as $2000$ ) or is divisible by $4$ but not by $100$ (such as $2012$ ). The $200$ th anniversary of the birth of novelist Charles Dickens was celebrated on February $7,$ $2012,$ a Tuesday. On what day of the week was Dickens born?

Friday

Saturday

Sunday

Monday

Tuesday

Answer: A

Concepts:modular arithmetic date and time

Difficulty rating: 1540

Solution:

From February $7,$ $1812$ to February $7,$ $2012$ there are $200 \cdot 365 = 73000$ ordinary days plus one for each leap day.

One quarter of the $200$ years contain a leap day, except $1900,$ giving $\tfrac14 \cdot 200 - 1 = 49$ leap days. So the span is $73049$ days.

Since $73049 = 7 \cdot 10435 + 4,$ the birth day was $4$ days before a Tuesday, which is a Friday.

Thus, the correct answer is A.

2012 AMC 12A Problem 9

Answer: A

Difficulty rating: 1540

Solution:

Problem 9 in Other Years