Logical Reasoning — CAT DILR

Logical Reasoning sets present arrangements, relations, rankings or overlapping conditions in prose, and the single highest-leverage habit across every sub-type is converting the verbal clues into a diagram as you read them, rather than attempting to hold the constraints in working memory. A puzzle that feels impossible when read purely verbally usually becomes close to mechanical once diagrammed correctly.

1. Arrangements — linear and circular

Place the clues that pin down an exact position first, then work outward from them using the relative clues. A clue stating "X sits at the left end" is absolute and should be placed immediately; a clue stating "Y sits two seats to the right of X" is relative and can only be used once X's position is fixed.

Circular arrangements need one extra piece of bookkeeping that linear ones do not: whether the arrangement faces inward or outward changes which direction is "clockwise." A puzzle describing people seated around a round table facing the centre has left and right reversed relative to the seating positions themselves compared with a table where everyone faces outward — misreading this single detail flips every relative-position clue in the puzzle at once.

Work the clues that eliminate possibilities before the clues that place someone directly. A negative clue ("Z does not sit next to Y") is often more powerful for narrowing down a small number of remaining valid layouts than a positive clue, once several positions are already fixed — checking every remaining constraint against a candidate layout before finalising it is what actually prevents an error.

2. Blood relations

Build a family tree with a fixed, consistent notation as you read — a horizontal line for a marriage, a vertical line for a parent-child link, and a "+"/"−" or M/F marker for gender — rather than trying to track the relationships as a chain of sentences. Every blood-relation puzzle is genuinely a tree-construction exercise, not a reasoning exercise, once the notation habit is automatic.

The most common error is treating a relationship word as symmetric when it is not. "A is B's father" and "B is A's father" describe entirely different trees; "A is B's sibling" is symmetric, but the puzzle's answer usually hinges on exactly one of the asymmetric relationships (parent, child) being read in the correct direction.

3. Directions and distances

A sequence of directional movements is a vector-addition problem, and net displacement is found by Pythagoras once the movements are resolved into perpendicular (north-south and east-west) components, not by adding the individual distances travelled. Walking 8 km north and then 6 km east does not put you 14 km from the start — it puts you $\sqrt{8^2+6^2}=10$ km away, along the diagonal connecting the two legs.

Track direction changes (left turn, right turn) relative to the direction currently being faced, not relative to a fixed compass reading, since "turn left" means something different depending on which way one is already facing. A short table of current-direction-plus-turn results, built once at the start of a directions puzzle, prevents re-deriving this at every step.

4. Set overlaps (two-set Venn)

$|A\cup B|=|A|+|B|-|A\cap B|,\text{Only }A=|A|-|A\cap B|,\text{Neither}=\text{Total}-|A\cup B|$

A two-set overlap question is solved by filling in a four-region diagram — only A, only B, both, and neither — and every stated number pins down exactly one region or a simple combination of them. In a class of 50 where 30 like Maths, 25 like Science and 10 like both: only-Maths $=30-10=20$, only-Science $=25-10=15$, at-least-one $=30+25-10=45$, and neither $=50-45=5$ — every value in the class is now accounted for.

5. Comparison chains

A set of clues comparing people or objects on a single attribute (height, age, marks, price) is solved by placing everyone on one number line, not by tracking each pairwise comparison as a separate fact. "A is taller than B but shorter than C" places $B<A<C$ directly on the line; each further clue either extends the line or merges with a position already placed.

Chains of comparisons combine transitively, but only within the same attribute and the same direction of comparison — knowing $A<B$ and $B<C$ gives $A<C$ directly, but a clue mixing two different attributes ("A is older than B, and B is taller than C") gives no combined relationship between A and C at all. The most common trap is assuming a combined ranking exists when the clues actually describe two independent attributes that were never meant to be merged.

6. Ranking and ordered deduction

"$k$th from the left" and "$k$th from the right" in a row of $n$ people relate by $k_{\text{left}}+k_{\text{right}}=n+1$ — a fact that turns "find the total number of people" questions into a one-line computation once both rankings for the same person are given, rather than requiring the row to be reconstructed in full.

