CALENDAR – Reasoning Notes (CUET | CLAT | IPMAT)
📘 CALENDAR – Reasoning
Notes (CUET | CLAT | IPMAT)
Calendar questions test the ability to calculate days,
dates, years, leap years, odd days, and patterns in the Gregorian calendar.
⭐ 1. BASIC CONCEPTS
1.1 Ordinary Year
- 365
days
- Number
of weeks = 52
- Odd
days = 365 mod 7 = 1
1.2 Leap Year
- 366
days (February 29 included)
- Odd
days = 366 mod 7 = 2
What makes a year a leap year?
A year is a leap year if:
- Divisible
by 4, AND
- Not
divisible by 100, EXCEPT
- Divisible
by 400 → Leap year.
Examples
- 2024 →
divisible by 4, not by 100 → Leap year
- 1900 →
divisible by 100 but not by 400 → Not leap year
- 2000 →
divisible by 400 → Leap year
⭐ 2. ODD DAYS (Most Important
Concept)
Odd days = days left after dividing total days by 7.
|
Period |
Odd Days |
|
1 Ordinary Year |
1 |
|
1 Leap Year |
2 |
|
100 years |
5 |
|
200 years |
3 |
|
300 years |
1 |
|
400 years |
0 |
400-year cycle repeats.
⭐ 3. DAY CALCULATION METHODS
3.1 Type 1 — Find the Day on a Given Date
Approach
- Count
total odd days from:
- completed
years
- completed
months of current year
- date
- Add
them and take mod 7.
🌟 Example (CUET-based)
Q1. What day was 15 August 1947?
Solution
(A) Odd days in completed years (1600 + 300 + 47)
- 1600
years → 0 odd days
- 300
years → 1 odd day
- Next
47 years →
- Leap
years = floor(47/4) = 11
- Ordinary
years = 36
- Odd
days = 11×2 + 36×1 = 58 → 58 mod 7 = 2
Total so far = 0 + 1 + 2 = 3 odd days
(B) Odd days from months (1947 is NOT leap year)
|
Month |
Days |
Odd Days |
|
Jan
|
31 |
3 |
|
Feb |
28 |
0 |
|
Mar |
31 |
3 |
|
Apr |
30 |
2 |
|
May |
31 |
3 |
|
Jun |
30 |
2 |
|
Jul |
31 |
3 |
Sum = 16 → 16 mod 7 = 2
(C) Odd days from date = 15 → 15 mod 7 = 1
Total odd days = 3 + 2 + 1 = 6
0 – Sunday
1 – Monday
2 – Tuesday
3 – Wednesday
4 – Thursday
5 – Friday
6 – Saturday
✔ Answer: Saturday
⭐ 4. TYPE 2 — Finding Day After /
Before N Days
Shortcut
Just compute N mod 7.
🌟 Example (IPMAT-based)
Q2. If today is Monday, what day will it be after 100
days?
100 mod 7 = 2
→ Move 2 days forward.
✔ Answer: Wednesday
⭐ 5. TYPE 3 — Same Calendar Years
Two years have the same calendar if:
- Having
same odd days, and
- Both
leap or both ordinary years.
Shortcut Rule
- Ordinary
year → next same calendar = +6 years
- Leap
year → next same calendar = +28 years
🌟 Example (CUET-based)
Q3. Which year has the same calendar as 2021?
2021 = ordinary year
→ Next matching year = 2021 + 6 = 2027
✔ Answer: 2027
⭐ 6. TYPE 4 — Leap Year Problems
🌟 Example (CLAT-based)
Q4. How many leap years are there between 2001 and 2100?
Check multiples of 4:
Leap years = floor(2100/4) – floor(2000/4)
= 525 – 500 = 25
But 2100 is NOT leap year → divisible by 100 but not by 400.
✔ Final: 24 leap years
⭐ 7. TYPE 5 — Day of Birth /
Anniversaries
🌟 Example (CUET)
Q5. If someone was born on Monday, what day will their
25th birthday fall on?
(Assume no leap-year birthdays.)
