The document provides examples for calculating squares of numbers nearest to certain values like 50, 100, 200, 300, 400, 1000, 1100 using a basic calculation method. It involves taking the base as the number rounded to the nearest value and comparing it to the given value. The difference is divided by the square of the difference and added to the base number to get the square. It also provides examples for squares ending with 5, examples where the unit digit sum is 10, methods to find square roots and cube roots. The document further discusses number systems, divisibility rules, number of divisors, recurring decimals to fractions conversion, remainder theorem and alligation.
1. The document provides various shortcuts and methods for multiplying, dividing, finding sums and performing other calculations on numbers.
2. Methods are given for multiplying 2-digit, 3-digit and numbers with repeating digits. Shortcuts are also provided for finding sums of natural numbers, squares, cubes, and other patterns.
3. The document outlines various tests and methods for determining if a number is divisible by 2, 3, 4, 7, 11, 13, and other numbers. Properties of squares, square roots, primes, HCF, LCM and other algebraic concepts are also summarized.
I am Ronald G. I am a Statistics Assignment Expert at statisticshomeworkhelper.com. I have done Ph.D Statistics from New York University, USA. I have been helping students with their statistics assignments for the past 5 years. You can hire me for any of your statistics assignments.
Visit statisticshomeworkhelper.com or email info@statisticshomeworkhelper.com.
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This document provides several possible answers for the indefinite integral F(x) of various trigonometric and exponential functions, with each integral equaling the function plus a constant C. Specifically, it lists the integrals of -cosx, -cotx, ex, sinx, ln|x|, secx, -cscx, and tanx as the functions minus or plus the respective functions with C added.
english mathematics dictionary
kamus bahassa inggris untuk matematika
oleh neneng
Nurwaningsih
(06081281520066)
Nurwaningsih30@gmail.com
PROGRAM STUDI PENDIDIKAN MATEMATIKA
FAKULTAS KEGURUAN DAN ILMU PENDIDIKAN
UNIVERSITAS SRIWIJAYA
INDRALAYA
2017
semoga bermanfaat
1) The document contains solutions to 10 calculus problems involving finding derivatives and evaluating functions. The problems include finding derivatives of trigonometric, logarithmic, and exponential functions, as well as evaluating functions at given values.
2) The solutions show the steps taken to solve each problem through substitution and application of derivative rules.
3) The techniques demonstrated include finding derivatives using basic rules, evaluating functions by substitution, and simplifying expressions involving trigonometric identities.
47 operations of 2nd degree expressions and formulasalg1testreview
The document discusses operations involving binomials and trinomials. It defines a binomial as a two-term polynomial of the form ax + b and a trinomial as a three-term polynomial of the form ax2 + bx + c. It states that the product of two binomials is a trinomial that can be found using the FOIL method: multiplying the first, outer, inner, and last terms. The FOIL method is demonstrated through examples multiplying binomial expressions. Expanding products involving negative binomials requires distributing the negative sign before using FOIL.
This document discusses solving numerical equations involving logarithmic and exponential functions. It provides examples of solving both log equations and exponential equations. To solve log equations, the problems are rewritten in exponential form by removing the log. To solve exponential equations, the exponents are brought down by rewriting the problem in logarithmic form. Steps include isolating the exponential or logarithmic term containing the unknown, rewriting the equation accordingly, and then solving for the unknown variable. Practice problems with solutions are provided to illustrate the process.
1. The document provides various shortcuts and methods for multiplying, dividing, finding sums and performing other calculations on numbers.
2. Methods are given for multiplying 2-digit, 3-digit and numbers with repeating digits. Shortcuts are also provided for finding sums of natural numbers, squares, cubes, and other patterns.
3. The document outlines various tests and methods for determining if a number is divisible by 2, 3, 4, 7, 11, 13, and other numbers. Properties of squares, square roots, primes, HCF, LCM and other algebraic concepts are also summarized.
I am Ronald G. I am a Statistics Assignment Expert at statisticshomeworkhelper.com. I have done Ph.D Statistics from New York University, USA. I have been helping students with their statistics assignments for the past 5 years. You can hire me for any of your statistics assignments.
Visit statisticshomeworkhelper.com or email info@statisticshomeworkhelper.com.
You can also call on +1 678 648 4277 for any assistance with statistics.
