Logical Reasoning and General Intelligence
Blood Relations Key — Father's/Mother's side: Paternal = father's, Maternal = mother's. Uncle types: Father's brother = Paternal Uncle, Mother's brother = Maternal Uncle. Cousin = Uncle/Aunt's child. Nephew/Niece = sibling's son/daughter.
Direction Rotation Trick — Clockwise: N-E-S-W (Never Eat Soggy Waffles). Right turn = next letter clockwise; Left turn = previous letter. 180° = opposite direction. Mark starting point, count turns systematically.
Coding Pattern Check — Letter shift: A=1, B=2...Z=26. If CAT→DBU, each letter +1. Check first/last letters first to spot pattern quickly (forward/reverse alphabet, position-value swap, or constant shift).
Dice Opposite Faces — Sum of opposite faces on standard dice = 7. So 1-6, 2-5, 3-4 are pairs. If two faces shown, the third pair's position determines hidden faces.
Syllogism Venn Method — Draw circles for each term. All A→B = small circle A inside B. Some A→B = overlapping circles. No A→B = separate circles. Check conclusion against combined diagram only.
Mirror Image Rule — Left↔Right swap only; Top-Bottom unchanged. Letters symmetric on vertical axis (A,H,I,M,O,T,U,V,W,X,Y) look same. Asymmetric letters reverse (b↔d, p↔q). Numbers: 0,1,8 symmetric; others reverse.
Water Image Rule — Top↔Bottom swap only; Left-Right unchanged. Imagine folding paper horizontally. Letters symmetric on horizontal axis (B,C,D,E,H,I,O,X) look same; others invert vertically.
Series Gap Pattern — Check differences between consecutive terms first. If irregular, check: squares (1,4,9,16), cubes (1,8,27), primes (2,3,5,7,11), or alternating operations (+, ×, −, ÷).
Quantitative Aptitude
Divisibility by 11 — Subtract odd-place digit sum from even-place sum. If result is 0 or divisible by 11, number is divisible by 11. Example: 2728 → (2+2)−(7+8)=−11, divisible.
LCM×HCF Formula — For two numbers A and B: LCM × HCF = A × B. Find any three to calculate the fourth instantly. Works only for two numbers, not three or more.
Percentage-Fraction Shortcuts — Memorize: 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. Speeds up calculation by converting to fractions first.
Time-Speed-Distance Triangle — Draw triangle: Distance on top, Speed and Time at bottom. D=S×T, S=D/T, T=D/S. Cover unknown, see formula. Relative speed: same direction=subtract, opposite=add.
SI vs CI Difference (2 years) — Difference = P×(R/100)². For 2 years only. Example: ₹1000 at 10% for 2yr → CI−SI = 1000×(10/100)² = ₹10 extra in compound interest.
Mensuration Quick Formulas — Circle: πr² area, 2πr perimeter. Triangle: ½×base×height. Sphere: (4/3)πr³ volume, 4πr² surface. Cylinder: πr²h volume, 2πr(r+h) total surface. Cube: a³ volume, 6a² surface.
Average Addition Rule — Adding number X to group increases average by (X − old avg)/new count. If N numbers average A, add value X: new average = (N×A + X)/(N+1).
Ratio Multiplication Rule — If A:B = 2:3 and B:C = 4:5, make B common. Multiply first ratio by 4, second by 3 → A:B:C = 8:12:15. Always equalize the common term.
Partnership Profit Split — Profit ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂). If A invests ₹3000 for 4 months, B invests ₹4000 for 3 months, ratio = 12000:12000 = 1:1.
BODMAS Trap Alert — Brackets, Orders (powers), Division, Multiplication (left→right), Addition, Subtraction (left→right). D and M have equal priority; A and S have equal priority. Always left-to-right within same level.
English Language
Subject-Verb Agreement Trick — Ignore intervening phrases. "The box of chocolates is" not "are" (box=singular subject). Either/Neither takes singular; Both takes plural. Collective nouns (team, family) usually singular in Indian English.
Articles: A vs AN — Use AN before vowel *sounds* (an hour, an MBA, an FIR), not just vowel letters. Use A before consonant sounds (a university, a European, a one-rupee coin). Sound matters, not spelling.
Common Confusions — Affect (verb) vs Effect (noun). Principal (main/headmaster) vs Principle (rule). Stationary (still) vs Stationery (paper). Compliment (praise) vs Complement (complete). Remember by association: stationEry = pEn.
Error Spotting Checklist — Check: (1) Subject-verb agreement, (2) Tense consistency, (3) Pronoun-antecedent match, (4) Preposition pairing (interested *in*, good *at*, differ *from*), (5) Article usage. Most errors fall in these five categories.