Syllogisms, statements and conclusions, seating arrangement, puzzles, and ranking, with worked examples and practice
This is the analytical core of the reasoning section: deduce what must be true from given statements. Unlike verbal reasoning, the answer is rarely a guessed pattern; it is forced by the rules of inference. Draw a diagram and stay strict about what "follows".
| Sub-type | Method |
|---|---|
| Syllogism | Draw Venn diagrams; a conclusion holds only if it is true in every possible diagram |
| Statements and conclusions | Accept the statements as true; a conclusion follows only if it must be true, not merely could be |
| Seating arrangement | Draw the row or circle; fix the most constrained person first |
| Puzzles (matching) | Build a grid; mark each clue as yes or no, eliminate |
| Ranking | Convert "from top" and "from bottom" into one line; use the total formula |
If a person is rank a from one end and b from the other in a line of N people, then N = a + b - 1 (the person is counted from both ends, so subtract one).
Statements: All pens are books. All books are tables. Conclusions: (i) All pens are tables. (ii) Some tables are pens.
Pens sit inside books, which sit inside tables, so every pen is a table; (i) follows. Since all pens are tables, certainly some tables are pens; (ii) follows. Both follow.
Statements: Some doctors are engineers. All engineers are graduates. Conclusion: Some doctors are graduates.
The doctors who are engineers must be graduates (since all engineers are graduates). So at least those doctors are graduates. The conclusion follows.
Statement: Many students failed the test. Conclusion: The test was very hard.
The failure could be due to poor preparation, not difficulty. The conclusion is possible but not forced. It does not follow.
Five recruits A, B, C, D, E stand in a row. C is to the immediate right of B. A is at one end. D is between C and E. Where does each stand (left to right)?
A is at an end; place A at the far left. B then C are adjacent (C just right of B). D is between C and E, so the order C, D, E holds. The row is A, B, C, D, E.
In a line of students, Ravi is 7th from the front and 12th from the back. How many students are in the line?
N = a + b - 1 = 7 + 12 - 1 = 18 students.
Four officers P, Q, R, S sit around a square table, one per side, all facing the centre. P is opposite R. Q is to the immediate left of P. Where is S?
P and R face each other across the table. Q sits immediately to P's left. The only remaining side is for S, who is therefore opposite Q (and to P's right).
Three friends, X, Y, Z, like one sport each: cricket, hockey, football. X does not like cricket. Z likes football. Who likes what?
Z likes football. X does not like cricket and football is taken, so X likes hockey. Y is left with cricket.