A constraint-satisfaction puzzle (who owns which pet, who sits where, matching one attribute set to another) is fastest solved with a grid — rows for one attribute, columns for another, marking each cell as confirmed-yes, confirmed-no, or undetermined as each clue is processed.

Process every direct, absolute clue before attempting any clue that only rules something out, since direct placements shrink the grid fastest and make elimination clues far more powerful once applied against a smaller remaining space.

Worked Examples

Example 1 (linear arrangement — medium). Six people P, Q, R, S, T, U sit in a row of six seats. P is at the left end. T sits immediately to the right of P. U sits at the right end. R sits immediately to the left of U. Q sits immediately to the right of S. Find the complete arrangement.

Place the absolute clues first: position 1 = P, position 6 = U. Then the relative clues anchored to them: position 2 = T (immediately right of P); position 5 = R (immediately left of U). Only positions 3 and 4 remain, for Q and S, with the clue "Q immediately right of S" fixing position 3 = S and position 4 = Q. Complete arrangement: P, T, S, Q, R, U.

Example 2 (blood relations — medium). A is B's father. C is B's sister. D is C's mother. How is A related to D?

B and C are siblings (B's sister is C, so C is also A's child, since A is B's father). D is C's mother, and since C's parents are the same as B's parents, D is also B's mother. A is the father and D is the mother of the same two children — A is D's husband.

Example 3 (directions — easy). A person walks 8 km north, then 6 km east. Find the straight-line distance from the starting point.

The two legs are perpendicular. Net distance $=\sqrt{8^2+6^2}=\sqrt{64+36}=\sqrt{100}=10$ km.

Example 4 (set overlaps — medium). In a class of 50 students, 30 like Maths, 25 like Science, and 10 like both. How many like neither subject?

At least one subject $=30+25-10=45$. Neither $=50-45=5$.

Example 5 (ranking — easy). In a row of students, Meera is 9th from the left and 14th from the right. How many students are in the row?

$k_{\text{left}}+k_{\text{right}}=n+1\Rightarrow 9+14=n+1\Rightarrow n=22$.

Example 5a (comparison chain — medium). Among five friends: A is taller than B. C is shorter than B. D is taller than A but shorter than E. Arrange all five from tallest to shortest.

From the height clues: $C<B<A$ (from the first two clues) and $A<D<E$ (from the third). Chaining these together on one number line: $C<B<A<D<E$. Tallest to shortest: E, D, A, B, C.

Example 6 (constraint grid — hard). Four friends — Anil, Bala, Chitra, Deepa — each prefer a different one of tea, coffee, juice and water. Bala likes coffee. Anil does not like tea, coffee or water. Chitra does not like juice. Deepa does not like water. Find each person's drink.

Bala is fixed as coffee (direct clue). Anil rules out tea, coffee and water, leaving only juice — so Anil = juice, by elimination among all four drinks. With coffee and juice now taken, only tea and water remain for Chitra and Deepa. Deepa rules out water, so Deepa = tea, leaving Chitra = water. Final: Bala = coffee, Anil = juice, Deepa = tea, Chitra = water.

Summary

Diagram every logical-reasoning puzzle as you read the clues — a table, family tree, or number line converts verbal complexity into a mechanical solving process, and this single habit matters more than any individual technique below it.

Place absolute clues before relative ones in arrangements, and check a table's facing direction before applying "clockwise."

Blood-relation puzzles are tree-construction exercises; track parent-child direction carefully, since it is rarely symmetric even when the puzzle's language sounds like it might be.

Directions problems are vector addition — net displacement uses Pythagoras on perpendicular components, never a simple sum of the distances walked.

Two-set overlaps fill a four-region diagram directly from the given numbers; ranking questions use $k_{\text{left}}+k_{\text{right}}=n+1$; and constraint grids are solved fastest by placing every direct clue before attempting elimination-only clues.