Arithmetic Aptitude

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Numbers

Natural, whole, integers; even & odd; prime & composite; divisibility rules; factors & multiples. Skills: number logic, factorization speed, basic number manipulation.

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Learning objectives Understand natural, whole, integers Identify even & odd, prime & composite numbers Apply divisibility rules Work with factors & multiples Develop number logic and factorization speed

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Problems on Numbers

Digit-based problems, remainder concepts, cyclicity, unit digit problems, number formation.

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Learning objectives Solve digit-based problems Apply remainder concepts Use cyclicity Solve unit digit problems Handle number formation

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Problems on H.C.F and L.C.M

Prime factorization and division methods, applications in word problems, LCM in recurring events, HCF in grouping.

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Learning objectives Apply prime factorization method Use division method Solve word problems with LCM/HCF Apply LCM in recurring events Apply HCF in grouping problems

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Decimal Fraction

Decimal operations, fraction–decimal conversion, recurring decimals, word problems.

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Learning objectives Perform decimal operations Convert between fraction and decimal Handle recurring decimals Solve word problems

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Simplification

BODMAS rule, fraction and percentage simplification, approximation methods, shortcut calculations.

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Learning objectives Apply BODMAS rule Simplify fractions and percentages Use approximation methods Apply shortcut calculations

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Square Root and Cube Root

Prime factor and long division methods, approximation, perfect squares & cubes recognition.

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Learning objectives Use prime factor method Apply long division method Use approximation Recognize perfect squares & cubes

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Surds and Indices

Laws of exponents, rationalization, simplifying surds, fractional powers.

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Learning objectives Apply laws of exponents Rationalize expressions Simplify surds Work with fractional powers

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Logarithm

Laws of logarithms, change of base, solving logarithmic equations, simplification problems.

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Learning objectives Apply laws of logarithms Use change of base Solve logarithmic equations Simplify using logarithms

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Percentage

Basic percentage, increase & decrease, successive percentage, reverse percentage, real-life applications.

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Learning objectives Calculate basic percentage Handle increase & decrease Apply successive percentage Apply reverse percentage Solve real-life applications

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Ratio and Proportion

Basic ratio, proportion equations, continued proportion, comparison problems.

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Learning objectives Understand basic ratio Solve proportion equations Apply continued proportion Solve comparison problems

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Chain Rule

Direct and inverse proportion, work-rate applications.

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Learning objectives Apply direct proportion Apply inverse proportion Solve work-rate applications

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Average

Simple average, weighted average, combined average, missing value problems.

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Learning objectives Calculate simple average Apply weighted average Find combined average Solve missing value problems

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Partnership

Profit sharing, time-weighted partnership, capital variation problems.

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Learning objectives Apply profit sharing Handle time-weighted partnership Solve capital variation problems

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Alligation or Mixture

Alligation rule, replacement problems, weighted mixing, two & three variable mixtures.

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Learning objectives Apply alligation rule Solve replacement problems Handle weighted mixing Solve two & three variable mixtures

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Time and Distance

Speed, distance, time relation; relative speed; unit conversions; meeting problems.

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Learning objectives Apply speed-distance-time relation Calculate relative speed Convert units Solve meeting problems

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Problems on Trains

Platform crossing, pole crossing, train overtaking, opposite direction problems.

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Learning objectives Solve platform crossing Solve pole crossing Handle train overtaking Solve opposite direction problems

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Boats and Streams

Upstream & downstream, effective speed, current calculation.

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Learning objectives Solve upstream & downstream problems Calculate effective speed Find current

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Races and Games

Head start, dead heat, relative speed comparison.

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Learning objectives Handle head start problems Solve dead heat problems Compare relative speed

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Height and Distance

Trigonometric ratios, angle of elevation and depression, shadow problems.

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Learning objectives Apply trigonometric ratios Use angle of elevation Use angle of depression Solve shadow problems

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Time and Work

Work efficiency, LCM method, alternate day work, combined work problems.

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Learning objectives Calculate work efficiency Apply LCM method Solve alternate day work Solve combined work problems

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Pipes and Cistern

Filling & emptying, leak problems, efficiency comparison.

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Learning objectives Solve filling & emptying problems Handle leak problems Compare efficiency

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Profit and Loss

Cost price & selling price, marked price & discount, successive discount, profit percentage comparison.

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Learning objectives Apply CP & SP Handle marked price & discount Apply successive discount Compare profit percentage

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Simple Interest

SI formula, principal calculation, time calculation, real-life problems.

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Learning objectives Apply SI formula Calculate principal and time Solve real-life problems

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Compound Interest

CI formula, difference between SI & CI, half-yearly & quarterly compounding, growth problems.

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Learning objectives Apply CI formula Find difference between SI & CI Apply half-yearly & quarterly compounding Solve growth problems

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True Discount

Present worth, banker's formula, application-based problems.

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Learning objectives Calculate present worth Apply banker's formula Solve application-based problems

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Banker's Discount

Banker's gain, present value, comparison with true discount.

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Learning objectives Calculate banker's gain Find present value Compare with true discount

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Stocks and Shares

Face value, market value, dividend calculation, yield problems.

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Learning objectives Understand face value and market value Calculate dividend Solve yield problems

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Problems on Ages

Age ratio problems, past & future age, linear age equations.

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Learning objectives Solve age ratio problems Handle past & future age Form and solve linear age equations

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Calendar

Leap year logic, odd days method, day calculation.

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Learning objectives Apply leap year logic Use odd days method Calculate day of week

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Clock

Angle between hands, coinciding positions, time calculation problems.

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Learning objectives Find angle between hands Determine coinciding positions Solve time calculation problems

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Area

Triangles, quadrilaterals, circles, composite figures.

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Learning objectives Calculate area of triangles, quadrilaterals, circles Solve composite figures

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Volume and Surface Area

Cube, cuboid, cylinder, cone, sphere, frustum.

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Learning objectives Calculate volume and surface area of cube, cuboid, cylinder, cone, sphere, frustum

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Permutation and Combination

nPr, nCr, circular permutations, selection problems.

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Learning objectives Apply nPr and nCr Solve circular permutations Solve selection problems

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Probability

Basic probability, complement rule, independent events, conditional probability.

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Learning objectives Apply basic probability Use complement rule Handle independent events Apply conditional probability

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Odd Man Out and Series

Number series, alphabet series, pattern detection, missing term.

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Learning objectives Identify number and alphabet series Detect patterns Find missing term