Analytical Ability
Clockwise-Direction Mnemonic — Remember "NEWS" clockwise from top: North→East→South→West. For 45° angles add NE, SE, SW, NW between them. Right turn = clockwise, Left turn = anti-clockwise.
Blood Relations Gender Trap — Brother's/Sister's daughter = Niece (female); Brother's/Sister's son = Nephew (male). Mother's/Father's brother = Uncle; their wives = Aunt. Spouse's siblings = Brother/Sister-in-law.
Coding Pattern Rule — In letter-shift coding, write alphabet positions (A=1, Z=26). If CAKE=3-1-11-5 becomes FBNH, check: +3 shift. Apply same shift to decode unknown words immediately.
Sequence Gap Tricks — Prime series: 2,3,5,7,11,13... Perfect squares: 1,4,9,16,25,36... Cubes: 1,8,27,64,125... Memorize first 15 of each; 80% sequence questions use these foundations.
Venn Diagram Formula — For two sets: n(A∪B) = n(A) + n(B) - n(A∩B). For three sets: add all three, subtract all pairs, add back the triple intersection. "Only A" = n(A) - overlaps.
Calendar Day Formula — Odd days = Total days mod 7. 365 days = 1 odd day; 366 = 2 odd days. Jan 1, 2000 was Saturday; count odd days forward to find any date's day quickly.
Seating Arrangement Anchor — Always fix one person's position first (usually mentioned as reference). Mark clockwise/anti-clockwise clearly. "Opposite" means diameter across; "adjacent" means immediate neighbor.
Data Sufficiency Template — Check: (A) Statement 1 alone sufficient? (B) Statement 2 alone sufficient? (C) Both together needed? (D) Each alone sufficient? (E) Even together insufficient? Follow this order always.
Mathematical Ability
Divisibility by 11 Rule — Alternating digit sum: subtract odd-position digits from even-position digits. If result is 0 or divisible by 11, the number is divisible by 11. Example: 121→(1+1)−2=0✓
Percentage-Fraction Equivalents — Memorize: 12.5%=⅛, 16.67%=⅙, 20%=⅕, 25%=¼, 33.33%=⅓, 50%=½, 66.67%=⅔, 75%=¾. Saves calculation time; directly convert in profit/loss problems.
Profit/Loss Shortcut — If cost price CP and marked price MP: Discount on MP, Profit on CP. Two successive discounts d1%, d2%: Net = (d1+d2−d1×d2/100)%. Not simple addition!
Compound Interest Trick — For 2 years: CI−SI = SI²/(100×P) where P=principal. For 3 years at same rate, extra CI over SI = 3×(R/100)²×P + (R/100)³×P.
Quadratic Sum-Product — For ax²+bx+c=0, roots α,β: Sum α+β = −b/a, Product αβ = c/a. If asked root values, use these first before quadratic formula to save time.
Alligation Method — When mixing two quantities at prices P1, P2 to get mean price Pm: Ratio = (P2−Pm):(Pm−P1). Draw cross-diagram: cheaper on left, costlier on right, mean in center.
AP/GP Instant Formulas — AP: nth term = a+(n−1)d; Sum = n/2×(2a+(n−1)d). GP: nth term = ar^(n−1); Sum = a(r^n−1)/(r−1) if r>1. Infinite GP sum = a/(1−r) only if |r|<1.
Binomial Middle Term — For (a+b)^n: if n is even, middle term is (n/2+1)th term. If n is odd, two middle terms are (n+1)/2 and (n+3)/2. Use ⁿCᵣ formula directly.
Mensuration Square Relations — Diagonal of square = side×√2. Diagonal of cube = side×√3. Diagonal of cuboid = √(l²+b²+h²). Circle circumference = 2πr; Area = πr². Memorize π≈22/7 or 3.14159.
Matrix Determinant 2×2 — For |a b; c d| = ad−bc. If determinant = 0, matrix is singular (no inverse). For 3×3, expand along first row using cofactors; practice this thrice.
Probability Addition Rule — P(A∪B) = P(A) + P(B) − P(A∩B). For mutually exclusive events P(A∩B)=0, so simply add. For independent events: P(A∩B) = P(A)×P(B). Don't confuse these two!
Communication Ability
Subject-Verb Agreement Trick — Subjects with "each/every/either/neither" take singular verbs. "A number of" = plural; "The number of" = singular. Ignore phrases between subject-verb (e.g., "along with," "as well as").
Phrasal Verb Patterns — Look: look into=investigate, look after=take care, look up to=respect, look down upon=despise. Put: put off=postpone, put up with=tolerate, put forward=propose. Memorize by verb families.
Idiom Meaning Clusters — Body parts: burn midnight oil=study late, cost an arm and leg=expensive, cold feet=nervous. Animals: let the cat out=reveal secret, raining cats and dogs=heavy rain, red herring=distraction.
Error Spotting Priority — Check in order: (1) Subject-verb agreement, (2) Tense consistency, (3) Pronoun reference, (4) Preposition usage, (5) Article errors. 70% errors fall in first three categories.
Sentence Completion Logic — Read sentence, predict word type needed (positive/negative/cause/contrast). Eliminate opposite-tone options first. Check for conjunctions: "although/however"=contrast; "because/therefore"=cause-effect.
Vocabulary Root Power — Bene- = good (benefit, benevolent); Mal- = bad (malicious, malfunction); -ology = study of (biology, psychology); -phobia = fear (claustrophobia). Learn 20 common roots for 200+ words.