REASONING SHORTCUT | 20 OCTOBER 2026
What day of the week was 25 March 2022? You do not need a calendar. Amit Sir solves it in a few lines with one idea, odd days, and the answer is Friday. The same method finds the day for any date, past or future, and it is the backbone of every calendar question in general aptitude and logical reasoning papers.
What is an odd day?
A week has 7 days, so any stretch of days can be split into complete weeks plus a few days left over. Those leftover days are the odd days: the remainder when the number of days is divided by 7. A complete week changes nothing, so only the odd days move the weekday forward. Counting from the start of the calendar, the total number of odd days up to a date tells you its day: 0 = Sunday, 1 = Monday, 2 = Tuesday, 3 = Wednesday, 4 = Thursday, 5 = Friday, 6 = Saturday.
The building blocks
An ordinary year has 365 days = 52 weeks + 1 day, so it has 1 odd day. A leap year has 366 days, so it has 2 odd days. A year is a leap year if it is divisible by 4, except century years, which must be divisible by 400. So 2000 and 1600 are leap years, but 1900 is not.
Centuries follow from this. 100 years contain 24 leap years and 76 ordinary years: 76 + 2 × 24 = 124 odd days, and 124 ÷ 7 leaves 5. Doubling and tripling gives 200 years → 3 and 300 years → 1. 400 years (which include one extra leap century) give 0 odd days, so the calendar repeats every 400 years. That is why 1600 years and 2000 years both count as 0.
For months, take the days of each month divided by 7: January 31 → 3, February 28 → 0 (29 → 1 in a leap year), March 31 → 3, April 30 → 2, May 31 → 3, June 30 → 2, and so on.
Worked example: 25 March 2022
Split the date into the complete years before it and the days of the current year.
- Complete years: 2021 years have passed = 2000 + 21. The first 2000 years give 0 odd days (a multiple of 400). The next 21 years (2001–2021) contain 5 leap years (2004, 2008, 2012, 2016, 2020), so they give 21 + 5 = 26 odd days, and 26 ÷ 7 leaves 5.
- This year up to the date: 2022 is not a leap year. January 31 → 3, February 28 → 0, March up to the 25th = 25 → 4. Total 3 + 0 + 4 = 7.
- Add and divide: 7 + 5 = 12, and 12 ÷ 7 leaves 5. Five odd days means Friday.
Amit Sir keeps the 7 from January to March as it is and divides only at the end. You may also reduce it to 0 straight away; the remainder at the end is the same.
Second example: 15 August 1947
Complete years: 1946 = 1600 + 300 + 46. 1600 years → 0, 300 years → 1, and 46 years contain 11 leap years, so 46 + 11 = 57 → 1. That is 0 + 1 + 1 = 2. Days of 1947 (not a leap year) up to 15 August: 31 + 28 + 31 + 30 + 31 + 30 + 31 + 15 = 227, and 227 ÷ 7 leaves 3. Total 2 + 3 = 5, so 15 August 1947 was a Friday.
Faster tricks for exam questions
Most questions give you one known day and ask for another. Then you only need the odd days between the two dates. One year later, the same date moves forward by 1 day (2 days if a 29 February falls in between). If today is Wednesday, the day after 100 days is 100 ÷ 7 → remainder 2, so Friday. In any year, 1 March and 1 November fall on the same weekday, because the 245 days in between are exactly 35 weeks.
Common traps
Three mistakes cost marks. First, treating every century year as a leap year: 1900 and 2100 are not. Second, forgetting a leap year in the count: in the 25 March 2022 example, missing 2020 gives 25 instead of 26 odd days and the wrong answer, Thursday. Third, counting the current year as complete: for a date in 2022, you count the complete years up to 2021 and then the days of 2022 separately.
Framework: the Gregorian calendar rules
The calendar used in India and worldwide is the Gregorian calendar. Its leap-year rule (divisible by 4; century years only if divisible by 400) makes the calendar repeat exactly every 400 years, which is 146,097 days or 20,871 weeks. Every odd-day shortcut above follows from that rule.
CLAT angle
- Calendar questions now appear less often in CLAT Logical Reasoning, which is mostly analytical and critical reasoning, but they remain common in other aptitude tests and in sectional practice.
- The odd-days method trains the same skill CLAT rewards: reducing a long count to a remainder.
- Options are usually adjacent weekdays, so one missed leap year picks a wrong option.
- “Given day, find day” questions need only the odd days between two dates.
- Leap-year exceptions (1900, 2100) are a favourite trap.
Key facts
| Fact | Detail |
|---|---|
| Ordinary year | 1 odd day |
| Leap year | 2 odd days |
| 100 / 200 / 300 / 400 years | 5 / 3 / 1 / 0 odd days |
| Leap year rule | Divisible by 4; century years only if divisible by 400 |
| Odd days → day | 0 Sun, 1 Mon, 2 Tue, 3 Wed, 4 Thu, 5 Fri, 6 Sat |
| Leap years 2001–2021 | 2004, 2008, 2012, 2016, 2020 (5) |
| 25 March 2022 | Friday (12 odd days → 5) |
| 15 August 1947 | Friday |
Mnemonic
“Years, then months, then ÷ 7.” Count the odd days of the complete years, add the odd days of this year up to the date, and divide the total by 7. The remainder, read from Sunday = 0, is the day.
Sources
The Gregorian calendar leap-year rule and standard odd-days methods taught in reasoning and aptitude preparation. Every date in this article and quiz was checked against a computer calendar.
Free in the CLAT Gurukul app
These notes (as a PDF lesson) and the 10-question CBT are in the app under Current Affairs → 20 Oct 2026. Get the app on Google Play or open app.clatgurukul.com.
Practice Quiz — 10 CLAT-Style Questions
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