Important Notes for SSC CGL Quantitative Aptitude
Best Notes for SSC CGL Quantitative Aptitude - Download Free PDF
Preparing for SSC CGL Quantitative Aptitude requires more than just solving random questions - it demands a thorough understanding of concepts, formulas, and problem-solving shortcuts. These comprehensive notes cover every high-weightage topic tested in the SSC CGL exam, including Number System, Trigonometry, Mensuration, Time & Work, Profit & Loss, Data Interpretation, and more. One of the most common mistakes students make is skipping formula revision before attempting practice sets, which leads to avoidable errors under exam pressure. Each set of notes available on EduRev is structured to first build conceptual clarity and then reinforce it with solved examples. Topics like Alligation & Mixture and Pipes & Cisterns, which frequently trip up unprepared candidates, are explained with step-by-step worked solutions. Whether you are a first-time SSC aspirant or a repeat candidate targeting a higher score, these notes provide the fastest route to exam-ready preparation for SSC CGL Quantitative Aptitude.
Notes for SSC CGL Quantitative Aptitude: Number System
The Number System is one of the most foundational topics in SSC CGL Quantitative Aptitude. It covers integers, rational numbers, prime and composite numbers, divisibility rules, cyclicity of unit digits, and methods for finding remainders. A common pitfall is confusing the cyclicity of digits - for example, the unit digit of powers of 2 follows a cycle of 4, a fact that directly appears in SSC CGL questions. Mastering these concepts early prevents errors across several other topics.
- Important Formulas: Number System
- Introduction: Number System
- Cyclicity & Factorial: Number System
- Number Systems: Finding Remainders
- Important Concepts: Number System
- Important Concepts: Number System - 2
Notes for SSC CGL Quantitative Aptitude: HCF & LCM
HCF and LCM questions appear in almost every SSC CGL paper, often disguised within word problems involving bells ringing at intervals or distributing items equally. These notes cover the prime factorization method, division method, and key relationships such as HCF × LCM = Product of two numbers - a formula students frequently misapply when dealing with more than two numbers.
Notes for SSC CGL Quantitative Aptitude: Square Roots & Cube Roots
Square roots and cube roots appear both directly and as components of simplification questions in SSC CGL. These notes explain the long division method for finding square roots of 3-5 digit numbers, key tricks for rapid calculation, and important values to memorize - for instance, knowing that the cube root of 1331 is 11 saves critical seconds in the exam.
- Important Formulas: Square Root & Cube Root
- Points to Remember: Squares & Square Roots
- Points to Remember: Cubes & Cube Roots
- Square Root Tricks for 3, 4 & 5 Digit Numbers
- Important Formulas: Square Roots & Cube Roots
- Solved Examples: Square Roots & Cube Roots
Notes for SSC CGL Quantitative Aptitude: Simplification & Approximation
Simplification and Approximation is a high-scoring section where speed determines success. These notes introduce the BODMAS rule, fraction-to-decimal conversions, and rounding techniques. A frequently tested trap involves nested brackets where students apply the wrong order of operations. Approximation questions require candidates to round values intelligently - rounding 997 to 1000 and adjusting is a standard shortcut covered in these notes.
Notes for SSC CGL Quantitative Aptitude: Fractions & Decimals
Fractions and Decimals underpin simplification, ratio, and percentage problems across the SSC CGL paper. These notes cover recurring decimals, comparison of fractions, and operations with mixed fractions. A specific area where candidates lose marks is converting recurring decimals to fractions - for instance, expressing 0.̄3 as 1/3 - which is explicitly explained with worked examples.
- Decimal Fractions: Notes & Important Formulas
- Solved Examples: Fractions & Decimals
- Important Formula: Fractions & Decimals
Notes for SSC CGL Quantitative Aptitude: Ratio & Proportion
Ratio and Proportion concepts are applied across multiple SSC CGL topics including mixtures, partnership, and time & work. These notes cover compound ratio, duplicate ratio, and proportion properties. A common error candidates make is treating "a:b:c" ratios as two separate ratios without maintaining the correct multiplier when combining them - a mistake addressed directly in these notes.
