Mathematics
Divisibility by 11 — Alternating sum of digits must be 0 or divisible by 11. For 4356: (4+5) – (3+6) = 0, so divisible by 11.
BODMAS Left-to-Right Trap — Division and Multiplication have equal priority; solve left-to-right. Same for Addition and Subtraction. 20÷5×2 = (20÷5)×2 = 8, NOT 20÷10.
Percentage-Fraction Quick Converts — 12.5%=⅛, 16.67%=⅙, 20%=⅕, 25%=¼, 33.33%=⅓, 50%=½, 66.67%=⅔, 75%=¾. Instant mental calculation shortcuts.
Profit Loss CP Formula — If SP > CP: Profit% = [(SP-CP)/CP]×100. If marked price MP with discount: SP = MP×(100-d%)/100, then compare to CP.
SI vs CI First Year Trick — Simple Interest and Compound Interest are identical for the first year. Difference appears only from Year 2 onwards when CI compounds on interest.
Speed-Distance-Time Triangle — Draw triangle: D on top, S and T at bottom. Cover what you need: D=S×T, S=D/T, T=D/S. Palm-cover method works instantly.
Time and Work Man-Days — Total work = Men × Days. If M₁ men do work in D₁ days, then M₂ men need D₂ = (M₁×D₁)/M₂ days. Cross-multiply shortcut.
Calendar Odd Days Count — Ordinary year=1 odd day, Leap year=2 odd days. Century divisible by 400 is leap, else not. For day-finding, sum odd days, divide by 7.
Pipes and Cisterns Sign Rule — Inlet pipes: positive (+), Outlet/leak pipes: negative (–). Net fill rate = Sum of rates. Time = 1/Net rate. Use LCM for easy calculation.
LCM-HCF Product Rule — For two numbers A and B: A × B = LCM × HCF. If any three values known, find the fourth instantly.
Ratio Simplification Trick — Convert ratios to same multiplier. If A:B=2:3 and B:C=4:5, make B equal: A:B:C = 8:12:15 (multiply first by 4, second by 3).
Age Calculation Timeline — Draw timeline with "now" as reference. Mark past/future positions. "n years ago" and "n years hence" create equations with consistent +n or –n.
General Intelligence and Reasoning
Coding: Letter Position — A=1, B=2...Z=26. For reverse: A=26, B=25...Z=1. Remember EJOTY at positions 5,10,15,20,25 as anchors for quick counting.
Direction Sense: NESW Clock — Visualize clock: North=12, East=3, South=6, West=9. Right turn=clockwise 90°, Left turn=anticlockwise 90°. About turn=180°.
Blood Relations: Generation Method — Maternal side=Mother's family, Paternal=Father's family. Brother's wife=Sister-in-law. Father's brother=Uncle. Mother's sister=Aunt. Draw family tree upward for clarity.
Venn Diagram Only Formula — Only A = Total A – (A∩B). For three sets: Only A = Total A – (A∩B) – (A∩C) + (A∩B∩C).
Series: Difference of Differences — If first differences unclear, check second differences. 2,5,10,17,26: differences are 3,5,7,9 (themselves in +2 pattern). Common in number series.