Quick Summary: Puzzles, Seating Arrangement, Blood Relations and Direction Sense give 1 to 3 marks in GATE General Aptitude 2027 across every paper (DA, RA, CS, ME, EE, CE, EC). They are the reasoning questions that look long but are mechanical once you know the drill: fix a reference, convert every clue into a position or a relation, and eliminate. This guide gives you the circular and linear arrangement method (with the left-right convention that trips most students), the family-tree notation for blood relations, the coordinate method for direction sense, 8 solved previous-year and GATE-style questions, two diagrams, a 5-question practice set and a one-page rule sheet.
📋 Table of Contents
Why this topic matters in GATE GA
GATE does not ask the ten-clue, eight-person seating monsters that bank exams love. It asks one clean puzzle with three to five clues, and it expects you to finish it in two minutes. Six people around a table, a row of five boxes, a walk with four turns, a two-line family statement: that is the GATE size. The questions are usually 2-mark, which makes them the most valuable reasoning questions in the section.
Students lose these marks for two reasons. First, they try to hold the whole arrangement in their head instead of drawing it in ten seconds. Second, they apply the wrong convention: “left” around a table depends on which way people face, and “right turn” while walking depends on the direction you are currently facing. This chapter fixes both habits.
Here is roughly how much the cluster has contributed. Candidates targeting 15/15 in GA should finish any puzzle here in two minutes with a diagram.
| Year | Marks from this topic (approximate, across papers) | Typical question type |
|---|---|---|
| 2019 | 1 to 3 | Ordering five people by clues, direction walk |
| 2020 | 1 to 2 | Scheduling puzzle, blood relation |
| 2021 | 2 to 3 | Circular table with handedness, distance between points |
| 2022 | 1 to 3 | Linear row with conditions, family tree |
| 2023 | 1 to 2 | Direction after several turns |
| 2024 | 2 to 3 | Seating with opposite pairs, ranking puzzle |
| 2025 | 1 to 3 | Floors in a building, relation chain |
| 2026 | 1 to 2 | Circular seating, shortest distance |
What the official GA syllabus says
Puzzles, arrangements, blood relations and direction sense are not named individually; they sit under “reasoning” in Analytical Aptitude, and direction questions border on Spatial Aptitude. The previous post covered Analogy, Series and Numerical Relations, and the next post begins the spatial section with 2D Transformations and Mirror Images. The complete syllabus and weightage are in the GATE General Aptitude 2027 hub.
Circular seating arrangement
The method has four steps and never changes:
- Draw the table with the given number of seats as dots, numbered clockwise.
- Fix the convention. When everybody faces the centre, a person’s left is clockwise and right is anticlockwise (imagine yourself at the top seat facing down into the table: your left hand points to the seat on the screen’s right, which is the next seat clockwise). When people face outward, it reverses. If the question says nothing, assume facing the centre.
- Start with the strongest clue: an “opposite” pair or an “immediate left/right” pair. Place it first. Clues with “not” come last; they only eliminate.
- Place, check every clue once, answer. Do not answer from a half-filled diagram.
Two facts worth memorising: with n seats, the person opposite seat k is seat k + n/2 (only when n is even). “Second to the left of X” means two seats clockwise from X, skipping one.
Solution: Number the seats 1 to 6 clockwise and put A in seat 1. Opposite of 1 is seat 4, so D = 4. Immediate left of A is clockwise, seat 2, so B = 2. Opposite of 2 is seat 5, so C = 5. Immediate right of D is anticlockwise from seat 4, which is seat 3, so E = 3. The only seat left is 6, so F = 6. Seat 6 lies between seat 1 (A) and seat 5 (C).
Answer: F sits between A and C.
Linear arrangement and ordering puzzles
Rows, stacks, floors, schedules and rankings are all the same puzzle: n items into n ordered slots. The method:
- Draw the slots and number them. For a row facing north, left is the lower number. For a stack of floors, the ground floor is 1 and numbers increase upward. For a schedule, slot 1 is first.
- Translate each clue into one of three forms: fixed (X is at slot 3), relative (X is immediately before Y, written as the block XY), or negative (X is not at an end).
- Place fixed clues, slide blocks into the remaining space, use negatives to kill cases. If two cases survive, look for the clue you have not used yet; GATE always provides exactly enough.
