According to the rules of the Gregorian calendar for leap years, which one of the following years is actually a leap year?

Introduction / Context:
Leap year questions test your understanding of the exact rules used in the Gregorian calendar, not just the simple “divisible by 4” rule. This question asks you to identify which one among several century years is a true leap year, which requires careful attention to the additional conditions for century years.

Given Data / Assumptions:

• We are using the Gregorian calendar rules.
• The years given are 2500, 1700, 1900, 2400 and 1800.
• We must decide which of these is a leap year.

Concept / Approach:
The leap year rules in the Gregorian calendar are:

• If a year is not a century year (not ending in 00), it is a leap year if it is divisible by 4.
• If a year is a century year (like 1700, 1800, 1900, 2000, 2400, 2500), then it is a leap year only if it is divisible by 400.

All years in the options end with 00, so they are century years. Thus, we only need to check divisibility by 400, not by 4 alone.

Step-by-Step Solution:
Step 1: Check 2500. Although 2500 is divisible by 4 and 100, 2500 / 400 = 6.25, not an integer. Hence 2500 is not divisible by 400 and is not a leap year. Step 2: Check 1700. 1700 / 400 = 4.25, which is not an integer, so 1700 is not a leap year. Step 3: Check 1900. 1900 / 400 = 4.75, not an integer, so 1900 is also not a leap year. Step 4: Check 2400. 2400 / 400 = 6 exactly, an integer, so 2400 is divisible by 400 and therefore is a leap year. Step 5: Check 1800 (extra distractor). 1800 / 400 = 4.5, not an integer, so 1800 is not a leap year.

Verification / Alternative check:
You can remember that 1600, 2000 and 2400 are classic examples of century leap years because they are evenly divisible by 400. In contrast, 1700, 1800, 1900, 2100, 2200, 2300, 2500 are not leap years. This memory trick helps confirm that among the given choices, only 2400 qualifies.

Why Other Options Are Wrong:
All of 2500, 1700, 1900 and 1800 are century years that fail the “divisible by 400” test. Even though they are divisible by 4 and 100, that is not enough for century years in the Gregorian system. Hence none of them can have a 29th February in their calendar.

Common Pitfalls:
Many learners incorrectly use only the “divisible by 4” rule, which works for non-century years but fails for century years. Others think that all years divisible by 100 and 4 are leap years, which is also wrong. Always remember the special condition: century years must be divisible by 400 to be leap years in the Gregorian calendar.

Final Answer:
Among the given options, the only leap year is 2400.