In calendar calculations, how many leap years are there in a continuous period of 300 years, using the standard rule that years divisible by 100 are not leap years unless they are also divisible by 400?

Introduction:
Questions about the number of leap years in a given span of years are very common in calendar aptitude problems. Here we are asked to find how many leap years occur in 300 consecutive years, using the usual Gregorian rule for leap years. Understanding this rule clearly is essential for solving many calendar-based questions quickly and correctly.

Given Data / Assumptions:
Total span of years considered = 300 years. Leap year rule: A year is a leap year if it is divisible by 4. Exception 1: Years divisible by 100 are not leap years. Exception 2: Years divisible by 400 are leap years again. We assume a block of 300 years starting from year 1 to year 300, which is the standard convention in aptitude questions.

Concept / Approach:
To count leap years correctly, we use the inclusion–exclusion style method. First, we count all years divisible by 4 in 300 years. Then we subtract the century years (divisible by 100) that are not leap years. Finally, we add back those century years that are divisible by 400, because they are leap years again. This avoids double counting and ensures accuracy.

Step-by-Step Solution:
Step 1: Count all years divisible by 4. Number of multiples of 4 in 300 years = 300 / 4 = 75. Step 2: Subtract years divisible by 100 (century years). Number of multiples of 100 in 300 years = 300 / 100 = 3 (i.e., 100, 200, 300). These are not leap years unless they are also divisible by 400. Step 3: Add back years divisible by 400. Multiples of 400 up to 300: 300 / 400 = 0 (no such year). So we do not add anything back. Step 4: Final count of leap years. Leap years = 75 − 3 + 0 = 72.

Verification / Alternative check:
Another way is to observe that in any 400-year cycle there are 97 leap years. Here we have only 300 years, from 1 to 300, which excludes any year divisible by 400. Therefore, all centuries (100, 200, 300) are non-leap, and our subtraction of exactly 3 such years from the 75 multiples of 4 is correct, giving 72 leap years.

Why Other Options Are Wrong:
75: This assumes every 4th year is leap and ignores the century rule. 73 or 74: These do not match the precise count obtained from the divisibility rules. 71: This undercounts by removing too many years as non-leap.

Common Pitfalls:
Many learners forget that not every year divisible by 4 is automatically a leap year. Missing the special rule for century years leads to the incorrect answer of 75. Some also mistakenly try to use averages from 400-year patterns without adjusting correctly for a 300-year span.

Final Answer:
The number of leap years in 300 consecutive years is 72.