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CAT (Common Admission Test) · Data Interpretation & Logical Puzzles

Blood Relations and Direction Sense

Family-tree relationship chains and directional distance tracking.

Seven concepts. Family trees and coded chains pin who is who; signed legs and facing-relative turns pin where you stand — both fail when you reason in words alone or treat every turn as if you still faced North.

  • CAT (Common Admission Test)
  • Easy level
  • 7 concepts
  • 17 practice questions

1Draw the family tree

Blood-relation stems are chains of parent, sibling and spouse links. Tracking them only in words mixes generations and invents genders the stem never stated. Draw a tree: elders on an upper generation, children one level down, a marriage link between spouses, and a shared parent hub for siblings. Resolve each phrase in the stem into one of those links before you name the asked relation.

Gender belongs on a node only when the stem or a gendered word (father, mother, brother, sister, son, daughter) forces it. A word like cousin or sibling leaves sex open — do not fill it in to make the tree look complete.

Figure. P sits one generation above Q; Q and R share a marriage link on the middle layer; S drops from both. The asked relation is the path P → Q → S.

Order of attack

  1. Anchor the eldersPlace the oldest generation first (grandparents, or whoever the stem names as parents of the rest). Every later person hangs from a parent–child link off that layer.
  2. Add marriages and siblingsSpouses share a generation; siblings share a parent hub on the generation above. Horizontal placement is schematic — only generation and link type are load-bearing.
  3. Read the asked edgeOnce every phrase is a link, the question is a path between two named nodes. Walk the path and name the relation; if a gender was never forced, leave the answer gender-neutral when the options allow it.

Three-generation sketch

P is the father of Q. Q is married to R. R is the mother of S. How is P related to S?

  • P father of QP (male) one generation above Q
  • Q married to R; R mother of SR female spouse of Q; S child of Q and R
  • Path P → Q → SP is grandfather of S

Pro tip. Marriage keeps Q and R on the same generation; the parent–child drop to S is what makes P a grandfather, not an uncle.

A stem says X is a sibling of Y, and Y is female. What must be true of X?
  1. X is male
  2. X is female
  3. X shares a parent with Y; sex of X is not forced
  4. X is one generation above Y

Sibling fixes the shared-parent link and the same generation. It does not state X's sex — filling male or female is the assumption trap.

2Self-reference phrases

Photo and pointing puzzles hide the speaker inside a phrase. 'Only son of my father' names the male speaker himself, and 'only daughter of my mother' names the female speaker herself — not a sibling waiting off-stage. Resolve that phrase to a definite person first; the rest of the chain is ordinary parent and child links.

Longer wording needs the same collapse, but only when the stem forces a unique person. Prefer chains through 'my father' / 'my mother' that pin the speaker; a bare 'only son of my grandfather' forks into father versus maternal uncle unless the stem rules the uncle out.

Figure. Collapse 'only son of my father' to the speaker first; the woman is then his daughter.

Order of attack

  1. Name the speakerMark who is speaking or pointing. Every 'my' in the stem is from that person.
  2. Collapse self-referenceRewrite 'only son of my father' / 'only daughter of my mother' as the speaker. Do not collapse 'only son of my grandfather' to 'father' unless the stem forces the speaker onto that son's line (a daughter of the grandfather would make the only son a maternal uncle).
  3. Chain the remainderWith the phrase replaced by a person, walk the remaining daughter / son / sibling links to the person in the photo.

Photo blood relation

Pointing to a photograph, a man says, 'She is the daughter of the only son of my father.' How is the woman related to the man?

  • 'Only son of my father'the man himself
  • 'Daughter of [the man]'the man's daughter
  • Asked relationdaughter

Pro tip. If the first ledger row still says 'father's son' instead of the speaker, you have not collapsed the self-reference — and that is where the trap lives.

A man says, 'He is the only son of my father.' Who is 'he'?
  1. The man's brother
  2. The man himself
  3. The man's father
  4. The man's uncle

'Only son of my father' is the speaker when the speaker is male. A brother would mean the father had more than one son, which the word only forbids.

3Coded relation chains

Some stems replace plain English with operator codes: A × B might mean A is the mother of B, and B − C might mean B is the brother of C. Decode each operator into an ordinary relation first, then chain the people left to right (or from an inner pair outward) until the asked link is named.

Do not invent a meaning for an operator the stem did not define. The code key is local to the question — a × that meant mother here is not a universal symbol.

Figure. After decoding, A sits above siblings B and C. The expression A × B − C asks for A's link to C — mother.

Decode then chain

  1. Write the keyCopy every operator definition from the stem into a one-line glossary before you touch the expression.
  2. Decode each pairReplace A × B with 'A is mother of B', and so on, until the expression is a short English chain.
  3. Name the asked linkWalk the chain to the person named in the question. Siblings of a child of A are also children of A when the marriage or single-parent link is forced.

Coded blood relation

If A × B means A is the mother of B, and B − C means B is the brother of C, then what is A in 'A × B − C'?

