Which one of the following century years is a leap year according to the Gregorian calendar?

Introduction / Context:
This question focuses on a very important special case of the leap-year rule: century years. Many people know the basic “divisible by 4” rule, but century years (ending in 00) follow an additional condition in the Gregorian calendar. Exam questions frequently test this knowledge.

Given Data / Assumptions:

• We are given century years: 1900, 1700, 1600, 1100, and 1500.
• We must decide which one is a leap year.
• The Gregorian leap-year rule is:
  • If a year is not a century year, it is a leap year if divisible by 4.
  • If a year is a century year, it is a leap year only if divisible by 400.

Concept / Approach:
All the given years end with 00, so all are century years. Therefore, we apply the stricter rule:

• A century year is leap if and only if it is divisible by 400.
• If it is not divisible by 400, it is an ordinary year with 365 days.

We simply check the divisibility of each year by 400.

Step-by-Step Solution:
Step 1: Test 1900 for divisibility by 400. 1900 / 400 = 4.75, not an integer. So 1900 is not a leap year. Step 2: Test 1700. 1700 / 400 = 4.25, not an integer. Therefore, 1700 is not a leap year. Step 3: Test 1600. 1600 / 400 = 4 exactly, an integer. Hence, 1600 is a leap year. Step 4: Test 1100. 1100 / 400 = 2.75, not an integer, so it is not a leap year. Step 5: Test 1500. 1500 / 400 = 3.75, again not an integer, so 1500 is not a leap year. Step 6: Therefore, among the given options, only 1600 satisfies the condition of being a century year divisible by 400.

Verification / Alternative check:
Consulting historical notes and standard legal definitions of the Gregorian calendar confirms that the years 1600 and 2000 are classic examples of leap century years. In contrast, 1700, 1800, and 1900 are explicitly listed as non-leap century years. This corroborates our simple divisibility test.

Why Other Options Are Wrong:
1900: Despite being divisible by 4, it is a century year and not divisible by 400, so it is not a leap year.

1700: Fails the divisibility-by-400 test and is therefore not a leap year.

1100: Another century year not divisible by 400, so it is an ordinary year.

1500: Not divisible by 400 and so does not qualify as a leap year.

Common Pitfalls:
Many students incorrectly apply only the “divisible by 4” rule and conclude that 1900 or similar years are leap years. This is incorrect for century years. Always remember the special condition: a century year must be divisible by 400 to be a leap year. Forgetting this leads to wrong answers in many calendar problems.

Final Answer:
The only century year given that is a leap year is 1600.