CAT Part 4: QA — Arithmetic First, the High-Yield Chapters, Exam-Ready Notes

Category: Management Entrance · Series: CAT Preparation · Read time: ~8 minutes**

QA rewards chapter-prioritisation: arithmetic alone is ~40% of the paper, and the arithmetic-plus-algebra block is two-thirds. This note maps the high-yield chapters, the method per family, and the 40-minute execution.

Table of Contents

1. The Weight Map: Where the Marks Are
2. The Arithmetic Core
3. The Algebra Block
4. Geometry and the Remainder
5. The 40-Minute Execution
6. How Exams Probe This Topic
7. Quick Revision: One-Glance Facts

1. The Weight Map: Where the Marks Are

• The distribution (recent CATs).**Arithmetic ~40% (9-10 of 22): percentages, ratios, profit-loss, time-work, time-speed-distance, averages-mixtures, simple-compound interest; Algebra ~25-30% (6-7): equations, inequalities, functions, logarithms, progressions, quadratics; Geometry ~15-20% (4-5): triangles-circles-polygons-coordinate; Number theory + modern math (~10-15%)**: divisibility, remainders, permutation-combination-probability.
• The strategy consequence. A candidate who has mastered arithmetic and algebra to 90% accuracy attempts 15-17 questions — a 99-percentile ceiling — before touching geometry’s hardest theorems; the “do everything equally” plan wastes the distribution.

2. The Arithmetic Core

• Percentages-ratios (the root chapters — everything else compounds on them): fraction-percentage conversions automatic (1/8 = 12.5%…); successive-change (a + b + ab/100); the multiplier habit.
• Profit-loss-discounts: the CP-SP-MP triangle; successive discounts; the dishonest-merchant (false-weight) setups.
• Time-work: the LCM-of-days units method (work = LCM; rates become integers) — pipes-and-cisterns identical with negative rates.
• Time-speed-distance: relative speed (sum/difference), trains (the length-to-cover rule), boats (the half-sum/half-difference shortcuts), the average-speed trap (never the mean).
• Averages-mixtures-alligation: the weighted-average cross; replacement ((1−1/x)ⁿ).
• Simple-compound interest: the difference identities; the fraction-rate tables.
• The arithmetic mindset: these are 1.5-2-minute questions — if your method takes 4 minutes, it is the wrong method; drill shortcuts, not just solutions.

3. The Algebra Block

• Quadratics-and-equations: the sum-product identities; the discriminant’s nature-of-roots; the max-min of quadratic expressions (completing the square).
• Inequalities-and-modulus: the wavy-curve (sign-chart) method; the modulus’s distance interpretation; AM-GM basics for min-max.
• Functions-graphs-logarithms: function-composition; the log identities and the domain discipline; the even-odd-symmetric properties questions exploit.
• Progressions: AP-GP formulas plus the sum-and-difference tricks; the series-telescoping patterns; the HP’s harmonic-mean trap.
• The algebra mindset: manipulation fluency — factor-and-simplify beats expansion every time.

4. Geometry and the Remainder

• Geometry’s core: the triangle families (similarity, the centroid-orthocentre-incentre properties, the right-triangle theorems), circles (the tangent-chord-angle relations, the common-tangent lengths), polygons’ area-angle formulas, coordinate basics (distance-section-slope, the line-pair positions).
• The strategy note. Geometry’s yield-per-hour is the lowest (many formulas, few questions) — master the core theorems, skip the exotic (3D-combined-solids rarities) unless time permits.
• Numbers-and-modern-math: the divisibility-remainder rules, the HCF-LCM word problems; P&C-probability’s conditional-and-arrangement standard setups — the last-mile chapters.

5. The 40-Minute Execution

• The three-pass method.**Pass 1 (~15 min): the clearly-solvable (your strong chapters’ standard patterns) — bank 8-10; Pass 2 (~15 min): the moderate (multi-step arithmetic, standard algebra); Pass 3 (~8 min):** the remaining, with the TITA-free-guess rule; the last 2 minutes for review.
• The skip trigger: no approach in 45 seconds → mark and move; the 2-minute-per-question average is a ceiling not a floor — the 30-second solve balances the 4-minute marathon question.
• The attempt maths: 14-16 attempts at 85-90% ≈ 99 percentile; the −1 punishes the hopeful guess on MCQs — eliminate to two, then decide.

6. How Exams Probe This Topic

• The practice regime: chapter-wise drills in the weight order (arithmetic → algebra → geometry), then mixed 22-question sectionals; the error-log by chapter and by error-type (concept-gap vs calculation-slip vs misread) drives the final-month plan.
• Cross-reference: Part 5’s mock analytics and Part 6’s working-professional schedule both assume this chapter-priority sequence.

7. Quick Revision: One-Glance Facts

• Weights. Arithmetic ~40%, algebra ~25-30%, geometry ~15-20%, numbers-modern ~10-15%.
• Core methods. LCM-units for time-work; successive-change formula; wavy-curve for inequalities; relative-speed rules.
• Execution. Three-pass; 45-second skip trigger; 14-16 attempts at 85%+; TITA always attempted.

Conclusion. QA is a prioritisation exercise: arithmetic-first mastery, the algebra block second, geometry’s core-only third — executed in three passes with ruthless skipping. The distribution guarantees that your best-spent 100 hours are in the first two blocks; spend them there and the 99-percentile QA score is arithmetic-and-algebra doing the heavy lifting.

Practice Corner: Five Weight Checks (with Answers)

1. Arithmetic’s approximate QA share? — ~40% (9-10 of 22 questions).
2. The two blocks that cover two-thirds of the paper? — Arithmetic plus algebra.
3. The pass-1 mandate? — Bank 8-10 clearly-solvable questions in ~15 minutes.
4. The skip trigger? — No approach in 45 seconds — mark and move.
5. The TITA rule? — Always attempted — no negative marking on TITA.

The Arithmetic Shortcut Set (One Line Each)

Successive percentage change: a + b + ab/100. Restore-original: +25% pairs with −20% (multipliers multiply to 1). Time-work: work = LCM of the days; rates become integers; outlets are negative rates. Relative speed: sum head-on, difference overtaking. Average speed: total distance ÷ total time — never the mean of speeds. Profit: the CP-SP-MP triangle with successive discounts composed by the multiplier method. Alligation: the cross gives the mixture ratio without algebra. Replacement: (1 − 1/x)ⁿ survives after n replacements of fraction 1/x. Eight lines, each worth a recurring question every year — and the reason arithmetic drills repay themselves faster than any other QA investment.