  • A × BA is the mother of B
  • B − CB is the brother of C (B and C siblings)
  • A mother of B; B sibling of CA is the mother of C

Pro tip. Once B and C are siblings and A is mother of B, A is mother of C as well — the code never needed a separate 'mother of C' operator.

If P ÷ Q means P is the father of Q, and Q + R means Q is the sister of R, what is P to R in 'P ÷ Q + R'?
  1. Brother
  2. Father
  3. Uncle
  4. Grandfather

P ÷ Q → P is father of Q. Q + R → Q is sister of R, so Q and R are siblings. Therefore P is also father of R.

4Turns are relative to facing

Direction puzzles give you a starting facing and a list of walks separated by turns. Each walk goes in the direction you are facing at that moment — not necessarily North — and a left or right turn rotates that facing before the next leg. The clockwise cycle when you keep turning right is North → East → South → West → North, so a right turn from West points you North, not South; treating every right turn as toward East on the page is the common failure.

Track each leg as signed displacement: east is positive horizontal, north is positive vertical. Update facing after every turn, then add the next leg along the new heading. When the question asks for straight-line distance from the start, combine the net east–west and north–south totals — often with \sqrt{x^2 + y^2} when the path bends at right angles.

Figure. Schematic compass path with segment lengths to scale (4 : 3 : 4). Four west and four east cancel, leaving a 3 km northward offset. Both right turns are read from current facing — the first from West lands on North, not South.

Order of attack

  1. Anchor facingWrite the starting direction before the first leg. Every later turn is measured from whatever you are facing now, not from North.
  2. Turn, then walkRight means clockwise on the compass cycle N → E → S → W; left is anticlockwise. Only after the facing updates do you lay down the next distance along that heading.
  3. Sum displacementsEast and west cancel; north and south cancel. The remaining pair is the net offset from the start, and its length is the shortest distance when that is what the question asks for.

Two right turns from West

A person starts facing West. She walks 4 km, turns right and walks 3 km, turns right again and walks 4 km. How far is she from the start?

  • Facing West; walk 4 km along headingdisplacement (−4, 0) km
  • Right from West → North; walk 3 km(−4, +3) km
  • Right from North → East; walk 4 km(0, +3) km
  • Net offset; straight-line distance3 km north of start

Pro tip. After the first right turn she is facing North, not South — that single mis-read sends the second leg downward and destroys the east–west cancellation that makes the answer a clean 3 km.

A walker is facing West. She turns right. Which direction is she now facing?
  1. North
  2. South
  3. East
  4. West

Right is clockwise on the facing cycle, so West → North. South would be a left turn from West, and East would mean she never turned at all.

5Signed net displacement

When every leg is already named by compass direction — East, North, West, South — you do not need a facing story. Place North up and East right, assign east positive x and north positive y, and add each leg as a signed pair. The net position is the vector sum of those pairs.

Shortest distance back to the start is the length of that net vector: d = \sqrt{x^2 + y^2}. Perpendicular legs (pure east then pure north) are a right triangle whose hypotenuse is that d.

Figure. East and north legs meet at a right angle and are drawn to scale (5 : 12); the dashed resultant is the 13 km straight-line distance from the start.

Order of attack

  1. Sign the axesEast +, west − on x; north +, south − on y. Write every leg once in that convention.
  2. Sum componentsAdd all x contributions and all y contributions separately. Opposite directions cancel inside each sum.
  3. Take the resultantIf the question wants straight-line distance, compute \sqrt{x^2 + y^2}. If it wants direction from the start, read the signs of the surviving x and y.

Direction distance

A person walks 5 km East, then 12 km North. How far is she from the starting point?

  • Net x (east–west)5 km
  • Net y (north–south)12 km
  • d = \sqrt{5^2 + 12^2} = \sqrt{25 + 144}\sqrt{169} = 13 km

Pro tip. Perpendicular legs form a 5–12–13 right triangle — recognise the triple before expanding the square root when the numbers invite it.

A walk ends with net displacement 9 km West and 12 km South. Straight-line distance from the start is
  1. 3 km
  2. 15 km
  3. 21 km
  4. 108 km

d = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15 km. Signs set the quadrant (south-west) but do not change the distance.

6Generations on the tree

Each parent–child link is one generation down. Siblings share a generation, and spouses share a generation with each other. Counting how many parent–child drops separate two people is how you decide grandfather versus father, uncle versus brother, and cousin versus sibling — words that look similar in prose but sit on different layers of the tree.

A person two parent–child links above you is a grandparent; one link above is a parent. Horizontal moves (sibling, spouse) never change the generation count.

Imagine the family tree sketch with layer numbers: elders at the top (layer 0), each parent–child edge dropping one layer, spouses and siblings staying put.

How it works

  1. Mark layersAssign generation 0 to the oldest person named, then +1 for each parent–child drop.
  2. Park spouses and siblingsAnyone married to a person on layer k, or sharing parents with them, also sits on layer k.
  3. Name from the gapA gap of one layer is parent/child (or in-law of that layer); a gap of two is grandparent/grandchild. Same layer with a shared parent is sibling.

