Mathematics
Divisibility by 11 — Alternating digit sum method: subtract sum of odd-position digits from even-position digits. If result is 0 or divisible by 11, original number is divisible by 11. Example: 121 → (1+1)−2=0, divisible.
BODMAS Trap Awareness — Division and Multiplication have equal priority (left to right), as do Addition and Subtraction. Don't automatically do all multiplication before division. Example: 20÷5×2 = (20÷5)×2 = 8, not 20÷(5×2).
Percentage-Fraction Shortcuts — Memorize: 12.5%=1/8, 16.67%=1/6, 33.33%=1/3, 66.67%=2/3, 87.5%=7/8. Instantly convert percentages to fractions for faster mental calculation in percentage problems.
Time-Distance "DIST" — Distance = Speed × Time. Remember "DIST" where I=multiplication sign. Rearrange: Speed = D/T, Time = D/S. Cover the unknown in D/S×T triangle diagram.
Compound Interest Shortcut — For 2 years: CI−SI = (SI²)/(100×P). The extra interest is simple interest on first year's interest. For quick CI vs SI difference questions.
LCM×HCF Formula — For two numbers: Product of numbers = LCM × HCF. If three values given, find fourth instantly. Example: numbers 12,18 → 12×18 = LCM(36)×HCF(6).
Algebra: (a+b)² Identity — Remember "Square-Twice-Square": a²+2ab+b². Similarly (a−b)²=a²−2ab+b². The middle term is always TWICE the product, commonly forgotten in expansions.
Ratio Multiplication Trick — To compare ratios like A:B=2:3 and B:C=4:5, make B equal. Multiply first by 4, second by 3: A:B:C=8:12:15. Equalize common terms for combined ratios.
Average Addition Formula — When new number added: New Average = Old Average + (Difference/New Total). If 1 person added, divide difference by new count. Saves recalculation time.
Profit Percentage Quick — Profit% = (Profit/CP)×100, Loss% = (Loss/CP)×100. Always divide by COST PRICE, never selling price, unless "Loss on SP" explicitly stated. Common trap in exams.
Mensuration: Circle 2πr — Circumference = 2πr, Area = πr². Remember "Circumference has 2, Area is square." Perimeter formulas have dimension 1, area formulas have dimension 2 (squared terms).
Time-Work: M₁D₁W₂ = M₂D₂W₁ — Men₁×Days₁×Work₂ = Men₂×Days₂×Work₁. Cross-multiply for work-efficiency problems. Add hours: M₁D₁H₁W₂=M₂D₂H₂W₁ for detailed questions.
Logical Reasoning and Mental Ability
Blood Relations: "Mother's Brother" — Maternal uncle = Mama, Paternal uncle = Chacha. Mother's side = maternal, Father's side = paternal. Draw family tree instantly for complex relations; saves confusion.
Direction Sense: NESW Clock — Visualize clock: North=12, East=3, South=6, West=9. Right turn=clockwise, Left=anticlockwise. 90° right from North→East. Helps in quick angle-turn calculations.