Calendar-Based Questions: Concepts & Solved Examples

Introduction

Calendar-based questions test a candidate’s ability to determine the day of the week for a given date. These questions require familiarity with the Gregorian calendar, leap years, and the concept of odd days.

Understanding Leap Years & Odd Days

• Leap Year: A year with 366 days (divisible by 4). Century years are leap years only if divisible by 400.
• Non-Leap Year: A year with 365 days.
• Odd Days: The number of extra days beyond complete weeks in a given period.

Counting Odd Days

To find odd days in a given period, divide the number of days by 7. The remainder represents the odd days.

Example:

• 1 Non-leap year = 365 days
  • Odd days = 365 % 7 = 1 day
• 1 Leap year = 366 days
  • Odd days = 366 % 7 = 2 days

Odd Days in a Century

Alternative Approach: Date Matching Trick

The last day of February is the same as:

• 4/4, 6/6, 8/8, 10/10, 12/12 (Easily remembered as pairs)
• 5/9, 9/5, 7/11, 11/7

This can help determine the day of the week for any given date.

Solved Examples

Example 1: Finding the Day of the Week

Q: If Jan 1, 2006, was a Sunday, what was the day on Jan 1, 2010?

Solution:

• Odd days from 2006 to 2009 = (1 + 1 + 2 + 1) = 5 days
• Dec 31, 2009, was a Thursday
• Jan 1, 2010, was Friday

Example 2: Finding the Day of a Past Date

Q: What was the day on 28th May 2006?

Solution:

• Odd days from 1600 years = 0
• Odd days from 400 years = 0
• Odd days in 5 years (2001-2005) = 6
• Odd days in 2006 (Jan-May) = 1
• Total odd days = 7 (0 odd days)
• Given day: Sunday

Example 3: Future Date Calculation

Q: What will be the day on 15th August 2010?

Solution:

• Odd days in 1600 years = 0
• Odd days in 400 years = 0
• Odd days in 9 years (2001-2009) = 4
• Odd days in 2010 (Jan-Aug) = 3
• Total odd days = 7 (0 odd days)
• Given day: Sunday

Example 4: Finding the Day After ‘n’ Days

Q: Today is Monday. After 61 days, what will be the day?

Solution:

• Since the week repeats every 7 days, we find:
  • 61 % 7 = 5 (odd days)
  • Monday + 5 days = Saturday

Example 5: Finding the Previous Year’s Same Date

Q: If 6th March 2005 was a Monday, what was the day on 6th March 2004?

Solution:

• 2004 was a leap year, so it had 2 odd days
• Since we exclude Feb 2004, we consider only 1 odd day
• 6th March 2004 = Sunday

Example 6: Finding All Wednesdays in a Given Month

Q: On what dates did Wednesday fall in April 2001?

Solution:

• 1st April 2001 was Sunday
• Wednesdays in April: 4th, 11th, 18th, 25th

Example 7: Finding the Last Day of a Century

Q: The last day of a century cannot be which of the following?

Solution:

• 100 years = 5 odd days → Friday
• 200 years = 3 odd days → Wednesday
• 300 years = 1 odd day → Monday
• 400 years = 0 odd days → Sunday
• The last day of a century cannot be Tuesday, Thursday, or Saturday.

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Conclusion

Understanding leap years, odd days, and date-based tricks can significantly enhance your ability to solve calendar-based questions efficiently. Practice with different date ranges to master these concepts!