Blood Relations, Directions and Coding — the Sets Worth Taking First
Family Trees: One Notation, Two Traps
Use one notation and never improvise a second. A row per generation, oldest at the top. = between a married pair. A vertical line down to children, siblings side by side. + after a name for male, − for female, and a ? when the sex is not given — that last symbol is the one that saves marks, because a set will often ask a question that is unanswerable precisely because the sex was never stated, and an option saying "cannot be determined" is then correct rather than lazy.
- Maternal versus paternal is a side, not a relation. Your mother's brother is your maternal uncle; your father's brother is your paternal uncle. A question that asks "how is P related to Q" is answered from Q's side, and reading it from P's side inverts every answer.
- "The only son of X's father" is X, if X is male. These riddle phrases resolve by substitution: work out who the described person must be before answering anything about them.
- In-law relations cross the = sign. Brother-in-law is either your spouse's brother or your sister's husband, and a set that says only "brother-in-law" has left both open — mark it as a branch and see which the later statements close.
- Cousins carry no sex and no side by themselves. If a set asks the sex of a cousin and never states it, the answer is that it cannot be determined; candidates lose this mark by assuming from the name.
Direction Paths: Facing, Turning, and Net Displacement
Draw north up and east right, and mark the facing at every turn rather than the absolute direction — because "turns left" means left of where the walker is facing, and a walker facing south who turns left is going east. That single confusion accounts for most wrong answers in these sets. Then two facts finish the arithmetic. Movements along the same axis add or cancel, so the net displacement has only a north-south component and an east-west component. And the straight-line distance between start and finish is the hypotenuse of those two: √(x² + y²), which in CAT is nearly always a 3-4-5, 5-12-13 or 6-8-10 triangle by construction.
- Left turn while facing N, E, S, W gives W, N, E, S respectively; a right turn gives the reverse cycle. Write that cycle once at the top of the rough sheet.
- Two left turns, or two right turns, reverse the facing. Three left turns equal one right turn, which is how a set hides a simple path inside six instructions.
- Shadows fix direction by time of day. At sunrise the sun is in the east, so shadows fall west; at sunset they fall east. A set that says "his shadow fell to his left in the morning" has told you he faces north.
- "How far and in which direction from the start" needs both numbers. Candidates compute the distance and pick an option with the wrong quadrant; the direction is read off the signs of x and y, not off the last leg walked.
Coding: Find the Rule, Then Test It Before You Trust It
Every coding set is one question — what operation turns the plaintext into the code? — and there are only a handful of answers. Write the letter positions of both strings under each other and look at the difference row. A constant difference is a shift. A difference that alternates is a positional shift. A sum of 27 in every column is the mirror. If the letters are the same but rearranged, it is a transposition, and if the code is shorter or longer than the word, something has been added or dropped rather than transformed. The discipline that matters is the last step: having found a rule from one pair, apply it to a second pair before answering. A set will give you two examples precisely so that a rule fitting only the first fails.
| Rule | Signature in the difference row | Example |
|---|---|---|
| Constant shift | Same number in every column, forward or backward. | RAIN → SBJO is +1 on each letter. |
| Positional shift | Differences run 1, 2, 3, 4 or alternate +1, −1. | CAT → DCW is +1, +2, +3. |
| Mirror (opposite letter) | Every column sums to 27. | MAT → NZG, since M↔N, A↔Z, T↔G. |
| Transposition | Same letters, different order — no arithmetic at all. | TIME → EMIT is the reversal. |
| Substitution by meaning | Words map to unrelated words; find the pair common to two sentences. | "pit na so" and "na re ka" share na, so na is the shared word. |
Key takeaways
- Family-tree, direction and coding sets are the cheapest sets in DILR when they appear: one small object drawn in about ninety seconds, after which the four questions are lookups. Rank them above an arrangement set of the same length.
- One family-tree notation: a row per generation, = for a couple, a vertical line to children, + male, − female, ? when the sex is not stated. A generation error costs the whole set; a sex error costs one question.
- In direction sets, "left" is left of the current facing — facing south and turning left goes east. Net displacement is √(x² + y²), and the direction is read from the signs of x and y, not from the last leg walked.
- For coding, write letter positions and read the difference row: constant = shift, running = positional shift, columns summing to 27 = mirror, same letters = transposition. Then test the rule on the second pair before answering.
Practice questions (8)
Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.
Pointing to a photograph, Ravi says, "She is the only daughter of my grandfather's only son." Ravi has no siblings other than as implied. Who is she?
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Answer: B — His sister
Resolve the phrase from the inside out. Ravi's grandfather's only son must be Ravi's own father — Ravi is male and is his son, so no other son exists. The only daughter of Ravi's father is therefore Ravi's sister. "Mother" is the trap for a candidate who stops at "grandfather's son" and pairs the wrong generation; the mother is his father's wife, not his daughter. An aunt would be the grandfather's daughter, one generation higher than the phrase reaches. And a cousin would require an uncle, which "only son" has explicitly ruled out — that phrase is the set's way of closing the branch.A man walks 6 km north, turns right and walks 8 km, then turns right and walks 6 km. How far is he from the start, and in which direction?
