Ranking, ordering, clocks and calendars

Ranking, clock angles and calendar questions each have a small formula or drawing that makes them mechanical; candidates who do not know it spend three minutes guessing. This lesson gives the method for each with checkable examples.

Ranking: count from both ends

If a person is 7th from the top and 12th from the bottom, the total is 7 plus 12 minus 1, which is 18. The minus one is because the person is counted twice.

Example: in a row of 40 students, Ravi is 15th from the left. What is his position from the right? 40 minus 15 plus 1, which is 26th. Check: 15 plus 26 is 41, one more than 40, as the formula predicts.

For ordering, draw the chain as you read. "P is taller than Q. R is shorter than Q but taller than S. T is taller than P" gives T, P, Q, R, S from tallest, and every question on the set becomes a lookup.

Clocks: the angle formula

The minute hand moves 6 degrees per minute. The hour hand moves 0.5 degrees per minute, which is 30 degrees per hour. At H hours and M minutes, the angle between the hands is the absolute value of 30H minus 5.5M. If the result is above 180, subtract it from 360.

Example: 3:40. 30 times 3 is 90; 5.5 times 40 is 220; difference 130 degrees. Example: 9:00. 270 minus 0 is 270, so the angle is 360 minus 270, which is 90 degrees, which matches the picture of a clock at nine.

Also: the hands overlap 11 times and are at right angles 22 times in 12 hours.

Calendars: odd days

An ordinary year has 365 days, which is 52 weeks and 1 odd day. A leap year has 2 odd days. So the same date moves forward one weekday each ordinary year and two after a leap year.

Example: 1 January 2025 was a Wednesday. 2025 is not a leap year, so 1 January 2026 is Thursday. 2026 is not a leap year, so 1 January 2027 is Friday. For a date later in the year, add the days of the months in between and divide by 7, keeping the remainder.

Common mistakes

• Forgetting the plus one or minus one in ranking formulas.
• Treating the hour hand as fixed at the hour mark in clock questions.
• Counting February as 28 in a leap year.

Practice habit: Solve two questions of each type daily, always writing the line, the formula or the odd-day count on paper. Check the clock answers against a drawn clock face until the formula feels trusted.