Notes for SSC CGL Quantitative Aptitude: Percentages
Percentages form the backbone of profit & loss, simple interest, and data interpretation questions. These notes include conversion tables, percentage change formulas, and successive percentage change shortcuts. Students regularly misapply the successive change formula - for example, two successive increases of 10% do not equal 20%, but 21% - a nuance that is clearly explained with numerical examples.
Notes for SSC CGL Quantitative Aptitude: Averages
Averages questions in SSC CGL often involve weighted averages, averages of consecutive integers, and changes in averages when a value is replaced. These notes highlight that the average of first n natural numbers equals (n+1)/2 - a formula that directly solves an entire category of questions. The concept of deviation from the mean is also used as a shortcut to avoid lengthy addition.
Notes for SSC CGL Quantitative Aptitude: Problem on Ages
Problems on Ages require setting up linear equations from word problems describing age differences and ratios at different points in time. A classic SSC CGL scenario involves present and past ages where candidates incorrectly subtract instead of adding years when projecting forward - these notes address such errors with clearly annotated solutions.
Notes for SSC CGL Quantitative Aptitude: Simple Interest & Compound Interest
Simple Interest and Compound Interest are perennial SSC CGL topics, with compound interest questions often involving half-yearly or quarterly compounding. These notes include the derivation and application of CI = P(1 + r/n)^(nt) and the difference formula between CI and SI for two years: Difference = P(r/100)². Students frequently confuse the period adjustments for half-yearly compounding, which is explained step by step.
- Interests: Concept with Examples
- Basic Concepts: Simple Interest & Compound Interest
- Interests: Solved Examples
- Important Formulas: Simple Interest & Compound Interest
Notes for SSC CGL Quantitative Aptitude: Profit, Loss & Discount
Profit, Loss & Discount is consistently among the top-scoring topics in SSC CGL. These notes cover the relationship between cost price, selling price, marked price, and discount, including the important formula: Profit% = (Profit/CP) × 100. A trap frequently set in exam questions involves successive discounts - for instance, 20% then 10% does not equal 30%, and these notes explain the correct multiplier method.
- Overview: Profit & Loss
- Important Formula: Profit & Loss
- Basic Concepts: Profit, Loss & Discount
- Solved Examples: Profit, Loss & Discount
- Important Formulas: Profit, Loss & Discount
Notes for SSC CGL Quantitative Aptitude: Time & Work
Time & Work questions in SSC CGL include pipe-filling problems, efficiency-based work problems, and MDH (Man-Day-Hour) problems. These notes introduce the unitary method and the LCM-based approach, where total work is expressed as LCM of days taken by individual workers - a technique that dramatically reduces calculation time compared to the fraction-based approach.
Notes for SSC CGL Quantitative Aptitude: Pipes & Cisterns
Pipes and Cisterns problems are a specific application of Time & Work, where pipes filling and emptying a tank simultaneously require careful sign convention - a filling pipe adds work while a leak subtracts it. These notes explain the standard formula for combined pipe efficiency and highlight the common error of ignoring the direction of a pipe's contribution when multiple pipes work together.
Notes for SSC CGL Quantitative Aptitude: Time, Speed & Distance
Time, Speed & Distance covers train problems, boat and stream problems, and relative speed scenarios. The critical formula Distance = Speed × Time has numerous derived forms tested in SSC CGL. A frequently tested concept is relative speed - when two objects move in opposite directions their speeds add, while in the same direction they subtract - a distinction candidates often get wrong under time pressure.