This document provides several possible answers for the indefinite integral F(x) of various trigonometric and exponential functions, with each integral equaling the function plus a constant C. Specifically, it lists the integrals of -cosx, -cotx, ex, sinx, ln|x|, secx, -cscx, and tanx as the functions minus or plus the respective functions with C added.
english mathematics dictionary
kamus bahassa inggris untuk matematika
oleh neneng
Nurwaningsih
(06081281520066)
Nurwaningsih30@gmail.com
PROGRAM STUDI PENDIDIKAN MATEMATIKA
FAKULTAS KEGURUAN DAN ILMU PENDIDIKAN
UNIVERSITAS SRIWIJAYA
INDRALAYA
2017
semoga bermanfaat
1) The document contains solutions to 10 calculus problems involving finding derivatives and evaluating functions. The problems include finding derivatives of trigonometric, logarithmic, and exponential functions, as well as evaluating functions at given values.
2) The solutions show the steps taken to solve each problem through substitution and application of derivative rules.
3) The techniques demonstrated include finding derivatives using basic rules, evaluating functions by substitution, and simplifying expressions involving trigonometric identities.
47 operations of 2nd degree expressions and formulasalg1testreview
The document discusses operations involving binomials and trinomials. It defines a binomial as a two-term polynomial of the form ax + b and a trinomial as a three-term polynomial of the form ax2 + bx + c. It states that the product of two binomials is a trinomial that can be found using the FOIL method: multiplying the first, outer, inner, and last terms. The FOIL method is demonstrated through examples multiplying binomial expressions. Expanding products involving negative binomials requires distributing the negative sign before using FOIL.
This document discusses solving numerical equations involving logarithmic and exponential functions. It provides examples of solving both log equations and exponential equations. To solve log equations, the problems are rewritten in exponential form by removing the log. To solve exponential equations, the exponents are brought down by rewriting the problem in logarithmic form. Steps include isolating the exponential or logarithmic term containing the unknown, rewriting the equation accordingly, and then solving for the unknown variable. Practice problems with solutions are provided to illustrate the process.
The document discusses solving numerical equations involving logarithmic and exponential functions in base 10 or base e. It provides examples of solving log and exponential equations by isolating the part containing the unknown, then rewriting the equation in the opposite form (log to exponential or exponential to log). The key steps outlined are: 1) isolate the exponential/log part containing the unknown, 2) rewrite the equation by "bringing down" exponents as logarithms or vice versa. Several examples are worked through demonstrating these steps.
This document provides information about Reed-Solomon encoding and decoding. It introduces Reed-Solomon codes, including their parameters like code length, number of information symbols, and error correcting capability. It describes the generator polynomial and how it is used to encode messages. The document also discusses the Massey FSR Synthesis Algorithm for Reed-Solomon decoding and Forney's Equation for calculating error magnitudes. An example is provided to demonstrate decoding a received codeword using the Massey algorithm.
This document provides examples of how to write ordered pairs for different parabolic functions to graph parabolas. It gives the ordered pairs for functions like y=x^2, f(x)=x^2+1, f(x)=2(x-1)^2, and f(x)=2(x-1)^2+3. By changing the coefficients or shifting the x-values, the ordered pairs can represent different parabolas that have the same basic shape but are stretched or shifted on the x-y plane. Writing the ordered pairs makes it straightforward to graph each parabolic function.
This document discusses solving numerical equations involving logarithmic and exponential functions. It provides examples of solving:
1) Logarithmic equations by dropping the log and writing the equation in exponential form.
2) Exponential equations by isolating the exponential term containing the unknown, then taking the log of both sides to write it in logarithmic form.
3) The document demonstrates solving sample equations of each type step-by-step and explains the differences between logarithmic and exponential equations.
The document discusses complex numbers. It begins by explaining that the equation x^2 = -1 has no real solutions, so an imaginary number i is defined such that i^2 = -1. A complex number is then defined as a number of the form a + bi, where a is the real part and bi is the imaginary part. Rules for adding, subtracting and multiplying complex numbers by treating i as a variable and setting i^2 to -1 are provided. Examples of solving equations and performing operations with complex numbers are given.
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The document proves the product rule for derivatives. It begins by writing the derivative of fg as the limit definition. It then subtracts and adds fg(x) to rewrite this in a form where the limit can be split into two pieces. Taking the limits individually and factoring terms provides the product rule, where the derivative of fg is f'g + fg'.
The document discusses mathematical expressions and polynomials. It provides examples of algebraic expressions and operations with polynomials, such as factoring polynomials. Factoring polynomials makes it easier to calculate outputs, simplify rational expressions, and solve equations. One example factors the polynomial 64x3 + 125 into (4x + 5)(16x2 - 20x + 25). It notes that factoring polynomials is useful for evaluating polynomial expressions more easily, as demonstrated by an example evaluating the factored form of 2x3 - 5x2 + 2x for various values of x.
The document discusses expressions and polynomials. It provides examples of algebraic expressions and operations that can be performed on polynomials, such as factoring. Factoring polynomials is useful for easier evaluation, simplifying rational expressions, and solving equations. One example factors the polynomial 64x3 + 125 into (4x + 5)(16x2 - 20x + 25). Factoring the polynomial 2x3 - 5x2 + 2x is recommended before evaluating it for specific values of x.
