Calendar Aptitude: Odd Days and Leap Years

• Generating 50 unique, easy-level calendar aptitude questions with one correct answer would be difficult (best suited to a question-generation tool)
• Instead, here is information to help you understand the topic of Calendars in aptitude tests

Calendar Basics

• A standard year has 365 days, while a leap year has 366 days.
• A leap year occurs every four years, except for years divisible by 100 but not by 400.
• Ordinary year: 365 days = 52 weeks + 1 day
• Leap year: 366 days = 52 weeks + 2 days
• The "odd days" are the extra days beyond the complete weeks.
• To find the day of the week for a given date, calculate the total number of odd days.

Counting Odd Days

• 1 odd day: (365 days mod 7 = 1)
• 2 odd days: (366 days mod 7 = 2)
• To determine the number of odd days in a given period, divide the number of days by 7 and take the remainder.
• A century has 100 years.
• 100 years = 76 ordinary years + 24 leap years = (76 x 1 + 24 x 2) odd days = 124 odd days = (17 weeks + 5 days) = 5 odd days.
• 200 years have (5 x 2) 10 odd days = 3 odd days.
• 300 years have (5 x 3) 15 odd days = 1 odd day.
• 400 years have (5 x 4 + 1) odd days = 0 odd days.
• The cycle of odd days repeats every 400 years.
• Number of days from January 1, 100 AD to December 31, 100 AD will have 5 odd days.
• Number of days from January 1, 1 AD to December 31, 400 AD will have 0 odd days.

Day Codes

• Sunday: 0
• Monday: 1
• Tuesday: 2
• Wednesday: 3
• Thursday: 4
• Friday: 5
• Saturday: 6

Month Codes

• January: 1
• February: 4
• March: 4
• April: 0
• May: 2
• June: 5
• July: 0
• August: 3
• September: 6
• October: 1
• November: 4
• December: 6

Century Codes

• 1600s: 6
• 1700s: 4
• 1800s: 2
• 1900s: 0
• 2000s: 6

Formula for Finding the Day

• Day = (Date + Month Code + Century Code + Year + (Year/4)) mod 7

Example Question Types

• What day of the week was January 1, 2000?
• What day of the week was August 16, 1947?
• What day of the week was 15 August 1947?
• What will be the day of the week on January 1, 2100?
• If today is Sunday, what will be the day 777 days from now?
• The calendar for 2007 will be the same for which year?
• On what dates of April 2015 did Wednesday fall?