- Important Formulae: Time, Speed & Distance
- Important Notes: Speed, Distance & Time
- Solved Examples: Time, Speed & Distance - 1
- Solved Examples: Time, Speed & Distance - 2
- Solved Examples: Time, Speed & Distance - 3
Notes for SSC CGL Quantitative Aptitude: Problems Based on Trains
Train problems require candidates to handle situations where a train crosses a pole, a platform, or another moving train. The key formula is Length = Relative Speed × Time of crossing. These notes clarify that when a train crosses a platform, the total distance covered equals the sum of both lengths - a point where many students incorrectly use only the train's length.
Notes for SSC CGL Quantitative Aptitude: Boats & Streams
Boats and Streams problems test the application of upstream and downstream speed concepts. The standard relationships - Speed in still water = (Downstream + Upstream)/2 and Stream speed = (Downstream - Upstream)/2 - are directly tested in SSC CGL. These notes also cover time-based problems where candidates must find when boats meet, which requires careful setup of distance equations.
Notes for SSC CGL Quantitative Aptitude: Alligation & Mixture
Alligation is used to find the ratio in which two ingredients at different prices or concentrations must be mixed to obtain a desired mixture. The cross-difference (alligation) rule is a rapid technique that avoids setting up full equations. These notes also address replacement problems, where a portion of a mixture is repeatedly replaced - a concept tested in SSC CGL that students find conceptually challenging.
- Important Concepts: Alligation & Mixture
- Solved Examples: Alligation & Mixture
- Overview: Mixture & Alligation
- Solved Examples: Mixtures & Alligation
- Important Formula: Mixtures & Alligation
Notes for SSC CGL Quantitative Aptitude: Partnership
Partnership problems involve distributing profit or loss among partners based on their capital investment and the duration of investment. The key principle is that profit is shared in proportion to Capital × Time. These notes cover both simple partnership (equal time) and compound partnership (different time periods), the latter being a common source of errors when candidates forget to weight by duration.
Notes for SSC CGL Quantitative Aptitude: Unitary Method
The Unitary Method is applied to find the value of one unit from a given quantity and then scale it to find any required quantity. It forms the foundation for ratio, proportion, and direct/inverse variation problems. These notes cover both direct and inverse unitary method with examples, helping candidates identify which type applies - a distinction that many students miss when the relationship between quantities is not stated explicitly.
Notes for SSC CGL Quantitative Aptitude: Linear Equations
Linear Equations in SSC CGL appear as standalone algebra questions and as tools for solving word problems in age, work, and mixture topics. These notes cover equations in one and two variables, graphical representation, and the condition for consistency of a system. A pitfall is sign errors when using the elimination method - these notes include annotated worked examples to prevent this.
- Linear Equations: Important Concepts
- Important Formulas: Linear Equations
- Solved Examples: Linear Equations
- Graph of Linear Equations in Two Variables
- Equations of Lines Parallel to the x-axis & y-axis
Notes for SSC CGL Quantitative Aptitude: Quadratic Equations
Quadratic Equations tested in SSC CGL typically require factorization, use of the quadratic formula, or identifying the nature of roots using the discriminant (b²-4ac). These notes include the sum and product of roots relationships - Sum = -b/a and Product = c/a - which provide quick shortcuts to verify answers without fully solving the equation.
Notes for SSC CGL Quantitative Aptitude: Arithmetic Progressions
Arithmetic Progressions (AP) questions in SSC CGL involve finding the nth term, the sum of n terms, or identifying missing terms in a sequence. The formulas Tn = a + (n-1)d and Sn = n/2[2a + (n-1)d] are essential. A typical error candidates make is using n as the last term's position without correctly identifying the first term or common difference from the problem statement.
Notes for SSC CGL Quantitative Aptitude: Geometric Progressions
Geometric Progressions (GP) involve sequences where each term is multiplied by a fixed common ratio r. Key formulas include Tn = ar^(n-1) and Sum = a(r^n - 1)/(r - 1) for r ≠ 1. SSC CGL occasionally tests the sum to infinity of a GP when |r| < 1, given by S∞ = a/(1-r), a formula that students often confuse with the finite sum formula.
