In the context of the Gregorian leap year rule, which of the following given years has exactly 366 days and therefore qualifies as a leap year?

Introduction / Context:
This calendar question focuses on identifying leap years, that is, years with 366 days. Leap year identification is crucial in many aptitude questions, because it affects the total number of days and therefore the day of the week for given dates. Understanding the century rules in the Gregorian calendar avoids common traps in exam questions.

Given Data / Assumptions:

• We are given four candidate years: 1900, 1200, 2500, and 1700.
• We need to decide which of these years has 366 days.
• The Gregorian leap year rule applies to these years.

Concept / Approach:
The Gregorian calendar defines a leap year as a year divisible by 4, except for century years. For century years, there is an additional condition: the year must be divisible by 400 to be a leap year. If a century year is divisible by 100 but not by 400, it remains an ordinary year of 365 days. Applying this rule carefully to each option allows us to determine which year actually has 366 days.

Step-by-Step Solution:
Step 1: Check 1900. It is divisible by 100 but 1900 / 400 = 4 remainder 300, so it is not divisible by 400. Step 2: Therefore 1900 is not a leap year and has 365 days. Step 3: Check 1200. It is divisible by 100, and 1200 / 400 = 3 exactly, so it is divisible by 400. Step 4: A century year divisible by 400 is a leap year, so 1200 has 366 days. Step 5: Check 2500. It is divisible by 100 but 2500 / 400 leaves a remainder, so it is not divisible by 400. Hence it is not a leap year. Step 6: Check 1700. It is divisible by 100 but 1700 / 400 also leaves a remainder, so it is not divisible by 400, and therefore not a leap year.

Verification / Alternative check:
We can verify the rule by recalling well known leap years such as 2000 and 1600 which are divisible by 400. Both are recognised as leap years. In contrast, years like 1900 and 2100 are commonly cited examples of century years that are not leap years because they do not satisfy the divisibility by 400 condition. When we apply the same logic to 1200, it clearly behaves like 1600 or 2000 and thus is a genuine leap year with 366 days.

Why Other Options Are Wrong:
1900 is a century year that is divisible by 4 and 100 but not by 400, so it has only 365 days. The same reasoning applies to 2500 and 1700, which are also divisible by 100 but not by 400. Since none of these meet the divisibility by 400 test, they remain ordinary years with 365 days each. Only 1200 passes the 400 divisibility test and so qualifies as a leap year with 366 days.

Common Pitfalls:
Many learners incorrectly assume that every year divisible by 4 is a leap year, forgetting the special rule for century years. This leads to mistakes in questions involving years like 1900 and 2100. Another common error is mixing up the direction of the rule and thinking that divisibility by 400 is optional. In reality, for century years the divisibility by 400 requirement is essential. Always separate the cases into general years and century years, and then apply the appropriate conditions.

Final Answer:
Therefore, among the given options, the only year with 366 days is 1200.