Verbal Ability & Reading Comprehension
Root-Word Families — Group words by common roots: *bene* (good) = benefit, benevolent; *mal* (bad) = malady, malicious; *chron* (time) = chronic, chronology. Speeds up analogies and vocabulary questions instantly.
Transition Word Anchors — "However/But" signals contrast; "Therefore/Thus" shows conclusion; "Moreover/Furthermore" adds support. In Para Jumbles, find these to link sentences; opening sentences rarely have backward-pointing transitions.
Tone Spectrum: SCAN — Satirical, Critical, Analytical, Neutral. Eliminate extreme tones first (rarely "ecstatic" or "furious" in academic passages). Author's tone in CAT is usually measured, not emotional.
Main Idea = First + Last — The central theme often appears in the opening and closing sentences of a passage. Middle paragraphs provide evidence. Start and end for quick comprehension.
Odd-One-Out: 3-vs-1 Test — Three sentences share theme, tone, or time frame; one differs. Check for tense shifts, subject changes, or scope mismatches to spot the outlier quickly.
Data Interpretation & Logical Reasoning
Blood Relations: Generation Flip — Maternal uncle's son = cousin (same generation). Father's brother = uncle (one up). Convert complex relations by counting generation steps: +1 (parent), -1 (child), 0 (sibling/cousin).
Direction Sense: WNES Clock — Visualize compass as clock: West=9, North=12, East=3, South=6. Right turn = +3 hours, Left = -3 hours. 90° right from North (12) = East (3).
Calendar Day Formula: Odd Days — Ordinary year = 1 odd day; Leap = 2. Century years: 1600,2000 (0 odd), 1700,1800,1900 (5 odd). Sum odd days ÷7, remainder gives day shift.
Seating Arrangement: Fix One First — Anchor the most constrained person/variable first. If "A sits opposite B and two seats left of C," place A, then others relative to A. Reduces possibilities exponentially.
Binary Logic: Truth Table Shortcut — If statements contradict, one is truth-teller, one liar. Test assuming each is truth-teller; only one assumption will satisfy all conditions without contradiction.
Coding-Decoding: Position Shift — If CAT→DBU, each letter shifts +1. For reverse: A=1, Z=26; learn position numbers for A-Z. Backward coding (A→Z) often uses 27-position value.
Network Routes: Node Degree — In route problems, count connections (degree) per node. Odd-degree nodes must be start/end points in a single-path traversal (Eulerian path concept).
Quantitative Aptitude
Divisibility: Digit Sum for 3 & 9 — Sum all digits; if divisible by 3, number is. For 9, same rule. Example: 12345 → 1+2+3+4+5=15 (÷3 yes, ÷9 no). Instant check without long division.
Percentage-Fraction Equivalents — Memorize: 12.5%=1/8, 16.67%=1/6, 20%=1/5, 25%=1/4, 33.33%=1/3, 66.67%=2/3, 87.5%=7/8. Converts percent problems to fraction arithmetic, much faster.
Alligation: Cross Method — For mixtures at prices P₁, P₂ giving mean M: ratio = (M-P₂):(P₁-M). Draw X, write P₁ top-left, P₂ bottom-left, M center; differences cross-give ratio.
AP Sum: Middle × Count — For arithmetic progression, Sum = (First + Last)/2 × n. Or middle term × n if odd count. Example: 1+2+...+99 = 50×99 = 4950.
GP: 2ⁿ Powers — Memorize 2¹⁰=1024≈10³; 2²⁰≈10⁶. For compound interest at ~7.2%, money doubles in 10 yrs (Rule of 72). Quick exponential estimates in growth problems.
Quadratic: Sum & Product — For x²+bx+c=0, roots α,β satisfy α+β=-b, αβ=c. If asked root properties, use these instead of formula. Example: roots differ by 3 → (α-β)²=(α+β)²-4αβ.
Boats & Streams: Average Speed — Downstream (B+S), Upstream (B-S). Speed in still water = (Down+Up)/2; Stream = (Down-Up)/2. Given times, use Speed=Distance/Time to find B and S separately.
Profit %: CP as Base — Always use CP as 100. If SP=120, profit=20%. But if given SP, then CP=100x, solve for x. Successive discounts: 20%+10% ≠ 30%; it's 28% (0.8×0.9=0.72).
Maxima via AM≥GM — For fixed product, sum is minimum when values equal. For fixed sum, product is maximum when equal. Example: x+y=10, xy max when x=y=5 → xy=25.