Analytical Ability
CLUE for Blood Relations — Child-Level-Up-Elder: Always draw family tree moving upward (parents, grandparents) or downward (children). Mark gender (△ male, ○ female) and generation levels to avoid confusion in complex chains.
Clock Method for Circular Arrangement — In clockwise arrangements, person A's right neighbor sits where clock hand moves next; left neighbor sits opposite. Number positions 1-8 like clock hours to track "opposite" (differ by 4) and "adjacent" seats instantly.
A1Z26 for Coding — A=1, B=2...Z=26. For letter-shift codes, identify the constant (+3, -2, ×2 pattern). For number codes, check place-value sum (CAT: 3+1+20=24). Reverse alphabet: A↔Z, B↔Y (A=26, Z=1).
BODMAS Trap in Data Sufficiency — When statements give equations, don't solve fully—just check if unique solution exists. Example: Two variables need two independent equations; one equation = insufficient alone, both together = sufficient.
Date Anchor: January 1st — Memorize Jan 1 day for current year (2024=Monday). Odd days: Jan-Feb=31+29=60 (1 odd day in leap year). Every month-end adds odd days: use knuckle trick (knuckle=31 days) to track.
NSEW Box for Direction Sense — Draw quick compass. Right turn = clockwise 90°. "Faces North, right turn, walks" = now facing East. Double the distance statements mentally: "10m N, 10m S" = cancel out = origin point.
Data Interpretation: Percentage Shortcut — For "% increase from A to B": (B−A)/A × 100. Quick: If 80→100, increase = 25%. If 100→80, decrease = 20% (not 25%—different bases). Pre-calculate 10%, 20%, 50% benchmarks from given totals.
Pie Chart: Angle-to-Percentage — 360° = 100%. Each 3.6° = 1%. Angle 72° = 20%, 90° = 25%, 120° = 33.33%, 180° = 50%. Visual estimation: quarter-circle = 25%, half = 50%, one-third ≈ 120°.
Series Pattern: Difference of Differences — For 2, 5, 10, 17, 26: find first difference (3,5,7,9), then second difference (2,2,2). Constant second difference = quadratic series. For ratio series, divide consecutive terms to spot ×2, ×3 patterns.
Venn Diagram: n(A∪B) — Formula: n(A∪B) = n(A) + n(B) − n(A∩B). For three sets: add all, subtract pairs, add back triple intersection. "Only A" = n(A) − overlaps. Always verify total = sum of all regions.
Mathematical Ability
Divisibility by 11 — Alternating digit sum: (sum odd positions) − (sum even positions). Example: 2728 → (2+2)−(7+8) = −11, divisible. If result is 0 or multiple of 11, number is divisible by 11.
Indices MADSPM Rule — Multiply=Add powers, Divide=Subtract, Power-to-power=Multiply. a^m × a^n = a^(m+n); (a^m)^n = a^(mn). Negative exponent: a^(−n) = 1/a^n. Zero power: a^0 = 1 (a≠0).
Binomial (a+b)² Traps — (a+b)² = a² + 2ab + b² (NOT a²+b²). (a−b)² = a² − 2ab + b². (a+b)(a−b) = a²−b². Common error: forgetting middle term 2ab in expansions.
Coordinate Distance — Distance between (x₁,y₁) and (x₂,y₂): √[(x₂−x₁)² + (y₂−y₁)²]. Midpoint: ((x₁+x₂)/2, (y₁+y₂)/2). Slope m = (y₂−y₁)/(x₂−x₁). Parallel lines have equal slopes; perpendicular slopes multiply to −1.
Percentage-Fraction Quick Conversion — 50%=1/2, 33.33%=1/3, 25%=1/4, 20%=1/5, 16.67%=1/6, 12.5%=1/8. "15% of 80" = (15/100)×80 = (3/20)×80 = 12. Saves calculation time in Profit-Loss and Ratio problems.
Profit-Loss: CP as Base 100 — Always assume CP=100 for percentage problems. If SP=120, profit=20%. If SP=80, loss=20%. For discount: Marked Price → discount% → Selling Price. Two successive discounts x%, y%: effective = [x+y−(xy/100)]%.
AP: nth Term & Sum — Arithmetic Progression: a_n = a + (n−1)d; Sum S_n = (n/2)[2a + (n−1)d] or (n/2)(first+last). Common mistake: using wrong formula for sum. GP: a_n = ar^(n−1); S_n = a(r^n−1)/(r−1) if r>1.
Quadratic Sum-Product Roots — For ax²+bx+c=0, sum of roots α+β = −b/a, product αβ = c/a. To form equation from roots p,q: x² − (sum)x + (product) = 0. Example: roots 2,3 → x²−5x+6=0.
Simple vs Compound Interest Gap — For 2 years: CI−SI = P(r/100)². For same principal, rate, time: the gap increases with compounding frequency. SI = Prt/100 (linear); CI = P[(1+r/100)^t − 1] (exponential growth).
Ratio Unitary Method — "A:B = 3:4, B:C = 5:6" → make B common: multiply first by 5, second by 4 → A:B:C = 15:20:24. For three quantities, equalize the middle term to chain ratios together.
Communication Ability
A/An Article Rule — 'A' before consonant sounds (a university—'yu' sound), 'An' before vowel sounds (an hour—silent h). "The" for specific/previously mentioned items; no article for general plurals (Cats are animals).
12 Tenses in 4×3 Grid — Four times (Present, Past, Future, Past-in-Past) × Three aspects (Simple, Continuous, Perfect). Present Perfect = has/have + V3 (connection to now). Past Perfect = had + V3 (before another past event).
Active-Passive Voice Swap — Object becomes subject; verb changes to "be + V3"; by + original subject. "She writes a letter" → "A letter is written by her." Tense of 'be' matches original tense (wrote → was written).
Common Phrasal Verb Patterns — "Put off" = postpone, "Put up with" = tolerate, "Look into" = investigate, "Look up to" = respect, "Break down" = stop functioning, "Break into" = enter forcefully. Particle changes meaning drastically.
Preposition: IN-ON-AT for Time — AT for exact time (at 5pm), ON for days/dates (on Monday, on May 1st), IN for months/years/long periods (in 2024, in summer). AT for points, ON for surfaces, IN for enclosures (space).
Synonym/Antonym Root Power — Latin roots: 'bene'=