According to the Gregorian leap year rules, which of the following years is a leap year?

Introduction / Context:
Leap year questions are very common in aptitude and calendar topics. They test your understanding of the exact rule used in the Gregorian calendar rather than a simplistic idea like every fourth year being a leap year. Century years are especially important because they follow an additional condition beyond divisibility by 4.

Given Data / Assumptions:

• Candidate years: 2500, 1700, 1900, and 2400.
• All of these are century years because they end with two zeros.
• We use the standard Gregorian calendar rule.
• We must identify which one is a leap year.

Concept / Approach:
In the Gregorian calendar, the leap year rule is as follows. A year is a leap year if it is divisible by 4. However, if the year is a century year (ending with 00), it must also be divisible by 400 to be a leap year. Thus, years like 1700, 1800, 1900, and 2100 are not leap years, while years like 1600, 2000, and 2400 are leap years.

Step-by-Step Solution:
Step 1: Recognise that each given year ends in 00, so each is a century year. Step 2: Apply the century year rule: a century year is a leap year only if it is divisible by 400. Step 3: Check 2500. Although it is divisible by 100, 2500 / 400 = 6.25, which is not an integer, so it is not divisible by 400. Hence 2500 is not a leap year. Step 4: Check 1700. Here 1700 / 400 = 4.25, not an integer, so 1700 is not divisible by 400 and not a leap year. Step 5: Check 1900. 1900 / 400 = 4.75, again not an integer, so 1900 is not a leap year under the Gregorian rule. Step 6: Check 2400. 2400 / 400 = 6, an integer, so 2400 is divisible by 400 and therefore is a leap year.

Verification / Alternative check:
You can recall known examples: the year 2000 was a leap year because it is divisible by 400, while 1900 was not. The same pattern applies to other century years. Once you remember that only multiples of 400 among the century years are leap years, it becomes easy to pick 2400 as the correct option without detailed division each time.

Why Other Options Are Wrong:
2500: Not divisible by 400, so fails the century leap year rule.

1700: Also not divisible by 400 and therefore not a leap year.

1900: Though divisible by 100 and by 4, it is not divisible by 400, so it is treated as a normal year with 365 days.

Common Pitfalls:
A common mistake is to apply only the divisibility by 4 rule to all years, leading students to think that 1900 and 2100 are leap years. Another pitfall is forgetting the extra condition specifically for century years. Always remember the full rule: divisible by 4 and not a century year, or divisible by 400 if it is a century year.

Final Answer:
Therefore, among the given options, the leap year is 2400.