- For “between” clues, “Q is between P and S” usually means immediately between in GATE; if a case needs the looser reading, the question says “somewhere between”.
Solution: Slots from top: 1 = English, 5 = Maths. Physics, Biology and Chemistry fill slots 2, 3, 4. Biology is immediately below Physics, so they form the block Physics-Biology. Chemistry is below Physics, so Chemistry cannot be slot 2. The block must be slots 2 and 3, Chemistry slot 4.
Answer: Biology.
Solution: The block NO can sit in slots 1-2, 2-3 or 3-4. Slots 2-3: M and P take 1 and 4; M is not first, so M = 4 and P = 1, but P must be after M. Rejected. Slots 3-4: M and P take 1 and 2; M = 2, P = 1, again P before M. Rejected. Slots 1-2: M and P take 3 and 4; M = 3, P = 4 satisfies everything.
Answer: N, O, M, P.
Blood relations
A blood-relation question is a chain of relations compressed into one sentence. Decode it from the innermost phrase outward, replacing each phrase with a single person. The phrases that collapse immediately:
| Phrase | Means |
|---|---|
| The only son of my father | Myself (if I am male) or my only brother (if I am female) |
| The only daughter of my mother | Myself (if female) or my only sister (if male) |
| My father’s father’s only son | My father |
| My mother’s only brother | My maternal uncle |
| The wife of my father’s son (not me) | My sister-in-law |
| The son of my grandfather’s only child | My brother or myself |
When a question gives several short statements (A is B’s sister, C is B’s mother), draw a family tree: one row per generation, a horizontal line for a married couple, vertical lines for children, and a small mark for gender. The relation you are asked for is then read straight off the tree. The gender of the speaker matters: “the only son of my father” is “myself” only if the speaker is male, so look for a gender clue (“he said”, “she said”).
Solution: Innermost: “my father’s father” is Rahul’s grandfather. “The only son of my grandfather” is Rahul’s father (Rahul’s father is a son of the grandfather, and there is only one). “The daughter of my father” is Rahul’s sister.
Answer: She is Rahul’s sister.
Solution: Tree: E (top), her son D, his daughter C, her children A and B. A is a daughter of C, and C is a daughter of D, so A is D’s granddaughter. E is irrelevant to the question.
Answer: Granddaughter.
Direction sense and distance
Treat the walk as moves on a coordinate grid: east is +x, north is +y. Start at the origin, apply each leg as a vector, and the final position gives both the distance (Pythagoras) and the direction from the start. This replaces every “turn right, turn left” headache with arithmetic.
- Turning: facing N, a right (clockwise) turn gives E, then S, then W. A left turn goes the other way. A 180° turn reverses. For 45° turns, use the eight-point compass: N, NE, E, SE, S, SW, W, NW in clockwise order, each step 45°.
- Net displacement: add all east legs and subtract west legs for x; add north and subtract south for y. Distance from start = √(x2 + y2). The direction is read from the signs: x > 0 and y < 0 is south-east, and so on.
- Common triples that give integer distances: (3, 4, 5), (6, 8, 10), (5, 12, 13), (8, 15, 17).
- Shadows: in the morning the sun is in the east, so shadows point west; in the evening they point east. If a man’s shadow falls to his right in the morning, his right points west, so he faces south.
Solution: North 5: position (0, 5). Facing north, a right turn faces east; 3 km east: (3, 5). Right turn faces south; 9 km: (3, −4). Right turn faces west; 6 km: (−3, −4). Distance = √(32 + 42) = √25 = 5 km. x is negative (west) and y is negative (south).
Answer: 5 km, south-west of O.
Shortcuts and traps
❌ Treating “second to the left” as the adjacent seat. It skips one seat.
❌ Turning relative to north every time instead of relative to the current facing direction.
❌ Reporting the total path length when the question asks the distance from the start.
❌ Assuming “the only son of my father” is “myself” when the speaker is a woman.
❌ Forgetting that a row “facing south” flips left and right compared with facing north.
❌ Answering from a diagram that has not been checked against every clue.
Solved previous-year and GATE-style questions
Years are given only where I am confident the question appeared; the rest are built to the same pattern. Many more are solved in the PiyushAI Aptitude Test Series with video explanations.
Solution: Arun’s distance d satisfies 5 < d < 7. Only 6.02 lies in that open interval; 4.99 is below 5 and 7.01 is above 7. Michael’s distance is a distractor.
