60-second revision
- Odd days = days left over after full weeks. Ordinary year = 1 odd day, leap year = 2.
- Leap year: divisible by 4; century years only if divisible by 400 (2000 yes, 1900 no).
- 100 years = 5 odd days, 200 = 3, 300 = 1, 400 = 0.
- Odd-day number to day: 0 Sunday, 1 Monday, 2 Tuesday, 3 Wednesday, 4 Thursday, 5 Friday, 6 Saturday.
- Clock angle = |30H − 5.5M|; if above 180°, subtract from 360°.
- Hands coincide 22 times a day, are at right angles 44 times and point in opposite directions 22 times.
- Hands coincide at 60H/11 minutes past H o'clock.
- Matching questions: check names, numbers, letters and codes part by part, not as a whole.
Calendar: odd days
Days of the week repeat every 7 days, so only the remainder after dividing a number of days by 7 matters. That remainder is the number of odd days. An ordinary year has 365 days = 52 weeks + 1 day; a leap year has 366 days = 52 weeks + 2 days.
| Period | Odd days |
|---|---|
| Ordinary year | 1 |
| Leap year | 2 |
| Month of 31 days | 3 |
| Month of 30 days | 2 |
| February (28 / 29 days) | 0 / 1 |
| 100 years | 5 |
| 200 / 300 / 400 years | 3 / 1 / 0 |
Day of the week for a given date
Add odd days for completed centuries, completed years and the days of the current year up to the date, then reduce modulo 7. Read the result: 0 is Sunday, 1 Monday, up to 6 Saturday.
Worked example: 15 August 1947. Up to 1600: 0. 1601–1900 (300 years): 1. 1901–1946 (46 years with 11 leap years): 46 + 11 = 57 → 1. 1947 up to 15 August: January 3, February 0, March 3, April 2, May 3, June 2, July 3, August 15 → 1; total 3 + 0 + 3 + 2 + 3 + 2 + 3 + 1 = 17 → 3. Sum 0 + 1 + 1 + 3 = 5 → Friday.
Moving forward from a known day
If a known date falls on a certain day, the same date next year moves by 1 day, or by 2 if a 29 February falls in between. To find the day after a number of days, divide by 7 and count the remainder forward. 100 days after Sunday: 100 = 14 weeks + 2, so Tuesday.
Repeating calendars
Two years have identical calendars if they start on the same day and are both ordinary or both leap. Keep adding odd days (1 for ordinary, 2 for leap) year by year until the total is a multiple of 7, then check the leap status. A leap year repeats after 28 years (if no non-leap century year such as 2100 falls in between); an ordinary year repeats after 6 or 11 years depending on its position relative to the leap year.
Clocks: angle between the hands
The minute hand moves 6° per minute; the hour hand moves 0.5° per minute (30° per hour). So the minute hand gains 5.5° per minute on the hour hand. At H hours M minutes, angle = |30H − 5.5M|; if this exceeds 180°, subtract it from 360° to get the smaller angle.
| Time | Working | Angle |
|---|---|---|
| 5:15 | |150 − 82.5| | 67.5° |
| 9:00 | |270 − 0| = 270 → 360 − 270 | 90° |
| 2:20 | |60 − 110| | 50° |
| 11:40 | |330 − 220| | 110° |
Coinciding, right-angle and opposite hands
The hands coincide once every 65 5/11 minutes, giving 11 meetings in 12 hours and 22 in a day. Between H and H + 1 o'clock they coincide at 60H/11 minutes past H. They are at right angles 22 times in 12 hours (not 24, because the right angles at 3 o'clock and 9 o'clock each serve two neighbouring hours), so 44 in a day, and opposite (180°) 11 times in 12 hours, 22 in a day.
Indexing, address and date matching
SSC matching questions give one entry (an address, a name with a code, a date) and ask which option is exactly identical, or which detail is different. These test care, not knowledge. Split the entry into parts and compare each part across the options.
- Names: spelling of every word (Verma/Varma, Sharma/Sarma, initials).
- House and flat numbers: digits, letters and separators (47/B versus 47-B).
- Locality and city spellings.
- PIN codes and phone numbers: compare digit by digit, especially swapped neighbours (452010 versus 452001).
- Dates: confirm the format (DD/MM/YYYY versus MM/DD/YYYY) before reading the month.
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