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Quantitative Aptitude - Calendar

Learn to compute weekdays for any date using odd-day cycles, century codes, and leap-year rules.

1. Concepts & Definitions

  • Odd Day: Extra days beyond complete weeks (7-day cycles).
  • Century Cycle: 400 years = complete cycle → 0 odd days; 100 → 5; 200 → 3; 300 → 1 odd day.
  • Month Codes: Jan = 0, Feb = 3, Mar = 3, Apr = 6, May = 1, Jun = 4, Jul = 6, Aug = 2, Sep = 5, Oct = 0, Nov = 3, Dec = 5.
  • Leap Year: Year divisible by 4; if century, must be divisible by 400. For Jan/Feb of a leap year, subtract 1.

2. Step-by-Step Calculation

  1. Write date (D), month code (M), year (YY), century code (C): C for 2000s = 6, 1900s = 0, 1800s = 2, 1700s = 4.
  2. Compute Year Code = YY + floor(YY/4).
  3. Total = D + M + Year Code + C - (leap correction).
  4. Day Index = Total mod 7 → 0 = Sunday, 1 = Monday, … 6 = Saturday.

3. Worked Example

Date: 15 Aug 1947

  • D = 15, M = 2 (August), YY = 47, C = 0 (1900s)
  • Year Code = 47 + floor(47/4) = 58
  • 15 + 2 + 58 + 0 = 75; Not leap → no correction
  • 75 mod 7 = 5 → Friday

4. Exam Tips

  • Always adjust the month code for leap-year Jan/Feb only.
  • Memorize century cycle codes; missing century code causes ±1-2 day errors.
  • Practice across leap-year boundaries and centuries.

5. Pitfalls to Avoid

  • Forgetting leap adjustment when date falls in Jan/Feb of a leap year.
  • Using wrong century code-e.g., treating 1900 as leap year erroneously.

6. Quick Revision Checklist

  • Memorize month and century codes.
  • Practice with ~25 dates (contemporary, past, and future).

Summary: Date → sum codes → mod 7 → map to weekday. Ensure correct leap-year handling for Jan/Feb.

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