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Odd Days Classic

Classic Odd Days problems ask for the number of 'odd days' between two dates. An odd day is the remainder when total days are divided by 7. This concept is fundamental to calendar reasoning, especially for finding weekdays without reference dates.

10Worksheets
200+Practice Questions
IntermediateDifficulty
2-3 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Odd Days Classic

Classic Odd Days problems ask for the number of 'odd days' between two dates. An odd day is the remainder when total days are divided by 7. This concept is fundamental to calendar reasoning, especially for finding weekdays without reference dates.

Prerequisites

Leap year identification Month lengths Date difference calculation Modulo 7 arithmetic
Why This Matters: Odd Days problems are core to calendar reasoning. You can expect 2-3 questions in SSC CGL and Banking exams.

How to Solve Odd Days Classic Problems

1

Step 1: Count the number of years between the two dates

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Step 2: Count the number of leap years in between

3

Step 3: Total days = (years × 365) + leap_years + remaining_days

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Step 4: Odd days = total days mod 7

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Step 5: For periods within a year, sum odd days month by month

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Step 6: For reference: 365 days = 52 weeks + 1 odd day

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Step 7: For leap year: 366 days = 52 weeks + 2 odd days

Pro Strategy: Each common year contributes 1 odd day. Each leap year contributes 2 odd days. Sum the odd days from all years and any extra days within the partial year.

Example Problem

Example: How many odd days are there from January 1, 2023 to January 1, 2024? Solution: Step 1: Years between = 1 (2023) Step 2: Leap years between = 0 (2023 is not leap) Step 3: Total days = 365 Step 4: Odd days = 365 mod 7 = 1 Answer: 1 odd day Example 2: Odd days from January 1, 2023 to January 1, 2025? Solution: 2023 (common) + 2024 (leap) = 365 + 366 = 731 days. 731 mod 7 = 731 - 7×104 = 731 - 728 = 3 odd days Answer: 3 odd days

Pro Tips & Tricks

  • Common year = 1 odd day
  • Leap year = 2 odd days
  • 400-year cycle has 146097 days = 20871 weeks + 0 odd days (exactly divisible by 7)
  • 100 years = 5 odd days (since 100 years have 24 leap years? Actually 100 years = 76 common + 24 leap = 76×1 + 24×2 = 76+48=124 mod7=5)
  • 200 years = 3 odd days, 300 years = 1 odd day, 400 years = 0 odd days
  • Odd days for months: Jan=3, Feb=0/1, Mar=3, Apr=2, May=3, Jun=2, Jul=3, Aug=3, Sep=2, Oct=3, Nov=2, Dec=3 (for common year)

Shortcut Methods to Solve Faster

Odd days in a year = 1 (common) or 2 (leap)
Odd days in a century = 5 (for 100 years, except multiples of 400)
Odd days in 400 years = 0
To find weekday of Jan 1 of any year, add odd days from reference year
Number of leap years between years Y1 and Y2 = (Y2/4 - Y1/4) - (Y2/100 - Y1/100) + (Y2/400 - Y1/400)

Common Mistakes to Avoid

Counting the number of leap years incorrectly
Forgetting that century years not divisible by 400 are not leap
Miscalculating odd days for partial years
Not using modulo 7 at the end

Exam Importance

Odd Days Classic is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
2-3 questions
BANKING PO
2-3 questions
RAILWAYS RRB
2-3 questions
CAT
1-2 questions
INSURANCE
2-3 questions

Ready to Master Odd Days Classic?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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