Logical Reasoning
Odd Days Formula — For centuries: 1600/2000 = 0 odd days, 1700/1800/1900 = 5/3/1 odd days respectively. 400-year cycle repeats with 0 odd days total.
Blood Relations Gender Trap — Spouse of sibling ≠ sibling. Brother's wife is sister-in-law, NOT sister. Mother's brother is maternal uncle, father's brother is paternal uncle (different persons).
Clock Angle Formula — Angle = |11M/2 - 30H| degrees. At H:M, hands make this angle. If >180°, take 360° minus the result.
Direction Sense RULD Trick — Start with Right. Clockwise: Right→Up→Left→Down (RULD). Two consecutive right turns = U-turn. Left + Right cancels out.
Coding A=1, Z=26 — In letter-shift codes, assign numbers. Forward shift: A+3=D. Reverse alphabet: A↔Z, B↔Y (sum=27). EJOTY positions are 5,10,15,20,25 (multiples of 5).
Calendar Anchor: Jan 1, 2000 — Was Saturday. Learn this base. Use odd days: +365 days = +1 odd day (non-leap), +366 = +2 odd days (leap year).
Circular Arrangement Formula — (n-1)! arrangements for n people in circle (clockwise = anticlockwise same). With direction matters: (n-1)! × 1. Fix one person, arrange rest linearly.
Abstract Reasoning
Dice Opposite Faces Sum — Standard dice: opposite faces sum to 7 (1-6, 2-5, 3-4). If three faces visible, unseen faces are 7 minus each visible.
Mirror Image LR Rule — Left-Right inverts, Top-Bottom stays same in plane mirror. Asymmetric letters reverse: b↔d, p↔q. Vertical-axis symmetric (A,H,M,T) unchanged.
Water Image TB Rule — Top-Bottom inverts, Left-Right stays same. Horizontal-axis symmetric letters (C,D,H,O) look unchanged. b becomes q (inverted).
Paper Fold Punch Logic — Folded n times = 2^n layers. One punch = 2^n holes. Symmetry matters: fold along center creates mirror-symmetric holes.
Quantitative Aptitude
Divisibility by 11 — Alternating sum test: (sum of odd-position digits) - (sum of even-position digits) must be 0 or divisible by 11. Example: 1331→(1+3)-(3+1)=0, divisible.
Percentage-Fraction Equivalents — 12.5%=1/8, 16.67%=1/6, 20%=1/5, 25%=1/4, 33.33%=1/3, 50%=1/2, 66.67%=2/3, 75%=3/4. Instant calculation saves 20 seconds per question.
Successive Percentage Formula — Two changes a% and b%: Net = a+b+(ab/100). Example: +20% then -10% gives 20-10+(20×-10/100)=8% net increase.
Alligation Rule — Cheaper/Dearer ratio = (Mean - Cheaper):(Dearer - Mean). Quantities are in inverse ratio of price differences from mean. Draw X-diagram.
Coordinate Geometry Distance — Distance = √[(x₂-x₁)²+(y₂-y₁)²]. Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2). Slope = (y₂-y₁)/(x₂-x₁). Parallel lines: equal slopes.
Permutation vs Combination — Permutation when ORDER matters (arrangements, passwords). Combination when order doesn't (selection, committees). nPr = nCr × r!.
Sum of First n Naturals — n(n+1)/2. Squares: n(n+1)(2n+1)/6. Cubes: [n(n+1)/2]². Example: 1+2+...+10=55, 1²+2²+...+10²=385.
Geometry: Triangle Area Shortcut — Area = ½×base×height = √[s(s-a)(s-b)(s-c)] where s=(a+b+c)/2 (Heron's). Equilateral with side a: (√3/4)a².
Data Interpretation Approximation — Round to nearest 5 or 10. 47.8% of 312 ≈ 50% of 300 = 150. Bar graphs: estimate half-bars mentally, don't compute exact.
Verbal Ability and Reading Comprehension
Confusable Pairs: Affect/Effect — Affect = verb (influence). Effect = noun (result). "Policy affects economy; effect was inflation." Exception: effect as verb = bring about.
Its vs It's Rule — It's = It is (apostrophe = missing letter). Its = possessive (no apostrophe). "It's raining; dog lost its collar." Like his/her, possessives have no apostrophe.
Principal/Principle Trick — Principal = main person/amount (ends with -pal, your pal). Principle = rule/law (ends with -ple, like multiple rules). School principal is your pal.
Para Jumbles: Find Opener — Look for introductory/context-setting sentence (no pronouns referring back, defines topic). Then find mandatory pairs (pronoun-antecedent, cause-effect, however-contrast). Closing sentence gives conclusion/future.
Error Spotting: SVA Check — Subject-verb agreement: Collective nouns (team, family) usually singular. "Each/Every/Either/Neither" = singular verb. "None" can be singular/plural depending on context.