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Answer: B — 8 km, east
Track the facing at each turn. He starts facing north; a right turn makes him face east, and a second right turn makes him face south. So the legs are 6 north, 8 east, 6 south — and the two 6 km legs cancel exactly, leaving a net displacement of 8 km due east. The 10 km north-east answer is what you get by applying Pythagoras to 6 and 8 without noticing the cancellation, which is why it is the most attractive wrong option here; the triangle is real but it belongs to a two-leg path. 14 km simply adds two legs, and 2 km north subtracts the wrong pair — the 8 km is on the other axis and cannot subtract from a north-south leg at all.If RAIN is coded as SBJO, how is CLOUD coded in the same scheme?
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Answer: A — DMPVE
Write the positions: R=18→S=19, A=1→B=2, I=9→J=10, N=14→O=15. The difference row is +1, +1, +1, +1, so the rule is a constant forward shift of one, and it holds in all four columns rather than in the first alone. Applying it to CLOUD gives D, M, P, V, E. BKNTC is the same shift in the wrong direction, which is the error a candidate makes by reading the difference row's sign carelessly. DNPWE shifts the second and fourth letters by two, a positional rule the first pair does not support. EMQVF shifts by two throughout, which fits no column of the given example.In a code, MAT is written as NZG. What is the rule?
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Answer: B — Each letter is replaced by its mirror letter, so the two positions sum to 27
Check the sums: M=13 with N=14 gives 27, A=1 with Z=26 gives 27, T=20 with G=7 gives 27. Every column sums to 27, which is the mirror rule — each letter is paired with the letter as far from the other end of the alphabet as it is from its own. The forward-shift option is true of the first column only, M to N, and it is the trap the set is built around: a rule found on one letter and never checked on the next two. Reversal would give TAM, and the code's letters are not the word's letters at all. A positional shift would need differences of 1, 2, 3, and the actual differences are +1, +25, −13.A person faces south, turns left, walks 4 km, turns left again and walks 3 km. Which direction is she now facing, and how far is she from the start?
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Answer: A — Facing north, 5 km away
Facing south, a left turn faces east — this is the step that decides the question, because left is relative to the walker and not to the map. She walks 4 km east. A second left turn from east faces north, and she walks 3 km north. The legs are on different axes, so nothing cancels, and the displacement is √(4² + 3²) = 5 km, with her facing north. "West, 7 km" comes from turning right instead of left and adding the legs. "North, 1 km" subtracts legs that lie on different axes and cannot be subtracted. "East, 5 km" has the arithmetic right and stops one turn early, which is the near-miss worth guarding against by writing the facing at every turn rather than only at the end.In a certain language, "pit na so" means "bring me water" and "na re ka" means "water is cold". Which word means water?
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Answer: B — na
The two sentences share exactly one code word, "na", and exactly one English word, "water", so na means water — that pairing of a single shared token on each side is the whole method for substitution sets, and it works without knowing anything about the language's word order. "pit" and "so" appear only in the first sentence, so nothing in the data distinguishes them from each other or fixes either to a meaning. The last option is the answer a candidate picks when they look for grammatical structure instead of counting overlaps; word order is unknowable here and irrelevant, because the intersection of the two sentences is unique.P is the brother of Q. R is the mother of Q. S is the father of R. T is the only child of S and R's only sibling is male. Which of the following cannot be determined?
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Answer: B — The sex of Q
Q's sex is never stated: P is Q's brother, which fixes P as male and says nothing about Q, and R being Q's mother is equally silent. So that is the undeterminable item, and the "?" symbol in the notation exists for exactly this. Everything else follows. S is R's father and R is P's mother — since P is Q's brother and R is Q's mother — so S is P's maternal grandfather, and R is P's mother. T is odd only in that the statement is contradictory-sounding: T is S's only child while R is S's child, so T must be R, which places T in R's generation; the "only sibling is male" clause is the distractor that tempts you to invent a fourth person. Reading the sex of Q off the name or off P's being a brother is the error the whole set is built to punish.You have read all four sets in a DILR section: an eight-condition seating arrangement, a two-table data set with a footnote, a coding set with two worked examples, and a tournament set whose scoring rule you must infer. In what order should you attempt them?
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Answer: A — Coding, then the two-table data set, then the seating arrangement, and the tournament set last or not at all
Rank by time to a solved object, not by apparent difficulty or by marks, since every set is worth the same. The coding set has two examples, which means the rule is checkable and the set is closed in about two minutes. A two-table set with a footnote is next: reading is the work, and the footnote usually is the question. An eight-condition arrangement is solvable but slow and can collapse if one condition is misread. A set whose scoring rule must be inferred is the one that can consume fifteen minutes and yield nothing, so it goes last. Attempting in screen order ignores the only lever the section gives you. And more conditions do not mean a faster set — they mean a longer one, even when they do pin the arrangement down.