Advanced Quantitative Aptitude Masterclass — Speed Techniques

• Divisibility by 3/9: sum of digits divisible by 3/9. By 11: alternating digit-sum difference divisible by 11 (or 0). By 7: double the last digit, subtract from the rest, repeat until a 2-digit check is possible. • Digital root (repeated digit-sum until single digit) is preserved under addition and multiplication — a fast way to spot-check multiplication answers: digital root of the product must equal the digital root of (digital root of A × digital root of B). • Base-multiplication shortcut for numbers near a power of 10 (e.g. 97×96): use (100−3)(100−4) = 100×93 + 12 = 9312 — far faster than long multiplication for 2-digit-near-100 pairs.

• Scan the table/chart title, units, and axis labels FIRST (10 seconds) before reading any question — most DI errors come from misreading the unit (lakh vs crore, % vs absolute value). • For "percentage change" questions, pre-calculate 10%, then adjust: 23% of a value ≈ 10% + 10% + (3% via 10%/3.33), faster than direct multiplication under time pressure. • Ratio-based DI: convert all values to a common base (index to 100) once at the start of the question set — every subsequent sub-question reuses that base instead of recalculating from raw figures.

• Ages problems: assign the smallest unknown as x and express every other age as x ± offset from the given ratio — avoids solving two-variable simultaneous equations for standard "ratio of ages" questions. • Mixture/Alligation: for two components mixed to a target ratio, the alligation cross method (difference of extremes divided crosswise) solves in one step what a full equation would take three steps to reach. • Pipes and cisterns with a leak: treat the leak as negative work-rate and add it algebraically to the filling rate(s) — the same Time & Work reciprocal-rate framework applies, just with a signed term.

In a mixed-difficulty quant section, attempt calculation-light questions (number series, simplification, approximation) first to bank guaranteed marks, then move to DI sets (which reward pre-reading), and leave multi-step geometry/mensuration for last since those have the highest chance of a silly arithmetic slip under fatigue. Never spend more than 90 seconds on a single question in the first pass — mark and revisit.