CAT Quantitative Aptitude

Model direct and inverse variation using proportional relationships.

Solve proportional-sharing and partnership problems using contribution and time ratios.

Determine unknown values in simple and weighted-average problems.

Solve mixture problems using alligation or repeated replacement.

Solve profit, loss, markup, and successive-discount problems.

Solve simple- and compound-interest problems involving growth, depreciation, and installment comparisons.

Complete a 30–45-minute timed set of CAT previous-year questions on ratios, averages, mixtures, and commercial arithmetic.

Complete a second 30–45-minute revision block by correcting the timed-set errors and completing a closed-book retrieval quiz covering current and earlier topics.

Model individual, combined, and changing-workforce problems using work rates and completion times.

Use efficiency ratios to compare workers and divide wages in proportion to work done.

Solve pipe-and-cistern problems involving inlets, outlets, and leaks.

Solve journeys using speed, distance, time, stoppage time, and average speed.

Apply relative speed to meetings, overtaking, races, train crossings, circular tracks, and escalators.

Solve upstream and downstream motion problems.

Complete a 30–45-minute timed set of CAT previous-year questions on work, motion, and rates.

Complete a second 30–45-minute revision block by correcting the timed-set errors and completing a closed-book retrieval quiz covering current and earlier topics.

Expand, simplify, and factor polynomial expressions using identities and the factor or remainder theorem.

Solve linear equations in one variable and pairs of simultaneous linear equations.

Form and solve linear equations from CAT-style word problems.

Solve quadratic equations by factorization, completing the square, or the quadratic formula.

Use the discriminant and relationships between roots and coefficients to analyze or construct a quadratic equation.

Simplify surds and rationalize expressions containing radical denominators.

Complete a 30–45-minute timed set of CAT previous-year questions on equations, polynomials, and surds.

Complete a second 30–45-minute revision block by correcting the timed-set errors and completing a closed-book retrieval quiz covering current and earlier topics.

Solve linear and quadratic inequalities using boundary points and sign intervals.

Solve equations and inequalities containing an absolute-value expression.

Determine the domain and range of an elementary algebraic function.

Evaluate composite functions and determine an inverse function when it exists.

Interpret intersections and intercepts of linear and quadratic graphs.

Find the maximum or minimum value of a quadratic expression.

Complete a 30–45-minute timed set of CAT previous-year questions on inequalities, modulus, functions, and graphs.

Complete a second 30–45-minute revision block by correcting the timed-set errors and completing a closed-book retrieval quiz covering current and earlier topics.

Solve equations involving integer or rational exponents.

Simplify logarithmic expressions using the laws of logarithms.

Solve logarithmic equations after enforcing domain restrictions.

Determine terms and sums of arithmetic and geometric progressions, including finite and infinite geometric sums.

Evaluate standard finite series by identifying and manipulating their patterns.

Apply AM-GM or a suitable substitution to optimize a positive algebraic expression.

Complete a 30–45-minute timed set of CAT previous-year questions on exponents, logarithms, progressions, series, and optimization.

Complete a second 30–45-minute revision block by correcting the timed-set errors and completing a closed-book retrieval quiz covering current and earlier topics.

Use parity, prime factorization, and divisibility rules to analyze integers and count multiples in a range.

Compute the HCF and LCM of two or more integers and apply their relationship.

Determine the number and sum of the positive divisors of an integer.

Compute remainders and terminal digits of large powers using modular arithmetic and cyclicity.

Find trailing zeros and the highest power of a prime dividing a factorial.

Interpret numbers in non-decimal bases and solve digit-value constraints.

Complete a 30–45-minute timed set of CAT previous-year questions on integers, divisibility, remainders, and digits.

Complete a second 30–45-minute revision block by correcting the timed-set errors and completing a closed-book retrieval quiz covering current and earlier topics.

Determine unknown sides or angles using intersecting- and parallel-line relationships, triangle angle properties, and congruence.

Use triangle similarity to calculate lengths and area ratios.

Calculate triangle areas using base-height relationships, Heron's formula, and standard special-triangle formulas.

Apply the Pythagorean theorem, standard right-triangle ratios, and elementary trigonometric ratios to right triangles and heights-and-distances problems.

Apply median, centroid, angle-bisector, incenter, inradius, and other standard cevian relationships to triangle problems.

Calculate unknown angles, lengths, or areas using the properties of quadrilaterals and regular polygons.

Complete a 30–45-minute timed set of CAT previous-year questions on lines, triangles, quadrilaterals, and polygons.

Complete a second 30–45-minute revision block by correcting the timed-set errors and completing a closed-book retrieval quiz covering current and earlier topics.

Use chord, arc, central-angle, and inscribed-angle relationships in a circle.

Use tangent, cyclic-quadrilateral, and power-of-a-point relationships.

Calculate the perimeter or area of composite two-dimensional figures.

Calculate the surface area and volume of prisms, cubes, cuboids, and cylinders.

Calculate the surface area and volume of cones, pyramids, frustums, and spheres.

Use similarity and scaling to compare areas and volumes.

Complete a 30–45-minute timed set of CAT previous-year questions on circles and mensuration.

Complete a second 30–45-minute revision block by correcting the timed-set errors and completing a closed-book retrieval quiz covering current and earlier topics.

Represent two-set and three-set classifications with Venn diagrams and apply inclusion-exclusion.

Apply the multiplication and addition principles to count possible outcomes.

Count linear and circular arrangements using permutations.

Count unordered selections and simple distributions using combinations.

Count arrangements subject to adjacency, repetition, or position restrictions.

Calculate probabilities using complements, mutually exclusive events, independence, and conditional counting.

Complete a 30–45-minute timed set of CAT previous-year questions on sets, counting, and probability.

Complete a second 30–45-minute revision block by correcting the timed-set errors and completing a closed-book retrieval quiz covering current and earlier topics.

Calculate distance, midpoint, and slope from Cartesian coordinates.

Form the equation of a line and determine the intersection of two lines.

Calculate the area of a triangle or polygon from its coordinates.

Identify the dominant mathematical structure and choose useful variables or constraints in a multi-topic CAT-QA problem.

Use answer choices, back-solving, or convenient-value substitution to solve an MCQ efficiently.

Use bounds, parity, divisibility, or sign constraints to eliminate answer choices.

Complete a 30–45-minute timed set of CAT previous-year questions using coordinate geometry and alternative solving methods.

Complete a second 30–45-minute revision block by correcting the timed-set errors and completing a closed-book retrieval quiz covering current and earlier topics.

Compare two valid solution methods and select the faster one under test conditions.

Classify CAT-QA questions by likely solving time during an initial scan.

Apply a two-pass question-selection strategy to a timed QA section.

Set attempt and accuracy targets that account for MCQ penalties and TITA questions.

Decide when to continue, skip, or revisit a question using a fixed time threshold.

Apply estimation, substitution, unit, and sign checks to prevent errors under time pressure.

Complete a timed CAT previous-year QA section under exam conditions using the planned selection strategy.

Complete a 30–45-minute analysis block by classifying section errors, identifying priority weaknesses, and constructing a spaced cumulative revision and mock-practice plan.