Arithmetic and Numerical Skills
Divisibility by 11 — Alternating sum of digits must be divisible by 11. For 8327: (8+2)-(3+7)=0, divisible. Quick check for long numbers in data interpretation questions.
Percentage-Fraction equivalents — Memorize: 12.5%=1/8, 16.67%=1/6, 14.28%=1/7, 33.33%=1/3, 66.67%=2/3. Converts percentage problems to simpler fraction calculations instantly.
Time-Speed-Distance triangle — Draw triangle: Distance on top, Time and Speed at bottom. Cover what you need: D=S×T, S=D/T, T=D/S. Never confuse formulas again.
Compound Interest shortcut — For 2 years: Total interest = SI for 2 years + (SI for 1 year)²/(100×P). Saves time over repeated principal calculations.
Profit percentage on CP vs SP — Profit% on CP = (Profit/CP)×100. To convert to SP base: multiply by CP/SP. Remember: CP base is standard in 90% questions.
Mensuration: Circle formulas — "2-pie-are" sounds like "to pay are": 2πr is circumference. Area is πr². Perimeter has 2, Area is squared—voice pattern helps recall.
Ratio-Proportion with K-method — If ratio is 3:4:5, write as 3K, 4K, 5K. Total=12K. Given any total, find K instantly; then all parts follow. Eliminates algebraic confusion.
Time-Work: Man-Day equivalence — M₁D₁=M₂D₂ (men×days constant). 10 men, 6 days = 60 man-days. If 15 men, then 60/15=4 days needed. Direct substitution method.
Average addition/removal — New average = Old avg ± (Difference×Items added)/(Total items). One person joins raising average by 2; if 10 people total, newcomer is Old avg+20.
Data Interpretation: Percentage change — % change = (New-Old)/Old ×100. Common trap: always divide by OLD value, not new. Mark "OLD" in denominator on rough work.
Intelligence Test and Reasoning
Blood Relations: Gender marking — Draw family tree immediately, mark M/F above each person. Uncle/Aunt, Brother/Sister clarity comes from visual map, not mental juggling.
Clock angle formula — Angle = |30H - 5.5M| where H=hour, M=minutes. At 3:15: |30(3)-5.5(15)|=|90-82.5|=7.5°. Handles all clock problems mechanically.
Direction Sense: NESW circle — Draw plus sign: N top, E right, S bottom, W left. Right turn=clockwise 90°, Left=anticlockwise. Mark starting point, trace path physically.
Coding-Decoding: Position values — A=1, B=2...Z=26. Reverse: A=26, Z=1. Most codes use ±n shifts or reverse positions. Check pattern in first two letters, apply to rest.
Calendar: Odd days concept — Ordinary year=1 odd day, Leap=2 odd days. Century year divisible by 400 is leap. Calculate odd days from reference year; 0=Sunday, 1=Monday...6=Saturday.
Number series: Difference of differences — If first difference irregular, check second difference (difference between differences). Many MPSC series follow square/cube or arithmetic-geometric hybrids; second difference reveals pattern.