Layer gap

M is the mother of N. N is the father of O. O is the sister of P. How many generations separate M from P?

  • M mother of NM on layer 0; N on layer 1
  • N father of OO on layer 2
  • O sister of PP on layer 2 with O
  • Layer gap M → P2 generations (M is grandmother of P)

Pro tip. The sister link parks P on O's layer — it does not add a third drop under M.

A is the brother of B. B is the mother of C. A's generation relative to C is
  1. Same generation as C
  2. One generation above C
  3. Two generations above C
  4. One generation below C

A and B share a generation; B is one parent–child link above C; so A is also one generation above C (maternal uncle).

7Facing sets left and right

When a stem asks which way a person's right hand points, or where a shadow falls at sunrise, left and right are body sides of that person — fixed by the direction they face. A walker facing West has the right hand toward North and the left hand toward South. Reading those sides from your own seat at the page, without rotating into their facing, flips the answer.

The same mirror appears when someone faces you: their left is on your right. Update facing first, then name the hand or the turn.

Figure. Facing arrow points West; the right-hand arrow is 90° clockwise on the compass, toward North.

Order of attack

  1. Fix their facingWrite the compass direction the person faces before naming any hand or 'to the right of'.
  2. Rotate the body frameRight is 90° clockwise from facing on the compass cycle; left is 90° anticlockwise. Facing West → right = North, left = South.
  3. Apply the askMap the hand, shadow, or neighbour onto that body frame. If they face you, swap left/right relative to your own.

Right hand at West

A man is facing West. In which direction is his right hand pointing?

  • FacingWest
  • Right = 90° clockwise from facingWest → North
  • Right-hand directionNorth

Pro tip. Sunrise shadows fall west of a person; combining that with a facing-West right-hand check is a common two-step exam item — facing still comes first.

A woman faces East. Which direction is to her left?
  1. East
  2. West
  3. North
  4. South

Left is 90° anticlockwise from facing: East → North. South would be her right.

Notes

  • Blood Relations - Diagram Method: Draw a family tree using symbols for gender, marriage, and parent-child links; never track long chains in words. Resolve each relational phrase into a link on the tree.
  • Coded Relation Chains: When relations are given as operator codes (A×B, A÷B), decode each operator, then read the chain left to right to find the final relationship.
  • Direction Sense - Coordinate Tracking: Set North up, East right; represent each move as a signed displacement and update the facing after every turn. Net position gives distance and direction.
  • Turn Handling: A left or right turn is relative to the current heading, not to North; always update the heading before the next leg.
  • Common trap: Ignoring the person's facing when interpreting 'to the right' in direction puzzles, or assuming gender in blood relations that is not stated.

Formulas

  • Shortest distance = \sqrt{x^2 + y^2} from net east-west (x) and north-south (y) displacements.
  • Clockwise turn cycle facing North: N -> E -> S -> W -> N.
  • 'Only son of my father' = the male speaker himself; 'only daughter of my mother' = the female speaker herself.
  • Each parent-child link is one generation; siblings and spouses share a generation.
  • Net displacement = vector sum of all legs (add signed components).

Exam traps & shortcuts

  • Sketch the family tree with standard symbols rather than reasoning in prose.
  • Decode coded relations from the rightmost operator inward to name the final relation.
  • Track direction moves on signed axes and sum components for the resultant.
  • Update facing after each turn before applying the next left/right instruction.

Reference tables

Collapse the phrase to a person before chaining any further relation.

Self-reference cheat sheet
PhraseResolves toWatch for
Only son of my fatherMale speaker himselfNot a brother
Only daughter of my motherFemale speaker herselfNot a sister
Only son of my grandfatherSpeaker's father only if speaker is on that son's lineElse maternal uncle — stem must force the fork
Daughter of my father's only sonSpeaker's daughter if speaker is that only sonCollapse 'father's only son' first

Count parent–child drops; ignore horizontal sibling and spouse moves.

Generations cheat sheet
LinkGeneration changeTypical name
Parent → childDown 1Father / mother / son / daughter
Grandparent → grandchildDown 2Grandfather / granddaughter
Sibling0Brother / sister
Spouse0Husband / wife on same layer

Right is clockwise on N → E → S → W; left is anticlockwise. Hands follow the same body frame.

Facing and turns
FacingRight turn / right handLeft turn / left hand
NorthEastWest
EastSouthNorth
SouthWestEast
WestNorthSouth

Recap

Night-before pegs for blood relations and direction sense.

Tree first
Every blood-relation chain becomes parent, sibling or spouse links on a sketched tree — never a paragraph of pronouns.
Self-reference
'Only son of my father' is the male speaker; collapse that phrase before you walk the rest of the photo stem. Do not force 'only son of my grandfather' to father when a maternal-uncle reading remains open.
Codes
Decode each operator to plain English, then chain — A mother of B and B brother of C makes A mother of C.
Facing before turn
Left and right rotate the current heading; a right from West lands on North, and that person's right hand also points North.
Net vector
Sum signed east–west and north–south; shortest distance is \sqrt{x^2 + y^2} (5–12–13 when the legs invite it).

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