The document discusses algorithms for finding the closest pair of points from a set of n points given as (x,y) coordinates. It presents three approaches: computing all pairwise distances which is O(n^2); sorting the points and comparing adjacent pairs which is the time to sort plus O(n); and divide and conquer which splits the points, solves subproblems recursively, and merges in O(n log n) time.
The document discusses functions and their basic language. It defines a function as a procedure that assigns each input exactly one output. It provides examples of functions, such as a license number to name function. It explains that a function must have a domain (set of inputs) and range (set of outputs). Functions can be represented graphically, through tables of inputs and outputs, or with mathematical formulas.
The document discusses mathematical expressions and polynomials. It provides examples of algebraic expressions and operations with polynomials, such as factoring polynomials. Factoring polynomials makes it easier to calculate outputs, simplify rational expressions, and solve equations. One example factors the polynomial 2x3 - 5x2 + 2x and shows it is easier to evaluate the factored form for different values of x than the original polynomial. The key purposes of factoring polynomials are to simplify calculations and operations.
This document provides examples and explanations of finding nth derivatives of various functions. It begins with examples of the nth derivatives of ln(x), ex, sin(x), and xsin(x). Common patterns are identified, such as the nth derivative of ln(x) being (-1)n-1(n-1)!/xn. Exercises are then provided to find formulas for the nth derivatives of additional functions like cos(x), xcos(x), xln(x), e5x, xn, and polynomials.
The document is a student's practical file submission for a numerical methods course. It contains 13 programs implementing various numerical methods to solve nonlinear equations and systems of linear equations. The student acknowledges their teacher and classmates for guidance and help in completing the practical file requirements.
The document discusses mathematical expressions and algebraic expressions. It provides examples of algebraic expressions like 3x^2 - 2x + 4 and explains how to perform operations on polynomial expressions, like factoring 64x^3 + 125 as (4x + 5)(16x^2 - 20x + 25). The key purposes of factoring polynomials are stated as making it easier to calculate outputs, simplify rational expressions, and solve equations. An example is given to evaluate the factored expression 2x^3 - 5x^2 + 2x for various values of x.
Emily was experimenting with Powerpoint and created some trippy pictures with her kid sister Valerie. However, she was surprised about how the pictures were created in Powerpoint 2003 and wasn't sure how it happened. Emily and her sister had fun making creative pictures together.
Dr. Paresh G. Solanki's curriculum vitae summarizes his qualifications and experience. He holds an MBBS and MD in Pharmacology. His current role is as a Drug Safety Physician at APCER PHARMA INDIA LTD, where he performs medical review and safety evaluation of drugs. Previously he has worked in clinical research and medical affairs. He has over 6 years of experience in clinical research, teaching, and medical evaluation. His areas of expertise include pharmacovigilance and clinical trial conduct.
- The document discusses a group of families who were evicted from their homes in a forest area and are now living in precarious conditions in the banks of the Luri River.
- Around 12 of the 24 homes had been demolished, and 6 families are now living exposed to the elements on the river banks.
- The evicted families have submitted an application to the district administration asking for alternative housing within 5 days, but their demands have not been addressed yet.
The document outlines criteria for evaluating short answer and extended response questions in ELA based on the M.D. LOC framework. The framework examines Meaning, Development, Language use, Organization, and Conventions. Each category is further defined to evaluate if the student provided the requested information, used sufficient and relevant details, demonstrated language control, had a logical structure, and used correct mechanics.
The document discusses solving numerical equations involving logarithmic and exponential functions in base 10 or base e. It provides examples of solving log and exponential equations by isolating the part containing the unknown, then rewriting the equation in the opposite form (log to exponential or exponential to log). The key steps outlined are: 1) isolate the exponential/log part containing the unknown, 2) rewrite the equation by "bringing down" exponents as logarithms or vice versa. Several examples are worked through demonstrating these steps.
This document provides information about Reed-Solomon encoding and decoding. It introduces Reed-Solomon codes, including their parameters like code length, number of information symbols, and error correcting capability. It describes the generator polynomial and how it is used to encode messages. The document also discusses the Massey FSR Synthesis Algorithm for Reed-Solomon decoding and Forney's Equation for calculating error magnitudes. An example is provided to demonstrate decoding a received codeword using the Massey algorithm.
This document provides examples of how to write ordered pairs for different parabolic functions to graph parabolas. It gives the ordered pairs for functions like y=x^2, f(x)=x^2+1, f(x)=2(x-1)^2, and f(x)=2(x-1)^2+3. By changing the coefficients or shifting the x-values, the ordered pairs can represent different parabolas that have the same basic shape but are stretched or shifted on the x-y plane. Writing the ordered pairs makes it straightforward to graph each parabolic function.