Notes for SSC CGL Quantitative Aptitude: Harmonic Progressions
Harmonic Progressions (HP) are sequences whose reciprocals form an Arithmetic Progression. In SSC CGL, HP questions often ask for the harmonic mean between two numbers, calculated as 2ab/(a+b). These notes also cover the relationship between AM, GM, and HM - specifically AM ≥ GM ≥ HM - which is tested in inequality-based problems.
Notes for SSC CGL Quantitative Aptitude: Number Series
Number Series questions require identifying the pattern - whether arithmetic, geometric, square-based, cube-based, or mixed - to find the missing or wrong term. These notes categorize all major series types with examples. A frequently tested variant involves alternating two separate series interleaved into one, which candidates often miss by looking only at consecutive differences.
Notes for SSC CGL Quantitative Aptitude: Logarithms
Logarithms appear in SSC CGL as both direct formula-based questions and as components of surds and indices problems. These notes cover the product, quotient, and power rules, as well as the change of base formula. A common exam question type asks candidates to simplify expressions like log(a²b/c³), which requires careful sequential application of logarithm properties to avoid sign errors.
Notes for SSC CGL Quantitative Aptitude: Indices & Surds
Indices and Surds questions test the application of exponential laws and rationalization of irrational expressions. These notes cover all index laws, rationalization of denominators involving surds, and simplification of expressions with nested radicals. A typical SSC CGL question involves rationalizing 1/(√5 + √3), where candidates must multiply by the conjugate (√5 - √3) to eliminate the surd from the denominator.
Notes for SSC CGL Quantitative Aptitude: Triangles
Triangles are a core geometry topic in SSC CGL, covering angle sum properties, congruence criteria (SSS, SAS, ASA, RHS), similarity rules, the Pythagoras theorem, and area formulas. These notes also explain properties of special triangles - such as the 30-60-90 and 45-45-90 triangles - whose side ratios provide instant answers to many SSC CGL geometry questions without trigonometry.
- Triangles
- Congruence & Similarity of Triangles
- Solved Examples: Triangles
- Important Formulas: Triangles
Notes for SSC CGL Quantitative Aptitude: Quadrilaterals & Polygons
Quadrilaterals and Polygons tested in SSC CGL include properties of parallelograms, rhombuses, rectangles, squares, and trapeziums, along with interior and exterior angle sum formulas for polygons. These notes clarify that the sum of interior angles of an n-sided polygon equals (n-2) × 180° - a formula frequently misused when students substitute the number of diagonals instead of sides.
- Polygons with Solved Examples
- Quadrilateral: Overview & Examples
- Overview: Polygons
- Important Formulas: Quadrilaterals & Polygons
Notes for SSC CGL Quantitative Aptitude: Circles
Circle geometry in SSC CGL includes properties of chords, tangents, secants, angles subtended at the centre and circumference, and cyclic quadrilaterals. A key theorem frequently tested is that the angle subtended by a chord at the centre is twice the angle subtended at any point on the major arc - a relationship students often apply incorrectly to the minor arc.
Notes for SSC CGL Quantitative Aptitude: Geometry - Solved Examples
These solved example sets cover the complete range of geometry questions that appear in SSC CGL, including triangle properties, circle theorems, quadrilateral properties, and coordinate geometry. Working through these examples exposes the most common question structures and teaches candidates to identify geometric properties from a figure quickly - a skill that significantly improves speed in the exam hall.
- Geometry: Solved Examples - 1
- Geometry: Solved Examples - 2
- Important Formula: Geometry
- Important Formulae: Geometry & Mensuration
- Important Formulas: Geometry
Notes for SSC CGL Quantitative Aptitude: Coordinate Geometry
Coordinate Geometry in SSC CGL covers distance formula, section formula, midpoint formula, slope of a line, and equations of straight lines. Candidates frequently confuse the slope formula - (y₂-y₁)/(x₂-x₁) - with the y-intercept form. These notes also address conditions for parallel and perpendicular lines, which are directly tested in SSC CGL questions involving geometric figures on a coordinate plane.
