According to the leap-year rules of the Gregorian calendar, which of the following years has 366 days?

Introduction / Context:
Leap-year questions test your understanding of the rules that determine which years have 366 days (a leap year) rather than the usual 365 days. In the Gregorian calendar, the leap-year rule for centuries is slightly different from the simple “divisible by 4” rule used for non-century years.

Given Data / Assumptions:

We are given the years: 1900, 1200, 2500, and 1700.
We must determine which of these has 366 days (i.e., is a leap year).
Gregorian leap-year rules:
- Every year divisible by 4 is a leap year,
- But if the year is divisible by 100, it is not a leap year,
- Unless it is also divisible by 400, in which case it is a leap year.

Concept / Approach:
We apply the leap-year rule step by step to each option. Since all given years are century years (ending in 00), we pay special attention to the “divisible by 400” condition. Only century years divisible by 400 are leap years with 366 days.

Step-by-Step Solution:
Step 1: Examine 1900. 1900 is divisible by 100, but 1900 / 400 = 4.75, not an integer. Therefore, 1900 is not divisible by 400 and is not a leap year. Step 2: Examine 1200. 1200 is divisible by 100, and 1200 / 400 = 3, an integer. So 1200 is divisible by 400 and is a leap year with 366 days. Step 3: Examine 2500. 2500 is divisible by 100, but 2500 / 400 = 6.25, not an integer. Therefore, 2500 is not a leap year. Step 4: Examine 1700. 1700 is divisible by 100, but 1700 / 400 = 4.25, not an integer. Therefore, 1700 is not a leap year.

Verification / Alternative check:
You can summarise the rule: a century year is a leap year only if it is divisible by 400. Testing each option quickly with this rule immediately identifies 1200 as the only year satisfying that condition. All others fail the divisibility-by-400 test and hence must have only 365 days.

Why Other Options Are Wrong:
1900, 2500, and 1700 are all divisible by 100 but not by 400, so they do not qualify as leap years under the Gregorian rules. Treating them as leap years would incorrectly assign them 366 days, which contradicts the well-established calendar system.

Common Pitfalls:
Many learners remember only the “divisible by 4” rule and forget the additional conditions for century years. This leads to incorrectly marking years like 1900 as leap years. Always remember the full rule: years divisible by 100 require an extra check for divisibility by 400 before being called leap years.

Final Answer:
Among the given options, the year that has 366 days is 1200.