Answer: (C) 6.02.
Solution: All women are left-handed. At least 3 of the 6 are right-handed, so at most 3 are left-handed. Suppose there are 3 women. Then all 3 left-handed people are the women, so each woman’s immediate right neighbour (left-handed) is also a woman. Starting from any woman and stepping to the right you would never leave the women, which is impossible when only 3 of the 6 seats are women. So there cannot be 3 or more women. With 2 women: seat them adjacent, say W1 with W2 to her immediate right, and a left-handed man to the immediate right of W2. That is 3 left-handed, 3 right-handed, all conditions met.
Answer: 2.
Solution: Put N at the origin. M = (0, 4). N is 1 km south-east of O, so O is 1 km north-west of N: O = (−1/√2, 1/√2) = (−0.707, 0.707). P is 2 km south of O: P = (−0.707, −1.293). MP: horizontal gap 0.707, vertical gap 4 + 1.293 = 5.293. Distance = √(0.7072 + 5.2932) = √(0.5 + 28.02) = √28.52 = 5.34.
Answer: (A) 5.34.
Solution: Seats 0 to 7 clockwise, T at 0, left = clockwise. Y and V occupy 1 and 7 in some order. Z is third to the left of T: seat 3. Z is second to the right of S, so S is two seats clockwise from Z: seat 5. U is adjacent to S (seat 4 or 6) and to Y (seat 1 or 7); the only way is U = 6, Y = 7, so V = 1. W and X take seats 2 and 4. Opposite T (seat 0) is seat 4, and W is not opposite T, so W = 2 and X = 4. Third to the left of V (seat 1) is seat 4.
Answer: X. (The answer is the same if you take left as anticlockwise; the arrangement simply mirrors.)
Solution: “The only daughter of my father” is the speaker herself (she is a daughter of her father, and there is only one). So the man’s wife is the speaker.
Answer: He is her husband.
Solution: Slots 1 (left) to 5 (right). Case R = 1: T is not in slot 2, so T is in 3, 4 or 5; the block P-Q-S (in either order) needs three consecutive slots among 2 to 5. If the block is 2-4 then T = 5; if the block is 3-5 then T = 2, which is adjacent to R, rejected. So T = 5, block in 2-4, and P adjacent to T puts P = 4, Q = 3, S = 2: order R, S, Q, P, T, with S left of Q as required. Case R = 5: T cannot be in slot 4, so T = 1 and the block fills slots 2 to 4; P adjacent to T forces P = 2, Q = 3, S = 4, but then S is to the right of Q. Rejected. Unique arrangement: R, S, Q, P, T.
Answer: Q is in the middle; T is at the right end.
Solution: Measure clockwise from north. Start 0°. After +90°: 90° (east). After −135°: −45°, which is 315° (north-west). After +180°: 495°, which is 135° (south-east).
Answer: South-east.
Solution: Compliance = 2. The block Admin-Billing (Admin below) needs two consecutive floors from {1, 3, 4, 5} without using 2: only 3-4 works, so Admin = 3, Billing = 4. Design and Engineering take floors 1 and 5; Engineering is above Design and on an odd floor, so Engineering = 5, Design = 1.
Answer: Engineering.
★ PiyushAI Test Series
Best GATE Aptitude Test Series 2027
General Aptitude is 15 marks in every GATE paper and the easiest 15 marks to lose to silly mistakes. The PiyushAI Aptitude Test Series by Piyush Wairale (IIT Madras) gives you topic-wise tests on exactly this chapter, full-length GA mocks in the real GATE interface, detailed video and text solutions, and All-India rank analysis.
Practice set
Attempt these in 8 minutes before opening the key.
- A cyclist rides 4 km east, turns left and rides 3 km. How far and in which direction is she from the start? (A) 7 km, north-east (B) 5 km, north-east (C) 5 km, south-east (D) 1 km, north
- Pointing to a man, Sita said, “His mother is the only daughter of my mother.” How is the man related to Sita? (A) Brother (B) Nephew (C) Son (D) Cousin
- Six people A, B, C, D, E and F sit around a circular table facing the centre. A is opposite D. B is to the immediate left of D. C is to the immediate right of A. E is opposite C. Who is to the immediate left of A? (A) B (B) E (C) F (D) C
- In a row of five chairs facing north, V sits at the left end. W is not adjacent to V. X sits between V and W, with exactly one chair between X and W. Y sits immediately right of W. Who sits at the right end? (A) Y (B) Z (C) W (D) X
- A wall clock reads 3:00 and its minute hand points east. In which direction does the hour hand point? (A) North (B) South (C) West (D) East
Show answer key
- (B). Facing east, a left turn faces north. Position (4, 3); distance √(16 + 9) = 5 km; x and y positive, so north-east.
