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Difficulty: EasyClocks and Calendars

In the Gregorian calendar, a standard year has 365365 days, whereas a leap year has 366366 days. Based on the rules for determining leap years, which of the following years had exactly 366366 days?

  1. A
    17001700
  2. B
    18001800
  3. C
    19001900
  4. 20002000Answer

Answer

The year 20002000 had exactly 366366 days because it is a century year perfectly divisible by 400400.
The correct answer is 20002000. All the given options are century years (ending in 0000). According to the Gregorian calendar, a century year is a leap year with 366366 days only if it is exactly divisible by 400400. Since 2000÷400=52000 \div 400 = 5, it is a leap year.

Step-by-Step Solution

1
Recall the criteria for determining a leap year in the Gregorian calendar.
A general year is a leap year if it is divisible by 44. However, century years (ending in 0000) must be divisible by 400400 to be considered leap years.
This special rule for centuries corrects the slight overestimation of the solar year caused by adding a leap day every 44 years.
2
Evaluate each given option using the century year rule.
Since 17001700, 18001800, 19001900, and 20002000 all end in 0000, divide each by 400400. Only 20002000 is perfectly divisible by 400400 (2000÷400=52000 \div 400 = 5).
Applying the correct divisibility rule isolated the only year that contains an extra day in February.

Key Concept

Identifying leap years across century boundaries.
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Topics

Clocks and Calendars

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