According to the leap year rules of the Gregorian calendar, how many leap years are there in any period of 100 consecutive years?

Introduction / Context:
This conceptual question checks your understanding of how often leap years occur in the Gregorian calendar. You are asked to determine how many leap years appear in a block of 100 consecutive years. This is a standard fact often used in more complex calendar problems and in estimating long term date shifts.

Given Data / Assumptions:
- We are using the Gregorian calendar system.
- Leap year rule: a year is a leap year if it is divisible by 4, except that a year divisible by 100 is not a leap year unless it is also divisible by 400.
- We consider any block of 100 consecutive years that spans one complete century (for example, 1901 to 2000 or 2001 to 2100).

Concept / Approach:
Within 100 years, the naive expectation might be that every fourth year is a leap year, giving 25 leap years. However, the century rule removes one of these leap years unless the century year is divisible by 400. In a typical 100 year span that includes a non leap century year, one of the years divisible by 4 is disqualified, leaving 24 leap years.

Step-by-Step Solution:
Step 1: In 100 consecutive years, the years divisible by 4 occur approximately every 4 years.Step 2: If you divide 100 by 4, you get 25, so there are 25 years divisible by 4.Step 3: Among these 25 years, some may be century years (ending in 00), which require the additional test of divisibility by 400.Step 4: In a typical block such as 1901 to 2000, the year 1900 is a century year divisible by 100 but not by 400, so it is not a leap year.Step 5: Therefore, out of the 25 candidates divisible by 4, one century year fails the leap year test.Step 6: This leaves 25 - 1 = 24 actual leap years in that 100 year span.

Verification / Alternative check:
Take a concrete example like 1801 to 1900. The years divisible by 4 are 1804, 1808, ... up to 1900. Counting them gives 25 candidates. However, 1900 is divisible by 100 but not by 400, so it is not a leap year. This again leaves 24 leap years. The same pattern applies to 1701 to 1800, 1901 to 2000 and so on, except for special cases centered on years divisible by 400 where the century rule behaves slightly differently but still yields 24 leap years in most standard 100 year blocks used in aptitude questions.

Why Other Options Are Wrong:
The answer 25 would be correct only if every year divisible by 4 were a leap year, which ignores the century exception. Answers like 4, 23 or 26 do not match the arithmetic count of years divisible by 4 and the correction for one disqualified century year, so they cannot be correct in a standard 100 year interval.

Common Pitfalls:
Many learners remember only the simple rule that a leap year occurs every 4 years and forget about the 100 and 400 year rules. Others misapply the rule and remove too many or too few century years. Always recall the full rule and test it on an explicit 100 year interval to see clearly that there are 24 leap years.

Final Answer:
There are 24 leap years in a period of 100 consecutive years in the Gregorian calendar.