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Leap Year Identification

Introduction

Knowing how to identify leap years is fundamental for calendar calculations and many date-based aptitude problems. Leap years affect February’s length (29 days) and change odd-day counts when calculating weekdays across years.

Pattern: Leap Year Identification

Pattern

The rule: A year is a leap year if it is divisible by 4; if it is a century year (divisible by 100) it must also be divisible by 400 to be a leap year.

Step-by-Step Example

Question

Is the year 1900 a leap year? What about 2000?

Solution

  1. Step 1: Check divisibility by 4

    1900 ÷ 4 = 475 → divisible by 4. 2000 ÷ 4 = 500 → divisible by 4. So both pass the first test.

  2. Step 2: If century year, check divisibility by 100

    1900 is divisible by 100 (1900 ÷ 100 = 19). 2000 is divisible by 100 (2000 ÷ 100 = 20). Since both are century years, proceed to the next check.

  3. Step 3: For century years, check divisibility by 400

    1900 ÷ 400 = 4.75 → not divisible by 400. 2000 ÷ 400 = 5 → divisible by 400.

  4. Final Answer:

    1900 → Not a leap year; 2000 → Leap year

  5. Quick Check:

    1900 fails the century rule (not divisible by 400) → not leap. 2000 passes all tests → leap ✅

Quick Variations

1. Non-century years: Only divisibility by 4 matters (e.g., 2016, 2020 are leap years).

2. Century exceptions: 1800 and 1900 are not leap years; 1600 and 2000 are leap years.

3. Use the rule to quickly decide Feb length (28 or 29 days) for any given year.

Trick to Always Use

  • Step 1 → If year % 400 == 0 → Leap year.
  • Step 2 → Else if year % 100 == 0 → Not a leap year.
  • Step 3 → Else if year % 4 == 0 → Leap year; otherwise not.

Summary

Summary

  • Check divisibility by 4 first for ordinary years.
  • If the year is a century (÷100), it must also be divisible by 400 to be leap.
  • Century years like 1900 are NOT leap years; 2000 is a leap year.
  • Use this rule to decide whether February has 28 or 29 days and to adjust odd-day counts in calendar problems.

Example to remember:
1900 → divisible by 100 but not by 400 → Not leap. 2000 → divisible by 400 → Leap year (Feb has 29 days).

Practice

(1/5)
1. Which of the following years is a leap year?
easy
A. 1900
B. 2000
C. 1800
D. 2100

Solution

  1. Step 1: Apply leap year rule

    A year divisible by 400 is always a leap year.

  2. Step 2: Check divisibility

    2000 ÷ 400 = 5 → divisible → leap year. Others (1900, 1800, 2100) ÷ 400 not divisible → not leap years.

  3. Final Answer:

    2000 → Option B

  4. Quick Check:

    2000 divisible by 400 → leap year ✅
Hint: Century year → leap only if divisible by 400.
Common Mistakes: Assuming all years divisible by 100 are leap years.
2. Which of the following is NOT a leap year?
easy
A. 1996
B. 2004
C. 2100
D. 2400

Solution

  1. Step 1: Apply rule for century years

    Century years must be divisible by 400 to be leap.

  2. Step 2: Test each year

    2100 ÷ 400 = 5.25 → not divisible → not leap. 1996 and 2004 ÷ 4 → leap years. 2400 ÷ 400 → leap.

  3. Final Answer:

    2100 → Option C

  4. Quick Check:

    2100 divisible by 100 but not 400 → not leap ✅
Hint: Century year → check 400; others → check 4.
Common Mistakes: Assuming 2100 is leap because it’s divisible by 4.
3. How many leap years are there between 2001 and 2100?
medium
A. 24
B. 25
C. 26
D. 27

Solution

  1. Step 1: Count total years

    2001-2100 → 100 years.

  2. Step 2: Find leap years

    Every 4th year → 100 ÷ 4 = 25. But 2100 not leap (divisible by 100 but not 400). So, 25 - 1 = 24.

  3. Final Answer:

    24 → Option A

  4. Quick Check:

    25 expected minus 2100 = 24 ✅
Hint: Total leap years = (years ÷ 4) - century years not divisible by 400.
Common Mistakes: Including 2100 as a leap year.
4. Which year will have 29 days in February?
medium
A. 1900
B. 2016
C. 2100
D. 2200

Solution

  1. Step 1: Apply 4-divisibility rule

    2016 ÷ 4 = 504 → divisible → leap year.

  2. Step 2: Check century rule

    Not a century year → no 400 test required.

  3. Step 3: Verify others

    1900, 2100, 2200 are century years but not divisible by 400 → not leap.

  4. Final Answer:

    2016 → Option B

  5. Quick Check:

    2016 leap → Feb has 29 days ✅
Hint: If year not century, just check divisibility by 4.
Common Mistakes: Applying 400-rule unnecessarily to non-century years.
5. Which of these statements is TRUE?
medium
A. 2100 is a leap year
B. 2000 is not a leap year
C. 1900 is a leap year
D. 2400 is a leap year

Solution

  1. Step 1: Apply rule

    Century year → leap only if divisible by 400.

  2. Step 2: Check divisibility

    2400 ÷ 400 = 6 → leap. 1900 and 2100 ÷ 400 not exact → not leap. 2000 ÷ 400 exact → also leap (but not in options as true statement).

  3. Final Answer:

    2400 is a leap year → Option D

  4. Quick Check:

    2400 divisible by 400 → leap ✅
Hint: Only years divisible by 400 among centuries are leap years.
Common Mistakes: Assuming all centuries are leap years.

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