Quantitative Aptitude for Competitive Examinations
Number System
Extracted objective-type questions, options, and answer key from Chapter 1.
H.C.F. and L.C.M. of Numbers
Standard objective problems on Prime Factorization, Highest Common Factor, and Lowest Common Multiple.
Decimal Fractions
Objective problems on recurring decimals, simplification, and fractional operations.
Simplification
BODMAS rule, Modulus, Vinculum, algebraic identities, and numerical simplification problems.
Square Roots and Cube Roots
Square roots, cube roots, prime factorization, long division, radical multiplication/division, and perfect square/cube problems.
Average
Arithmetic mean, weighted average, consecutive series, age/salary problems, speed averages, cricket run rates, and data sufficiency.
Problems on Numbers
Number representation, consecutive numbers, digits and place values, two-digit/three-digit reversing, fractions and reciprocals.
Problems on Ages
Age ratios, present, past and future ages, age differences, average age, and age-based algebraic equations.
Surds and Indices
Laws of indices, definition of surds, order of surds, operations on surds, and exponential equations.
Logarithms
Definition of logarithm, laws of logarithms, base change formula, common logarithms, characteristic and mantissa, logarithmic equations.
Percentage
Percentage definitions, core conversion formulas, percentage increase/decrease, successive changes, commodity price neutrality, population growth & depreciation, demographic breakdowns, mixture percentages, and data sufficiency.
Profit and Loss
Cost price, selling price, profit/loss percentages, chain transactions, ratio of CP & SP, equal profit and loss (x²/100), dishonest dealer & false weights, mixed varieties, discounts & marked price, and data sufficiency.
Ratio and Proportion
Ratios, proportions, 3rd & 4th proportionals, mean proportional, compounded ratios, division of amounts in ratios, and data sufficiency.
Partnership
Simple and compound partnerships, equivalent capital calculation, profit division by investment-time ratio, working partner management fees, and data sufficiency.
Chain Rule
Direct and indirect proportion, unitary method, composite work-time-manpower formulas (M1 D1 H1 / W1 = M2 D2 H2 / W2), and military garrison ration problems.
Pipes and Cisterns
Inlets and outlets filling and emptying rates, leakage delays, alternate-hour operations, clogged pipe flow reductions, and cylinder flow rate calculations.
Time and Work
Basic work rates, combined completion times, efficiency ratios, wage distributions, alternate day schedules, and men-women-children workforce equivalences.
Time and Distance
Speed-time-distance formulas, km/hr to m/sec conversions, relative speed in same/opposite directions, average speed for equal distances, overtaking time, and stoppage delays.
Boats and Streams
Downstream and upstream speeds, boat speed in still water vs. stream speed, round-trip calculations, and perpendicular stream crossing times.
Problems on Trains
Train length, crossing stationary objects/poles, relative speed of two trains, overtaking times, and post-crossing speed relations.
Races and Games of Skill
Race distance ratios, head starts in distance/time, multi-runner comparisons, billiards/card game points handicap, and speed conversion ratios.
Calendar
Odd days calculation, leap year rules, century odd days, identical calendar years, and day of the week determination.
Clocks
Clock face geometry, minute & hour hand speed ratios, angle calculation formulas, coincidence frequency, right angles, and fast/slow clock gain/loss.
Area
Data sufficiency questions on areas & perimeters of rectangles, squares, triangles, circles, semi-circles, sectors, and composite 2D figures.
Volume and Surface Areas
Data sufficiency questions on volumes, capacities, and total/curved surface areas of cubes, cuboids, cylinders, cones, and spheres.
Races and Games of Skill
Objective questions on head starts, relative speeds in races, multi-runner comparisons, and point handicaps in games of skill.
Calendar
Objective questions on odd days calculation, leap year rules, century odd days, identical calendar years, and weekday shifts.
Clocks
Objective questions on clock hands angles, coincidence intervals, right angles, straight lines, strike counts, and gain/loss calculations.
Stocks and Shares
Stock cost prices, discount/premium, brokerage, annual income, yield percentage, and investment comparisons.
Permutations and Combinations
Factorials, word permutations with repeating letters, vowel grouping conditions, committee selections, and combined selections.
Probability
Basic probability rules, coin tosses, die rolls, card picks, marble draws, truth/lie combinations, and conditional events.
True Discount
Present worth calculations, true discount formulas, sum due, SI vs TD relations, and deferred payment offer comparisons.
Banker's Discount
Banker's discount on bill face value, true discount on present worth, banker's gain, discount date, and rate percentage.
Heights and Distances
Trigonometric ratios, angle of elevation, angle of depression, ladder problems, lighthouse observations, and cloud reflections.
Odd Man Out and Series
Finding odd man out, wrong number in series, missing term in sequence, pattern identification, arithmetic, geometric and prime series.