Arithmetic
Divisibility by 11 — Alternating digit sum: subtract sum of odd-position digits from even-position digits; if result is 0 or multiple of 11, number is divisible by 11. Quick check for large numbers.
SI vs CI for 2 years — Difference = P(R/100)². For principal ₹1000 at 10%, difference is always ₹10. Use this to reverse-calculate principal or rate quickly.
Speed-Distance-Time Triangle — Cover 'S' in triangle with D at top, S and T at bottom. D = S×T, S = D/T, T = D/S. Visual recall prevents formula confusion.
Percentage-Fraction Shortcuts — Memorize: 12.5% = 1/8, 16.67% = 1/6, 20% = 1/5, 33.33% = 1/3, 62.5% = 5/8, 87.5% = 7/8. Saves calculation time.
Boats and Streams Formula — Downstream = B+S (Both add), Upstream = B-S (U subtract). Speed of Boat = (D+U)/2, Speed of Stream = (D-U)/2.
Pipe Filling Trick — If pipe A fills in 'a' hours and B in 'b' hours, together they fill in (a×b)/(a+b) hours. For A fills, B empties: (a×b)/(b-a).
Age Problem Setup — Present ages are x and y. 'k years ago' → (x-k) and (y-k). 'k years hence' → (x+k) and (y+k). Ratio changes, sum/difference stays constant.
Profit % on Cost vs Selling — If profit is x% on CP, profit on SP = x/(100+x) × 100%. For 25% on CP = 20% on SP.
Logical Reasoning and Aptitude
EJOTY Coding — Letters at positions 5, 10, 15, 20, 25: E-J-O-T-Y. Quick position recall: A=1, E=5, J=10, O=15, T=20, Y=25, Z=26.
Odd Days Calculation — Ordinary year = 1 odd day, Leap year = 2 odd days. Century years: 1600,2000 = 0 odd days; 1700,1800,1900 = 5 odd days each.
Blood Relation Gender Trap — No gender words? Can't determine! "Parent, child, sibling, cousin" are gender-neutral. Only "mother, father, son, daughter, uncle, aunt, nephew, niece" confirm gender.
Direction Sense: NEWSPAPER — North-East-West-South clockwise gives wrong order! Use NEWS: North-East-South-West clockwise (90° right turns). Or SUN RISES IN EAST for orientation anchor.
Dice Opposite Faces — Sum of opposite faces = 7 (standard dice: 1-6, 2-5, 3-4). If three adjacent faces shown, opposite face = 21 minus sum of visible faces.
Clock Angle Formula — Angle = |11M/2 - 30H| where M=minutes, H=hours. If >180°, take 360° minus angle. At 3:15, angle = |11×15/2 - 30×3| = 7.5°.
Syllogism: No+Some — "No A is B" + "Some B are C" = No conclusion about A-C. Only "All" statements guarantee conclusions. At least two positives needed for positive conclusion.
English Language
FANBOYS Coordinators — or, nd, or, ut, r, et, o. These seven coordinating conjunctions join equal clauses; comma before them in compound sentences.