Verbal, Non-verbal and Spatial Reasoning

1. Chapter at a Glance

The Reasoning and Military Aptitude Test section of AFCAT has 20–25 questions and decides many final merit positions, because well-prepared candidates score almost full marks here. The same skills appear in the Officer Intelligence Rating (OIR) test on day one of the SSB, where verbal and non-verbal reasoning decide whether you are screened in. The section has two parts: verbal reasoning (analogy, classification, series, coding, blood relations, directions, syllogisms, arrangements) and non-verbal / spatial reasoning (figure series, mirror and water images, embedded figures, paper folding and cutting, dice, cubes, pattern completion). "Military aptitude" in AFCAT is essentially spatial ability and quick logical judgement.

2. Analogy and Classification

In an analogy (A : B :: C : ?) find the exact relationship between A and B, then apply it to C. In classification (odd one out), find the common property of three and the exception.

3. Number and Letter Series

• Check the differences first (constant, increasing, squares, alternate). Then check ratios (×2, ×3, ×2 + 1). Then squares and cubes (n², n³, n² ± 1). Then mixed or alternate series.
• Example: 2, 6, 12, 20, 30, ? — differences 4, 6, 8, 10, so the next is 30 + 12 = 42 (also n(n + 1)).
• Example: 3, 7, 15, 31, 63, ? — each term ×2 + 1, so 127.
• Letter positions: A = 1 … Z = 26; reverse positions: A = 26 … Z = 1. Remember "EJOTY" = 5, 10, 15, 20, 25.
• Letter series: Z, X, U, Q, ? — positions 26, 24, 21, 17 (−2, −3, −4), so next −5 → 12 = L.

4. Coding and Decoding

• Letter shifting: ARMY → BSNZ (each letter +1). Check whether the shift is constant, alternating or increasing.
• Reverse coding: the word is written backwards, sometimes with a shift: NAVY → YVAN.
• Opposite letters: A↔Z, B↔Y … (pairs add to 27): FLY → UOB.
• Number coding: each letter replaced by its position, or the sum of positions: CAT = 3 + 1 + 20 = 24.
• Substitution coding: "If sky is called water and water is called road, what do we drink?" — we drink water, which is called "road". Answer with the code word, not the real word.

5. Blood Relations

• Draw a family tree: males as squares (or +), females as circles (or −), marriage as a double line, generations stacked vertically.
• Key terms: mother's or father's sister's son — cousin; brother's son — nephew; sister's husband — brother-in-law; son's son — grandson; daughter's son — grandson (daughter's son is called "nati" in Hindi).
• Pointing-to-a-photo questions: start from the speaker ("my") and move step by step. "He is the son of my father's only son" → the speaker himself is the father's only son, so "he" is the speaker's son.
• Gender cannot be assumed from a name; if it is not given, the answer may be "cannot be determined".

6. Direction Sense

• Right turn = 90° clockwise; left turn = 90° anticlockwise; "about turn" = 180°.
• Example: walk 6 km south, turn left and walk 8 km → facing east; distance from start = √(36 + 64) = 10 km towards the south-east.
• Shadow questions: in the morning the sun is in the east, so shadows fall to the west; in the evening they fall to the east. At noon there is almost no shadow.

7. Syllogisms, Statements and Arrangements

• Use Venn diagrams. "All A are B" — A inside B. "Some A are B" — overlapping circles. "No A is B" — separate circles.
• Rules: two "some" statements give no definite conclusion; a "no" statement with "all" gives a negative conclusion; "Some A are not B" is the only way to express partial exclusion.
• Complementary pair: when neither conclusion follows individually but one of them must be true ("Some A are B" / "No A is B"), the answer is "either I or II follows".
• Statement–assumption: an assumption is something the speaker takes for granted. Statement–course of action: choose actions that are practical and directly address the problem.
• Seating arrangement: draw the line or circle first; place fixed persons (ends, middle, "opposite"), then fill relative positions. In a circle with people facing the centre, the left of a person is clockwise.
• Ranking: total = rank from top + rank from bottom − 1.

8. Clocks and Calendars

• Angle between the hands = |30H − 5.5M| degrees. The hands coincide 11 times in 12 hours and are at right angles 22 times in 12 hours.
• Mirror image of a clock time: subtract from 11:60 (3:00 appears as 9:00; 2:40 appears as 9:20).
• Odd days: an ordinary year has 1 odd day, a leap year 2. A century year is a leap year only if divisible by 400 (2000 was, 1900 was not).
• The same calendar repeats after 28 years in most cases; an ordinary year's calendar often repeats after 6 or 11 years.

9. Non-Verbal and Spatial Reasoning (Military Aptitude)

• Figure series: identify the element that changes — rotation (45°, 90°), number of lines or dots, shading, or movement of a symbol around the corners.
• Mirror image: left and right are interchanged, top and bottom stay. Water image: top and bottom are interchanged, left and right stay.
• Embedded figures: the given simple figure must appear exactly, same size and orientation, inside the complex figure.
• Paper folding and cutting: unfold step by step; each fold doubles the number of holes; holes appear symmetrically about the fold line.
• Dice: on a standard die, opposite faces add to 7 (1–6, 2–5, 3–4). If two positions share a common face, the faces in the same relative position are opposite to each other.
• Cubes: a cube painted on all faces and cut into n³ small cubes gives 8 cubes with three faces painted, 12(n − 2) with two, 6(n − 2)² with one and (n − 2)³ with none.
• Counting figures: if a triangle is divided by n straight lines drawn from one vertex to the opposite side, the number of triangles = (n + 1)(n + 2)/2 (two lines give 6 triangles). For other figures, count systematically by size — single pieces first, then combinations.

10. Data Sufficiency, Statement Analysis and Decision Making

AFCAT and the SSB screening stage both test whether a candidate can judge information calmly before acting. Data sufficiency checks whether you know when you have enough facts. Statement analysis checks whether you can separate what is said from what is merely assumed. Decision-making questions check practical judgement — the very quality an officer needs.

11. Master Formula Table

12. Master Summary Table

13. Mind Map

14. Tips and Tricks

15. Important One-Liners

• EJOTY gives the positions 5, 10, 15, 20, 25.
• Opposite letters in the alphabet always add up to 27.
• Facing north, the right hand points east.
• In the morning a person's shadow falls to the west.
• A 90° clockwise turn equals a right turn.
• The clock hands overlap 11 times in 12 hours.
• Opposite faces of a standard die add up to 7.
• A cube cut into 27 small cubes has exactly one cube with no painted face.
• In a mirror image, left and right are reversed; in a water image, top and bottom are reversed.
• Two particular ("some") premises never give a definite conclusion.
• A century year is a leap year only if divisible by 400.
• Total persons in a row = position from left + position from right − 1.

16. PYQ-Based Questions with Detailed Answers

17. Quick Revision Summary