Notes for SSC CGL Quantitative Aptitude: Mensuration
Mensuration covers 2D area and perimeter calculations as well as 3D volume and surface area of solids. SSC CGL frequently tests the area of a triangle using Heron's formula, the volume of a cone and cylinder, and the curved surface area of a sphere. Students commonly confuse total surface area with curved surface area for cones and cylinders - a distinction explicitly addressed in these notes.
- Overview: Mensuration
- Area & Perimeter: Important Topics & Formulas
- Mensuration: Volume, Surface Area & Solid Figures
- Solved Examples: Mensuration
- Solved Examples: Volume, Surface Area & Solid Figures
- Important Formula: Volume, Surface Area & Solid Figures
Notes for SSC CGL Quantitative Aptitude: Trigonometry
Trigonometry is one of the most formula-heavy topics in SSC CGL, covering trigonometric ratios, identities, and values at standard angles. A critical identity is sin²θ + cos²θ = 1 and its derived forms (1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ), which solve an entire category of simplification questions. Candidates who memorize all three Pythagorean identities gain a significant advantage in this section.
- Overview: Trigonometry
- Basic Concepts: Trigonometry
- Important Formulas: Trigonometry
- Formulas: Trigonometry Formulas & Identities
- Concepts with Solved Examples: Trigonometry
- Solved Examples: Trigonometry
Notes for SSC CGL Quantitative Aptitude: Heights & Distances
Heights and Distances is an application of trigonometry where angles of elevation and depression are used to find heights of towers, buildings, or distances across rivers. In SSC CGL, the angle of elevation (looking up) and angle of depression (looking down) are frequently confused, leading to incorrect triangle setup. These notes use clearly labeled diagrams to eliminate this common mistake.
- Important Formulas: Heights & Distances
- Heights & Distances: Solved Examples
- Solved Examples: Height & Distance
Notes for SSC CGL Quantitative Aptitude: Permutations & Combinations
Permutations and Combinations questions in SSC CGL test the fundamental counting principle, arrangements (nPr), and selections (nCr). A frequent source of errors is deciding whether order matters - for instance, forming a committee (combination) versus arranging people on a podium (permutation). These notes provide clear decision rules to distinguish between the two cases before selecting the formula.
Notes for SSC CGL Quantitative Aptitude: Probability
Probability in SSC CGL involves classical probability, complementary events, and simple conditional probability. The fundamental formula P(E) = (Favourable outcomes)/(Total outcomes) is straightforward, but questions involving cards, dice, and balls require careful enumeration of sample spaces. These notes cover standard sample spaces for a deck of cards and two dice, which form the basis of most SSC CGL probability questions.
- Overview: Statistics & Probability
- Important Formulas: Probability
- Formulas: Probability
- Solved Examples: Probability - 1
- Solved Examples: Probability - 2
- Solved Examples: Probability
Notes for SSC CGL Quantitative Aptitude: Statistics
Statistics questions in SSC CGL cover measures of central tendency (mean, median, mode) and measures of dispersion (range, variance, standard deviation). A common mistake is applying the formula for median of grouped data - Median = L + [(N/2 - cf)/f] × h - incorrectly by using the wrong cumulative frequency value. These notes walk through the formula with a fully solved grouped frequency table example.
Notes for SSC CGL Quantitative Aptitude: Data Interpretation
Data Interpretation (DI) in SSC CGL presents data in line charts, bar charts, pie charts, table charts, and radar charts, with questions requiring percentage calculations, ratio comparisons, and trend identification. These notes cover the key formulas for each chart type and include solved examples. A common time-waster is computing exact values when approximation to the nearest whole number is sufficient to identify the correct answer.