- (C). “The only daughter of my mother” is Sita herself. The man’s mother is Sita, so he is her son.
- (C). A = 1, D = 4. Immediate left of D is clockwise, seat 5, so B = 5. Immediate right of A is anticlockwise, seat 6, so C = 6. E opposite C is seat 3, so F = 2. Immediate left of A is seat 2: F.
- (A). V = 1. One chair between X and W: X = 3 would put W = 5 and leave no chair for Y on the right, so X = 2, W = 4 (not adjacent to V, as required), Y = 5 and Z = 3. The right end is Y.
- (B). At 3:00 the hour hand is 90° clockwise from the minute hand. 90° clockwise from east is south.
One-page rule sheet
2. With n seats (n even), opposite of seat k is seat k + n/2. “Second to the left” skips one seat.
3. Place the first person at the top and keep them fixed; start with opposite and immediate-neighbour clues; use “not” clues last.
4. Linear: number the slots; translate clues to fixed, block or negative form; slide blocks, kill cases.
5. Row facing south: left and right are swapped relative to the page.
6. Blood relations: resolve the innermost phrase first. “Only son of my father” = me (male speaker) or my brother (female speaker).
7. Draw a family tree for multi-statement questions: generations in rows, couples joined horizontally.
8. Direction: east +x, north +y; add legs as vectors; distance = √(x2 + y2); direction from the signs.
9. Turns are relative to the current facing: clockwise N to E to S to W; 45° steps on the eight-point compass.
10. Pythagorean triples: (3, 4, 5), (6, 8, 10), (5, 12, 13), (8, 15, 17).
11. Morning shadows point west, evening shadows point east.
12. Check the finished diagram against every clue before answering.
Common mistakes
❌ Confusing clockwise with left when people face outward or when the question says “facing away from the centre”.
❌ Taking “P is between Q and R” as immediate when the question allows gaps, or the reverse; read the exact wording.
❌ Resolving a blood-relation sentence from the left instead of from the innermost phrase.
❌ Ignoring the gender of the speaker.
❌ Adding up the legs of a walk and reporting the path length instead of the straight-line distance.
❌ Turning relative to north instead of relative to the current heading.
FAQs
How many puzzle and arrangement questions appear in GATE GA?
Usually 1 question, sometimes 2, and it is often a 2-mark question. Across papers the cluster contributes 1 to 3 marks a year.
Which left-right convention does GATE use for circular seating?
Unless stated otherwise, people face the centre, so left is clockwise and right is anticlockwise. In most GATE questions the final answer is the same under either convention because the arrangement simply mirrors, but draw it the standard way anyway.
Do I need bank-exam level practice for seating puzzles?
No. GATE puzzles have 4 to 8 people and 3 to 5 clues. Practise speed and accuracy on GATE-size puzzles rather than ten-clue bank puzzles.
Is the PiyushAI Aptitude Test Series enough for GA?
Yes. The Best GATE Aptitude Test Series 2027 has dedicated tests on puzzles, arrangements, blood relations and direction sense, tests on every other GA chapter, full-length GA mocks in the GATE interface, solved PYQs from 2010 to 2026 and All-India rank analysis. With the free guides on this site it covers the whole GA section.
How should I handle a direction question with diagonal moves?
Resolve each diagonal leg into x and y components (a north-east leg of d km is d/√2 east and d/√2 north), add the components, and apply Pythagoras at the end.
Stop losing easy marks. Practise this topic under exam pressure.
Previous in series: Analogy, Series & Numerical Relations for GATE Aptitude 2027 | Next in series: 2D Transformations for GATE Spatial Aptitude 2027: Rotation, Reflection, Mirror & Water Images
Related guides: GATE General Aptitude 2027 hub | All GATE General Aptitude articles | GATE DA Syllabus 2027 | GATE RA Syllabus 2027
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