Reasoning Reference Sheet

Coding–Decoding8

• Letter positions: A=1 … Z=26 (learn EJOTY: E5, J10, O15, T20, Y25)
• Reverse position of a letter = 27 − (its position); A↔Z, B↔Y…
• Opposite letter pair sums to 27 (e.g. C+X = 3+24 = 27)
• Letter-shift coding: note the +n / −n gap between each pair of letters
• Number coding: map each letter to a number, spot +, −, ×, or position pattern
• Substitution coding: words stand for other words — build a dictionary
• Symbol/condition coding: apply the given rules strictly, in order
• Check both directions — the same shift decodes the answer back

Blood Relations8

• Draw a family tree: △ male, ○ female, = married, | child link
• ‘Son of the only daughter of X’ ⇒ X is the maternal grandparent
• Paternal = father's side, Maternal = mother's side
• Reduce a long chain one relation at a time from the person named
• ‘A is B's …’ — read from B's viewpoint to name A
• In pointing/photo questions: ‘my father's son’ = self or brother
• Generation gap: parents +1, grandparents +2, children −1
• Watch gender neutrality: cousin/spouse can be either gender

Direction Sense7

• N-E-S-W clockwise; right turn = clockwise, left turn = anticlockwise
• Sunrise = East; shadow at sunrise falls to the West (and vice-versa)
• At noon shadows are shortest; morning shadow → West, evening → East
• Net displacement by Pythagoras: √(Δx² + Δy²)
• Track coordinates: East +x, West −x, North +y, South −y
• Two left/right turns reverse original direction (180°)
• Facing direction after k right turns = rotate 90°×k clockwise

Series (Number & Alphabet)7

• Test for +/− constant, ×/÷ constant, then squares/cubes
• Differences of differences constant ⇒ quadratic pattern
• Alternate-term series: two interleaved patterns
• Primes, squares (1,4,9,16…), cubes (1,8,27…), Fibonacci (add previous two)
• Alphabet: convert letters to positions, find the gap pattern
• ±1 shift often hides in ‘skip-a-letter’ sequences (A,C,E…)
• Wrong-term series: find the rule, then the term that breaks it

Analogy & Classification6

• Find the exact relation in the given pair, then apply it identically
• Common links: synonym, antonym, part–whole, cause–effect, worker–tool
• Number analogy: check ×, +, square, or same divisor relation
• Letter analogy: compare position gaps and mirror (27 − pos) patterns
• Odd-one-out: 3 share a property, 1 doesn't — test category, parity, prime
• Beware of two possible answers — pick the closest, most specific relation

Syllogism8

• ‘All A are B’ ⇒ some B are A (converse of All is Some)
• ‘No A is B’ ⇒ No B is A (No converts both ways)
• ‘Some A are B’ ⇒ Some B are A
• Two particular (Some) premises give NO definite conclusion
• Two negative premises give NO definite conclusion
• A conclusion is valid only if it must be true in every Venn case
• Use Venn diagrams; test ‘possibility’ conclusions separately
• ‘Some A are not B’ does not imply ‘Some B are not A’

Clocks7

• Hour hand moves 0.5°/min; minute hand 6°/min; gain 5.5°/min
• Angle between hands = |30H − 5.5M| degrees (take ≤180°)
• Hands coincide every 65 5/11 min (11 times in 12 h)
• Hands are opposite (180°) 11 times in 12 h
• Right angle (90°) forms 22 times in 12 h
• In a correct clock, both hands together 22 times a day
• Gain/lose: a clock gaining x min/day drifts x/1440 per minute

Calendars7

• Odd days decide the weekday; 1 ordinary year = 1 odd day, leap = 2
• 100 yrs = 5 odd days, 200 = 3, 300 = 1, 400 = 0 odd days
• Leap year: divisible by 4 (century only if divisible by 400)
• Same calendar repeats after 6, 11 or 28 years depending on leap position
• Day gap: count odd days between the two dates
• Reference: 1 Jan 1900 was a Monday (or use the odd-days method)
• Jan=0, Feb=3, Mar=3, Apr=6… (month codes) for the doomsday shortcut

Ranking & Ordering5

• Rank from top + rank from bottom = total + 1
• xth from left & yth from right ⇒ total = x + y − 1
• People between two positions = |x − y| − 1
• ‘At least’ counts give a minimum total — add the counted person once
• Build one line by chaining the pairwise ‘above/below’ clues

Seating Arrangement6

• Linear: fix the most-constrained person first, then place relative clues
• Circular facing centre: left = clockwise, right = anticlockwise
• Circular facing outward: left/right are reversed
• n people around a circle: (n−1)! arrangements
• Immediate neighbours share an edge; ‘between’ excludes the endpoints
• Draw the diagram; test cases when a clue allows two placements

Dice & Cubes6

• Standard die: opposite faces sum to 7 (1-6, 2-5, 3-4)
• Two dice with same two faces & orientation ⇒ remaining faces are opposite
• Cube cut into n³ smaller cubes: corners 8 (3 faces painted)
• Edges = 12(n−2) painted on 2 faces; faces = 6(n−2)² on 1 face
• Inner unpainted cubes = (n−2)³
• Only opposite faces are never adjacent — all others can touch

Mirror & Water Images5

• Mirror image: left ↔ right swap (vertical mirror), top stays
• Water image: top ↔ bottom flip (horizontal mirror at the base)
• Symmetric letters (A,H,I,M,O,T,U,V,W,X,Y) are unchanged in a vertical mirror
• Clock in a mirror shows time = 11:60 − actual (12:00 − time)
• For numbers, mirror reverses order and flips each digit's shape

Paper Folding & Cutting4

• Each fold doubles the holes symmetrically about the fold line
• Unfold step-by-step, mirroring cuts across each crease
• n folds ⇒ up to 2ⁿ symmetric copies of a single cut
• Track the axis of symmetry created by every fold

Mathematical Operations4

• Apply BODMAS: Brackets → Orders → ÷ × → + −
• Symbol substitution: replace coded symbols with real operators, then solve
• ‘Interchange signs/numbers’: swap as instructed, then evaluate each option
• Balance-the-equation: test options to make LHS = RHS

Venn Diagrams (Reasoning)4

• Represent each class as a circle; overlaps = common members
• Choose the diagram matching real relations (e.g. Dog, Animal, Cat)
• Fully separate sets ⇒ disjoint circles; subset ⇒ circle within a circle
• |A∪B∪C| = ΣΙ − Σ(pairs) + (all three) for counting regions

Counting Figures5

• Count systematically: smallest units first, then combinations
• Triangles in a triangle divided into n rows grow as a known series
• Squares in an n×n grid = 1² + 2² + … + n²
• Rectangles in m×n grid = ⁽ᵐ⁺¹⁾C₂ × ⁽ⁿ⁺¹⁾C₂
• Label parts and tally to avoid double-counting