CSAT
Logical Reasoning and Analytical Ability
CSAT
Logical Reasoning — Quick Revision
One-page CSAT revision of logical reasoning: syllogism pairings, conditional logic, seating conventions, ranking, coding, series, clock and calendar rules.
SyllabusCSAT · Logical reasoning and analytical ability
Every rule on this sheet is a CSAT mark waiting to be collected. Revise it before each mock test.
Syllogisms
| Premise 1 | Premise 2 | Conclusion |
|---|---|---|
| All A are B | All B are C | All A are C |
| All A are B | No B is C | No A is C |
| Some A are B | All B are C | Some A are C |
| Some A are B | No B is C | Some A are not C |
| All A are B | Some B are C | None definite |
| Some + Some / No + No | — | None definite |
| Statement | Converts to |
|---|---|
| All A are B | Some B are A |
| Some A are B | Some B are A |
| No A is B | No B is A |
| Some A are not B | Nothing |
High-yield logic rules
- “Some” = at least one, possibly all.
- A possibility conclusion follows unless a definite statement rules it out.
- If P then Q → only “if not Q then not P” is valid.
- “P only if Q” = P → Q. “P unless Q” = not Q → P. “No P without Q” = P → Q.
Arguments
| Type | Correct option is… |
|---|---|
| Assumption | Unstated and necessary (negation test) |
| Conclusion | Forced by the statement alone |
| Course of action | Practical, proportionate, addresses the stated problem |
| Strengthen / weaken | A new fact that changes the likelihood of the conclusion |
Arrangements, Relations and Directions
| Rule | Value |
|---|---|
| Facing centre | Left = clockwise; right = anticlockwise |
| Facing north (row) | Right = east on the diagram |
| Turn right from north / east / south / west | East / south / west / north |
| Distance | $\sqrt{x^2 + y^2}$ |
| Morning shadow | Falls west |
| Ranking total | Top rank + bottom rank − 1 |
| People between ranks $p < q$ | $q - p - 1$ |
Coding and Series
- EJOTY = 5, 10, 15, 20, 25. Opposite letters sum to 27 (A–Z, B–Y, … M–N).
- Series check order: differences → second differences → ratios → squares/cubes → alternating series.
Clocks and Calendars
| Rule | Value |
|---|---|
| Angle between hands | $\lvert 30H - 5.5M \rvert$ (use $360^\circ -$ result if over $180^\circ$) |
| Minute hand / hour hand speed | $6^\circ$ / $0.5^\circ$ per minute |
| Coincide / right angle / opposite per day | 22 / 44 / 22 |
| Odd days: ordinary / leap year | 1 / 2 |
| Odd days: 31-day / 30-day month | 3 / 2 |
| Odd days: 100 / 200 / 300 / 400 years | 5 / 3 / 1 / 0 |
| Leap year | Divisible by 4; century years only if divisible by 400 |
| Anchor dates | 15 August 1947 = Friday; 26 January 1950 = Thursday |
Traps
Three classic errors
- Treating the converse of an if–then statement as valid.
- Flipping left and right for people facing south or facing the centre.
- Adding two odd days for a leap year when 29 February is not inside the span.
Related Topics
- Logical Reasoning: Syllogisms and Arguments
- Logical Reasoning: Puzzles and Arrangements
- Logical Reasoning — practice questions
- All quick-revision sheets
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