Odd days in 25 years:
- Leap
years = 6
- Ordinary
years = 19
Odd days = 6×2 + 19 = 31 → 31 mod 7 = 3
Monday + 3 = Thursday
✔ Answer: Thursday
⭐ 8. TYPE 6 — Calendar Matching
(Month-Level)
Rule
Two months have the same calendar if:
- Same
number of days
- Start
on same weekday
🌟 Example
Q6. A 31-day month starts on Wednesday. Which next month
has same calendar?
31-day month → next same calendar month = after 6 months
✔ Answer: August if
February is the starting month (example assumption)
⭐ 9. TYPE 7 — Counting Number of
Sundays / Mondays
🌟 Example (CUET-pattern)
Q7. How many Sundays are there in February 2024? (Leap
year)
February 2024 → 29 days
Total weeks = 4 weeks and 1 day
If 1st Feb 2024 was Thursday → Sundays fall on:
- 4th
- 11th
- 18th
- 25th
= 4 Sundays
✔ Answer: 4
⭐ 10. TYPE 8 — Finding Day of 1st
January of a Given Year
Shortcut:
Odd days =
Years passed + leap years count mod 7
🌟 Example (IPMAT-based)
Q8. What day was 1 Jan 2010?
Years passed = 2009
Leap years = floor(2009/4) – floor(2000/100) + floor(2000/400)
= 502 – 20 + 5 = 487
Odd days = (2009 + 487) mod 7
= 2496 mod 7 = 3
0-Sun, 1-Mon, 2-Tue, 3-Wed
✔ Answer: Wednesday
⭐ 11. TYPE 9 — Day Difference
Between Two Dates
🌟 Example (CUET)
Q9. How many days are between 15 May 2022 and 10 August
2022?
May (remaining): 16 days
June: 30
July: 31
August: 10
Total = 87 days
✔ Answer: 87
⭐ 12. Quick Reference Table of
Odd Days (Months)
|
Month |
Odd Days (Ordinary Year) |
Odd Days (Leap Year) |
|
Jan |
3 |
3 |
|
Feb |
0 |
1 |
|
Mar |
3 |
3 |
|
Apr |
2 |
2 |
|
May |
3 |
3 |
|
Jun |
2 |
2 |
|
Jul |
3 |
3 |
|
Aug |
3 |
3 |
|
Sep |
2 |
2 |
|
Oct |
3 |
3 |
|
Nov |
2 |
2 |
|
Dec |
3 |
3 |
📝 25 MCQs on Calendar –
With Answers & Explanations
1. What day was 1 January 2000?
a) Friday
b) Saturday
c) Sunday
d) Monday
Answer: b) Saturday
Explanation: 2000 is divisible by 400 → leap year starting on Saturday.
2. What day will it be 100 days after Monday?
a) Wednesday
b) Thursday
c) Friday
d) Saturday
Answer: a) Wednesday
Explanation: 100 mod 7 = 2 → Monday + 2 = Wednesday.
3. Which year will have the same calendar as 2023?
a) 2028
b) 2034
c) 2033
d) 2029
Answer: d) 2029
Explanation: Ordinary year → next same calendar after +6 years.
4. How many odd days are there in 300 years?
a) 1
b) 2
c) 3
d) 5
Answer: a) 1
Explanation: 300 years → 1 odd day.
5. How many leap years are between 2001 and 2100?
a) 24
b) 25
c) 26
d) 23
Answer: a) 24
Explanation: 2100 is not leap year → 24 leap years.
6. If 1 Jan 2017 was Sunday, what day was 1 Jan 2018?
a) Monday
b) Tuesday
c) Wednesday
d) Thursday
Answer: a) Monday
Explanation: 2017 ordinary → +1 day.
7. If 5 March 2024 is Tuesday, what day is 5 March 2025?
a) Wednesday
b) Thursday
c) Friday
d) Saturday
Answer: c) Friday
Explanation: 2024 leap → +2 days → Tuesday +2 = Thursday
Next year (2025) same date shift = +1 → Friday.
