Quantitative Aptitude

Divisibility, remainders, unit digits, factors and recurring decimals — the base layer every other Quant topic uses. CGL asks 1–3 direct questions per Tier 1 shift (missing-digit divisibility, remainders and unit digit are near-certain) and a few more in Tier 2.

BODMAS, identity-based fractions, surds and indices, square/cube roots and approximation. These are the fastest marks in Tier 1 — usually 1–2 questions per shift — and the same skills (identities, surd handling) power the algebra questions.

Highest common factor and lowest common multiple — a small but near-guaranteed slot in CGL. Most questions are template word problems: greatest divisor with remainders (HCF of differences), least number with given remainders (LCM + r), bells, tiles and ratio pairs.

The language of the whole arithmetic section — profit-loss, interest, discount and DI are all percentage questions in disguise. Tier 1 asks 1–2 direct questions per shift (successive change, more/less flips, election and population problems) and Tier 2 leans on it heavily.

Ratio technique with its three biggest exam containers: proportion (mean/third/fourth proportional), partnership (capital × time profit splits) and ages (present vs shifted ratios). Tier 1 reliably has 2 questions from this cluster; most are 30–45 second marks once the multiplier habit is built.

One guaranteed question in almost every Tier 1 shift: a member joining or leaving, a batsman's innings, or a weighted two-group average. The whole topic collapses to one habit — convert averages to sums (Sum = Avg × n) before touching anything.

Simple and compound interest — a near-certain slot in every shift. Tier 1 favourites: direct SI, amount at CI with clean chips, CI–SI differences and doubling chains. Tier 2 adds instalments and multi-year rate cases. Everything runs on the multiplier-chip habit.

The highest-yield arithmetic block in Tier 1. CP–SP basics, successive discounts, the marked-price chain and dishonest-dealer cases appear in nearly every shift; Tier 2 layers on trade chains and price-shift comparisons. Everything reduces to multiplier chips.

Alligation is the highest-leverage tool in arithmetic — it solves mixtures, dilutions, adulteration profits and even average-group questions in one crossing. Replacement chains and two-mixture blending complete the set. Expect one sure question per Tier 1 shift and more in Tier 2.

Rates, LCM units and the men-days chain solve nearly every question: combined work, efficiency ratios, pipes and cisterns, mid-work join/leave, alternate days, provisions and wages. One slot is near-guaranteed in Tier 1, with staged pipe problems and wage splits rising in Tier 2.

Trains, relative speed, boats & streams, average-speed traps and races — two dependable slots per Tier 1 shift and more in Tier 2. Everything hangs on D = S×T, the 5/18 conversion, and the add/subtract rule for relative speed.

Identities, $x+\frac1x$ expressions, $a^3+b^3+c^3-3abc$, surds, linear equations and simple max–min. Algebra gives 2–4 marks-rich questions in every CGL shift, and almost all of them fall to a handful of identities plus value-putting — the highest return per hour of study in advanced maths.

Lines and angles, triangles and their four centres, similarity and BPT, Pythagoras, quadrilaterals, polygons and circles. The single largest advanced-maths block in CGL (3–5 questions per shift), and nearly every question runs off a memorised angle result, a triplet, or a ratio rule.

Areas and perimeters of triangles, quadrilaterals, circles, sectors and regular polygons, plus paths, wheels and percentage-change effects. A reliable 1-3 questions per shift; the formulas are few and heavily recycled, so this converts to marks faster than almost any other advanced topic.

Volumes and surface areas of cubes, cuboids, cylinders, cones, spheres, hemispheres, prisms and pyramids, plus melting-recasting, capacities and painted-cube counts. About 1-3 questions per shift; every question reduces to one formula plus a unit conversion, so memorising the formula sheet is nearly the whole job.

Ratios, the standard-value table, the three identities, complementary angles, value-putting and max-min values. Tier 1 reliably holds 2-4 trig questions and they fall almost mechanically to the value table, one identity, or a 3-4-5 style triangle — among the cheapest marks in the paper.

Applied trigonometry: angles of elevation and depression, the 30-45-60 rules, two-angle configurations, moving observers and compound figures. Every question reduces to one right triangle and one tangent — learn the three standard-angle multipliers and the cot-difference formula and this becomes near-guaranteed marks.

Mean, median, mode and simple dispersion: raw-data medians, the mode = 3·median − 2·mean relation, grouped-data formulas, range and SD with shift-scale effects. Every question is formula-driven with small numbers — statistics is among the most scoring blocks in the Quant paper once the six formulas above are memorised.

Reading tables and charts: totals, percentage change, pie-chart angles and shares, row averages, weighted averages and successive growth. DI rewards calm reading more than calculation — every question is one fraction or one product away, and the data is given in clean, round numbers by design. Tier 2 sets often attach a 5-question block to one table, so per-table setup pays twice.