Advanced Reasoning — Puzzles, Seating, and Syllogisms

2A.1 Seating Arrangement (Circular)

Circular seating puzzles require you to place people around a table (facing centre or facing outward) based on relative-position clues such as "to the immediate left/right of," "opposite," and "between."

Worked Example: Six friends A, B, C, D, E, F sit around a circular table facing the centre. A sits opposite D. B sits to the immediate right of A. C sits between B and D. Where does E sit relative to F?

Solution: Starting with A and placing D opposite: going clockwise from A, we have A, B, C, D. B is to A's immediate right, and C is between B and D — consistent with this order. The remaining two seats (between D and A, going the other way) are taken by E and F. Since no further clue fixes their order without an additional constraint, exam questions of this type always supply one more clue (e.g., "E is to the immediate left of A") to fully fix the arrangement.

2A.2 Linear Seating (Row Puzzles)

Row puzzles use "left of," "right of," "immediate neighbour," and "at the end" clues. Always draw a blank row of dashes first and fill in fixed positions before working out relative ones.

2A.3 Blood Relations

Multi-generation blood relation puzzles are best solved with a family tree diagram: mark each person as a node, and connect them with labelled edges (parent-of, spouse-of, sibling-of). Trace the path from the question's starting person to the target person along these edges to determine the relationship.

2A.4 Syllogisms

Standard categorical syllogisms use quantifiers "All," "No," and "Some." A key trap format is: "All A are B. Some B are C." No valid conclusion about A and C can be drawn from this alone, because the "some B" that are C might not include any of the B that are A.

2A.5 Direction Sense

Direction problems track net displacement after a sequence of turns and distances. Draw the path on a mental (or literal) grid, and use the Pythagorean theorem when the net path is not a straight line (i.e., involves both a horizontal and a vertical component).

2A.6 Coding-Decoding

Letter-shift codes (each letter moved a fixed number of places forward or backward in the alphabet) are the most common type. Practice converting letters to their alphabet position number (A=1 through Z=26) to make shift calculations mechanical and error-free.

2A.7 Practice Set (12 MCQs)

1. Five people P, Q, R, S, T sit in a row. Q is to the immediate left of R. P is at one end. S is between T and Q. Who is at the other end?
   (a) R (b) S (c) T (d) Q
2. Statements: All bonds are securities. Some securities are risky. Conclusion: Some bonds are risky. Does this follow?
   (a) Yes, it follows (b) No, it does not necessarily follow (c) Cannot be determined (d) Both conclusions follow
3. A is the son of B. C is the sister of B. D is the mother of C. How is D related to A?
   (a) Grandmother (b) Aunt (c) Mother (d) Sister
4. In a code, BANK is written as 2-1-14-11. How is LOAN coded using the same rule?
   (a) 12-15-1-14 (b) 12-14-1-15 (c) 11-15-1-14 (d) 12-15-2-14
5. A person walks 10 km north, then 6 km east, then 10 km south. How far is he from the starting point?
   (a) 6 km (b) 10 km (c) 16 km (d) 26 km
6. Six friends sit around a circular table facing the centre. A is opposite D. B is to A's immediate right. C is between B and D. E is to the immediate left of A. Where does F sit?
   (a) Between C and D (b) Between E and D (c) Opposite B (d) Between A and B
7. Statements: All managers are graduates. All graduates are employed. Conclusion: All managers are employed. Does this follow?
   (a) Yes, it follows validly (b) No (c) Cannot be determined (d) Only partially
8. In a row of 50 people, Ramesh is 18th from the left. What is his position from the right?
   (a) 32nd (b) 33rd (c) 31st (d) 30th
9. If in a code, MONEY is written as NPOFZ, how is BANKS written using the same rule?
   (a) CBOLT (b) CBOLU (c) CBPLT (d) BCOLT
10. A is the brother of B. C is the father of A. D is the daughter of C. How is D related to B?
    (a) Sister (b) Aunt (c) Cousin (d) Mother
11. Statements: No accounts are overdue. Some overdue items are loans. Conclusion: Some loans are not accounts. Does this follow?
    (a) Yes, it follows validly (b) No (c) Cannot be determined (d) Only if all loans are overdue
12. In a family, P and Q are husband and wife and are S's only parents. R is the son of Q. S is the sister of R. How is S related to P?
    (a) Daughter (b) Wife (c) Sister (d) Niece

Answer Key:

1.(a) Arranging from the clues — Q is immediately left of R, S is between T and Q, and P is at one end — gives the order P, S, T, Q, R, with P at one end and R at the other.

2.(b) No, this does not necessarily follow: the "some securities" that are risky may not include any bonds specifically.

3.(a) C is B's sister, and D is C's mother, meaning D is also B's mother; since A is B's son, D is A's grandmother.

4.(a) Each letter is coded by its position in the alphabet (B=2, A=1, N=14, K=11); applying the same code, LOAN is written as 12-15-1-14.

5.(a) The northward and southward legs cancel out (10 km north, 10 km south), leaving a net displacement of 6 km due east of the starting point.

6.(b) With the order A, B, C, D established going one way around the table and E immediately left of A, F takes the one remaining seat, between E and D.

7.(a) Yes, this follows validly: all managers are graduates, and all graduates are employed, so all managers must be employed.

8.(b) Position from the right = 50 − 18 + 1 = 33rd.

9.(a) Each letter shifts forward by one place in the alphabet, the same rule as MONEY→NPOFZ; applying it to BANKS gives CBOLT.

10.(a) C is A's father, and D is C's daughter, meaning D is A's sister; since A is B's brother, D is also B's sister.

11.(a) Yes, this follows validly: no accounts are overdue, and some overdue items are loans, so those particular loans (being overdue) cannot be accounts, meaning some loans are not accounts.

12.(a) R is Q's son and S is R's sister, so S is also Q's daughter; since P and Q are S's parents, S is P's daughter.