8. How many Sundays are there in February 2024? (Leap
year)
a) 4
b) 5
c) 3
d) Cannot be determined
Answer: a) 4
Explanation: Feb has 29 days → 4 Sundays.
9. 15 August 1947 was on which day?
a) Thursday
b) Friday
c) Saturday
d) Sunday
Answer: c) Saturday
Explanation: Standard historical fact.
10. If today is Thursday, what day was it 40 days ago?
a) Friday
b) Saturday
c) Sunday
d) Monday
Answer: d) Monday
Explanation: 40 mod 7 = 5 → Thursday – 5 = Monday.
11. Which year among these is a leap year?
a) 1900
b) 2100
c) 2004
d) 2019
Answer: c) 2004
Explanation: Divisible by 4, not a century year.
12. If 1 January 2020 was Wednesday, what day was 1
January 2021?
a) Wednesday
b) Thursday
c) Friday
d) Saturday
Answer: c) Friday
Explanation: 2020 leap → +2 days → Wednesday + 2 = Friday.
13. How many odd days are in 100 years?
a) 1
b) 2
c) 3
d) 5
Answer: d) 5
Explanation: Standard rule → 100 years = 5 odd days.
14. Which month of a non-leap year has exactly 28 days?
a) February
b) None
c) All months
d) April
Answer: c) All months
Explanation: Every month has at least 28 days.
15. What day is 26 January 2026?
a) Saturday
b) Sunday
c) Monday
d) Tuesday
Answer: d) Monday
Explanation: Direct calendar computation.
16. What is the next year after 2040 having the same
calendar?
a) 2046
b) 2068
c) 2051
d) 2048
Answer: b) 2068
Explanation: 2040 is leap → next same calendar after 28 years.
17. If 10 June 2023 was Saturday, what day was 3 June
2023?
a) Saturday
b) Friday
c) Thursday
d) Sunday
Answer: b) Friday
Explanation: 10 – 3 = 7 days → same weekday → Saturday – 1 week =
Saturday → But difference is 7 days? Actually 10–3=7 → 1 week → same day →
Saturday. Revised? Let's fix.
Correct Answer: a) Saturday
18. What day will 1 Jan 2030 be?
a) Monday
b) Tuesday
c) Wednesday
d) Thursday
Answer: b) Tuesday
Explanation: Standard known fact.
19. If 2018 starts on Monday, what day does 1 March 2018
fall on?
a) Wednesday
b) Thursday
c) Friday
d) Saturday
Answer: c) Thursday
Explanation:
Jan (31 = 3 odd)
Feb (28 = 0)
Total = 3 → Monday + 3 = Thursday.
20. How many odd days are in 2024 (leap year)?
a) 0
b) 1
c) 2
d) 3
Answer: c) 2
Explanation: Leap year = 2 odd days.
21. How many days are between 1 March 2023 and 1 June
2023?
a) 90
b) 92
c) 91
d) 89
Answer: b) 92
Explanation:
March 31
April 30
May 31
Total = 92.
22. If 2025 is an ordinary year, which day will 1 Jan
2026 be?
a) Wednesday
b) Thursday
c) Friday
d) Saturday
Answer: a) Thursday
Explanation: Ordinary year → +1 day.
23. Which year among the following will repeat the 2015
calendar?
a) 2021
b) 2026
c) 2025
d) 2037
Answer: b) 2026
Explanation: Ordinary year → +11-year cycle also matches.
24. What day of the week was 1 July 2020?
a) Tuesday
b) Wednesday
c) Thursday
d) Friday
Answer: c) Wednesday
Explanation: From 1 Jan 2020 (Wednesday) + 182 days → Wednesday.
25. If 12 October 2024 is Saturday, what day will 12
October 2025 be?
a) Sunday
b) Monday
c) Tuesday
d) Wednesday
Answer: b) Sunday
Explanation:
2024 leap → +2 → Saturday +2 = Monday
But 12 Oct → one-year shift normally +1, leap → +2.
Correct shift = +1 (because date is after Feb 29)
Saturday +1 = Sunday.
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