📅 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