Reasoning Ability
• Blood Relations: Two-Generation Rule — Male's wife = daughter-in-law (to his parents); female's husband = son-in-law (to her parents). Draw quick tree with ♂/♀ symbols; maternal = mother's side, paternal = father's side.
• Direction Sense: WENS Clock — Place directions as clock: West=9, North=12, East=3, South=6. Left/right turns match clock rotation; back=180° jump. Pythagoras for diagonal distances: √(x²+y²).
• Inequality Symbol Chain — In A>B≥C<D: only certain pairs provable (A>B, B≥C). Never combine across direction change: C<D blocks A>D conclusion. Statements must share common term to link.
• Seating Arrangement: Fix One First — In circular/linear puzzles, anchor the most restricted person (e.g., "X sits between Y and Z") as reference. Circular: fix one to kill rotational ambiguity; clockwise/anticlockwise matters.
• Coding: Alphabet Position — A=1, Z=26; remember EJOTY = 5,10,15,20,25 as anchors. Letter ±n: A+3→D; reverse alphabet: A↔Z (1+26=27), use 27−position. Number coding: check digit-sum, prime patterns.
• Syllogism: Venn Diagram for All/Some/No — "All A are B" = A circle inside B. "Some A are B" = overlap. "Some not" needs at least one A outside B. Two positive premises can't yield negative conclusion.
Quantitative Aptitude
• Divisibility Quick Checks — 3,9: sum of digits divisible. 4: last 2 digits divisible. 6: even + divisible by 3. 8: last 3 digits. 11: alternating digit sum (1st−2nd+3rd−...) divisible by 11. 7: double last, subtract from rest.
• HCF×LCM = Product of Numbers — For two numbers: A×B = HCF×LCM. If three numbers given with LCM, find HCF by prime factorization (lowest powers). Co-primes: HCF=1, LCM=product.
• Percentage ↔ Fraction Anchors — 12.5%=1/8, 16⅔%=1/6, 20%=1/5, 33⅓%=1/3, 66⅔%=2/3. For x% of y: reverse as y% of x (20% of 50 = 50% of 20 = 10). Two successive changes: x+y+(xy/100).
• Simple Interest: PRT/100 — SI = (Principal × Rate × Time)/100. Amount = P + SI. If SI for 2 years = 600, 1 year = 300. Doubling time: 100/R years at SI.
• Compound Interest: Annual vs. Half-Yearly — A = P(1+R/100)^T. Half-yearly: use R/2, 2T. Quarterly: R/4, 4T. CI−SI for 2 years = P(R/100)²; gives P if R known. Growth≈R% per period for small R.
• Profit & Loss: MP-CP-SP Triangle — Discount on MP, Profit on CP. SP = MP(1−D%/100). Profit% = (SP−CP)/CP×100. False weight: Profit% = (Error/True−Error)×100. Successive discounts: combine as x+y−xy/100.