📅 Introduction to Day and Date Problems

What Are Day and Date Problems?

Day and date problems involve determining the day of the week for a given date, calculating intervals between dates, and understanding calendar patterns. These questions are essential for:

  • Competitive Exams: SAT, GMAT, GRE, Bank PO, SSC, UPSC
  • Logical Reasoning: Calendar-based puzzles and reasoning
  • Real-life Applications: Event planning, scheduling, historical date calculations

Learning Objectives

  • Master the Odd Days Concept for quick calculations
  • Understand Leap Year Rules and century exceptions
  • Learn to calculate day of any given date efficiently
  • Solve 30 MCQs with detailed solutions
  • Develop time-saving techniques for competitive exams

🔑 Key Concepts

Odd Days Concept

Odd Days are the extra days beyond complete weeks in a given period. This is the fundamental concept for solving calendar problems.

📐 Calculation Method:

1. Divide total number of days by 7

2. The remainder represents the odd days

Example: 30 days = 4 weeks + 2 days → 2 odd days

Types of Years

📊 Ordinary Year (365 days)

  • Years not divisible by 4
  • Has 1 odd day (365 ÷ 7 = 52 weeks + 1 day)
  • Examples: 2001, 2002, 2003, 2005, 2100

🚀 Leap Year (366 days)

  • Years divisible by 4 (except centuries)
  • Centuries divisible by 400 are leap years
  • Has 2 odd days (366 ÷ 7 = 52 weeks + 2 days)
  • Examples: 2004, 2008, 2012, 2000, 2400

📐 Important Formulas

Odd Days Calculation Table

📊 Standard Values:

  • 1 Ordinary Year = 1 odd day
  • 1 Leap Year = 2 odd days
  • 100 Years = 5 odd days
  • 200 Years = 3 odd days
  • 300 Years = 1 odd day
  • 400 Years = 0 odd days

🧮 Month-wise Odd Days:

  • January, March, May, July, August, October, December = 3 odd days
  • April, June, September, November = 2 odd days
  • February (Ordinary Year) = 0 odd days
  • February (Leap Year) = 1 odd day

Quick Calculation Rules

Day Codes

Sunday = 0, Monday = 1, Tuesday = 2, Wednesday = 3, Thursday = 4, Friday = 5, Saturday = 6

Century Codes

1600s-2000s = 6, 1700s-2100s = 4, 1800s-2200s = 2, 1900s-2300s = 0

📝 Solved Examples

Example 1: Basic Day Calculation

Problem:

If today is Monday, what day will it be after 61 days?

Solution:

Each day of the week repeats after 7 days.

61 ÷ 7 = 8 weeks + 5 days

Monday + 5 days = Saturday

Answer: Saturday

Example 2: Leap Year Calculation

Problem:

January 1, 2008 was Tuesday. What day was January 1, 2009?

Solution:

2008 is a leap year → 2 odd days

Tuesday + 2 days = Thursday

Answer: Thursday