Reasoning Chapters

1. NUMBER AND LETTER SERIES2. ALPHANUMERIC SERIES3. MISSING NUMBER4. ANALOGY SIMILARTY5. CLASSIFICATION6. DIRECTION 7. BLOOD RELATION8. SEATING ARRANGEMENT9. PUZZLE10. ORDER AND RANKING11. SYLLOGISM12. CLOCK13. CALENDER14. WORD FORMATION15. DICE16. CUBE AND CUBOID17. MIRROR AND WATER IMAGE18. VENN DIAGRAM19. STATEMENT AND ASSUMPTION

CALENDAR

Important Formulas & Concepts

  • Zeller’s Congruence Formula: Used to find the day of the week for any given date.
    Formula:
    h = (q + ⌊(13(m+1))/5⌋ + K + ⌊K/4⌋ + ⌊J/4⌋ + 5J) mod 7
    Where:
    - h = day of week (0 = Saturday, 1 = Sunday, 2 = Monday, ..., 6 = Friday)
    - q = day of the month
    - m = month (3 = March, 4 = April, ..., 12 = December; January and February counted as months 13 and 14 of previous year)
    - K = year of the century (year % 100)
    - J = zero-based century (year / 100)
  • Doomsday Algorithm: A quick mental math method to find the weekday.
    It uses anchor days for centuries and memorizes "Doomsdays" of months.
    Example doomsdays: 4/4, 6/6, 8/8, 10/10, 12/12, 5/9, 9/5, 7/11, 11/7.
  • Leap Year Rules:
    - Year divisible by 4 → Leap year
    - Century year (divisible by 100) must be divisible by 400 to be a leap year
    Example: 2000 is leap, 1900 is not.
  • Number of Days in Months:
    Jan-31, Feb-28/29, Mar-31, Apr-30, May-31, Jun-30, Jul-31, Aug-31, Sep-30, Oct-31, Nov-30, Dec-31.

Explanation & Sample Problem

To find the day of the week on a particular date, we use formulas like Zeller’s Congruence or the Doomsday algorithm. Let's solve an example using Zeller’s formula:

Example: Find the day of the week on 15th August 1947.

  • Given: q = 15 (day), m = 8 (August), year = 1947
  • Since August > 2, m = 8, year stays 1947.
  • K = 47 (1947 % 100)
  • J = 19 (1947 / 100)

Apply formula:

    h = [15 + floor(13(8+1)/5) + 47 + floor(47/4) + floor(19/4) + 5*19] mod 7
      = [15 + floor(117/5) + 47 + 11 + 4 + 95] mod 7
      = [15 + 23 + 47 + 11 + 4 + 95] mod 7
      = 195 mod 7
      = 6

Where h=6 corresponds to Friday (0=Saturday, 1=Sunday,...6=Friday). So, 15th August 1947 was a Friday.

Previous Year Questions with Solutions

  1. SSC CGL 2020: What day of the week was 15th August 1947?
    Answer: Friday (Solved above)
  2. RRB NTPC 2019: Find the day of the week on 1st January 2000.
    Solution: January and February are treated as months 13 and 14 of previous year.
    q=1, m=13, year=1999, K=99, J=19
    h = (1 + floor(13*14/5) + 99 + floor(99/4) + floor(19/4) + 5*19) mod 7
    h = (1 + 36 + 99 + 24 + 4 + 95) mod 7 = 259 mod 7 = 0 → Saturday
    Answer: Saturday
  3. SSC CHSL 2018: How many Sundays are there in March 2021?
    March 2021 starts on Monday (1st March 2021 is Monday). Sundays fall on 7,14,21,28.
    Answer: 4 Sundays
  4. HSSC JE 2019: What day of the week was 26th January 1950?
    Using Zeller’s formula or known calendars:
    Answer: Thursday
  5. SSC MTS 2021: If 1st January 2021 was a Friday, what day was 31st December 2021?
    2021 is not a leap year, so total 365 days = 52 weeks + 1 day.
    So, 31st Dec 2021 will be same day + 364 days + 1 day = Friday + 1 day = Saturday.
    Answer: Friday (Careful: The day repeats every 7 days; 31st Dec 2021 was actually Friday.)
  6. SSC GD 2019: How many leap years are there between 1900 and 2000?
    Leap years between 1901 and 2000 are every 4 years except 1900 is not leap.
    Count: 1904, 1908, ..., 2000 (2000 is leap since divisible by 400)
    Total = 24 leap years.
    Answer: 24
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