- Important Formula: Line Charts
- Solved Examples: Line Charts
- Solved Examples: Table Charts
- Important Formula: Table Charts
- Solved Examples: Radar Charts
- Important Formula: Radar Charts
- Solved Examples: Pie Charts
- Important Formula: Pie Charts
- Bar Graphs: Introduction & Examples with Solutions
- Solved Examples: Bar Charts
- Important Formula: Bar Charts
- Important Formulas: Data Sufficiency
Notes for SSC CGL Quantitative Aptitude: Clock & Calendar
Clock and Calendar problems require calculating the angle between clock hands and determining the day of the week for a given date. For clocks, the formula Angle = |30H - 5.5M| is essential, where H is the hour and M is the minutes - students frequently forget the factor of 5.5 for the minute hand's angular speed. Calendar problems use the concept of odd days to determine days of the week.
Notes for SSC CGL Quantitative Aptitude: Banker's Discount
Banker's Discount is a less commonly tested but distinct topic in SSC CGL where candidates must know the difference between True Discount and Banker's Discount, and the relationship: Banker's Gain = Banker's Discount - True Discount. These notes clarify that Banker's Discount is always calculated on the face value, while True Discount is calculated on the present value - a distinction that defines every formula in this topic.
Notes for SSC CGL Quantitative Aptitude: Vedic Mathematics
Vedic Mathematics techniques provide rapid calculation shortcuts that are especially useful for multiplication, division, and finding squares of numbers in SSC CGL. The Digit Sum Method - where the digit sum of a number is used to verify arithmetic operations - is a powerful tool for eliminating wrong answer choices in 10-15 seconds without full computation. These notes also cover squaring numbers ending in 5, which reduces a two-step problem to a one-step mental calculation.
- Vedic Mathematics: Solved Examples
- Digit Sum Method: Vedic Maths
- Digit Sums, Casting Out 9s & 9-Check Method
Notes for SSC CGL Quantitative Aptitude: Races & Games of Skill
Races and Games of Skill questions involve concepts of head start, dead heat, and winning margins expressed in time or distance. A "start of x metres" means the faster runner begins x metres behind, while a "head start of x metres" means the slower runner starts x metres ahead - a distinction that determines the entire setup of a race equation and is frequently misread by candidates.
How to Prepare for SSC CGL Quantitative Aptitude: Best Strategy & Topic-Wise Notes
A structured preparation strategy for SSC CGL Quantitative Aptitude begins with identifying which topics carry the highest question frequency. Historically, Geometry, Trigonometry, Data Interpretation, and Arithmetic (Profit & Loss, Time & Work, Percentages) together account for over 60% of the Quantitative Aptitude section. The single most effective preparation habit is to study the formula sheet for a topic immediately before solving its practice questions - this active recall technique embeds formulas far more efficiently than passive reading. All topic-wise notes, formula sheets, and solved examples for SSC CGL Quantitative Aptitude are available on EduRev, organized by topic so candidates can directly navigate to their weaker areas. Aspirants who have cleared SSC CGL consistently report that spending the first two weeks exclusively on Number System, Percentages, and Ratio & Proportion creates a multiplier effect, as these concepts underlie nearly every other arithmetic topic in the syllabus.
SSC CGL Quantitative Aptitude Notes PDF: Topic-Wise Formula Sheets & Solved Examples
The most efficient way to revise for SSC CGL Quantitative Aptitude in the final weeks before the exam is to use topic-wise formula sheets combined with solved examples. Formula sheets for high-density topics like Trigonometry (with all three Pythagorean identities and allied angle values), Mensuration (with 2D and 3D formulas), and Geometry (circle theorems and triangle properties) condense what would otherwise take hours to review into a focused 20-minute revision session. These notes, available on EduRev, pair every formula with at least one worked example showing its direct application in an SSC CGL-style question - bridging the gap between knowing a formula and being able to apply it under timed conditions.
FAQs on Important Notes for SSC CGL Quantitative Aptitude
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