This document discusses solving numerical equations involving logarithmic and exponential functions. It provides examples of solving:
1) Logarithmic equations by dropping the log and writing the equation in exponential form.
2) Exponential equations by isolating the exponential term containing the unknown, then taking the log of both sides to write it in logarithmic form.
3) The document demonstrates solving sample equations of each type step-by-step and explains the differences between logarithmic and exponential equations.
The document discusses complex numbers. It begins by explaining that the equation x^2 = -1 has no real solutions, so an imaginary number i is defined such that i^2 = -1. A complex number is then defined as a number of the form a + bi, where a is the real part and bi is the imaginary part. Rules for adding, subtracting and multiplying complex numbers by treating i as a variable and setting i^2 to -1 are provided. Examples of solving equations and performing operations with complex numbers are given.
Mathematics assignment sample from assignmentsupport.com essay writing services https://writeessayuk.com/
The document proves the product rule for derivatives. It begins by writing the derivative of fg as the limit definition. It then subtracts and adds fg(x) to rewrite this in a form where the limit can be split into two pieces. Taking the limits individually and factoring terms provides the product rule, where the derivative of fg is f'g + fg'.
The document discusses mathematical expressions and polynomials. It provides examples of algebraic expressions and operations with polynomials, such as factoring polynomials. Factoring polynomials makes it easier to calculate outputs, simplify rational expressions, and solve equations. One example factors the polynomial 64x3 + 125 into (4x + 5)(16x2 - 20x + 25). It notes that factoring polynomials is useful for evaluating polynomial expressions more easily, as demonstrated by an example evaluating the factored form of 2x3 - 5x2 + 2x for various values of x.
The document discusses expressions and polynomials. It provides examples of algebraic expressions and operations that can be performed on polynomials, such as factoring. Factoring polynomials is useful for easier evaluation, simplifying rational expressions, and solving equations. One example factors the polynomial 64x3 + 125 into (4x + 5)(16x2 - 20x + 25). Factoring the polynomial 2x3 - 5x2 + 2x is recommended before evaluating it for specific values of x.
The document discusses algorithms for finding the closest pair of points from a set of n points given as (x,y) coordinates. It presents three approaches: computing all pairwise distances which is O(n^2); sorting the points and comparing adjacent pairs which is the time to sort plus O(n); and divide and conquer which splits the points, solves subproblems recursively, and merges in O(n log n) time.
The document discusses functions and their basic language. It defines a function as a procedure that assigns each input exactly one output. It provides examples of functions, such as a license number to name function. It explains that a function must have a domain (set of inputs) and range (set of outputs). Functions can be represented graphically, through tables of inputs and outputs, or with mathematical formulas.
The document discusses mathematical expressions and polynomials. It provides examples of algebraic expressions and operations with polynomials, such as factoring polynomials. Factoring polynomials makes it easier to calculate outputs, simplify rational expressions, and solve equations. One example factors the polynomial 2x3 - 5x2 + 2x and shows it is easier to evaluate the factored form for different values of x than the original polynomial. The key purposes of factoring polynomials are to simplify calculations and operations.
This document provides examples and explanations of finding nth derivatives of various functions. It begins with examples of the nth derivatives of ln(x), ex, sin(x), and xsin(x). Common patterns are identified, such as the nth derivative of ln(x) being (-1)n-1(n-1)!/xn. Exercises are then provided to find formulas for the nth derivatives of additional functions like cos(x), xcos(x), xln(x), e5x, xn, and polynomials.
The document is a student's practical file submission for a numerical methods course. It contains 13 programs implementing various numerical methods to solve nonlinear equations and systems of linear equations. The student acknowledges their teacher and classmates for guidance and help in completing the practical file requirements.
The document discusses mathematical expressions and algebraic expressions. It provides examples of algebraic expressions like 3x^2 - 2x + 4 and explains how to perform operations on polynomial expressions, like factoring 64x^3 + 125 as (4x + 5)(16x^2 - 20x + 25). The key purposes of factoring polynomials are stated as making it easier to calculate outputs, simplify rational expressions, and solve equations. An example is given to evaluate the factored expression 2x^3 - 5x^2 + 2x for various values of x.
Emily was experimenting with Powerpoint and created some trippy pictures with her kid sister Valerie. However, she was surprised about how the pictures were created in Powerpoint 2003 and wasn't sure how it happened. Emily and her sister had fun making creative pictures together.
Dr. Paresh G. Solanki's curriculum vitae summarizes his qualifications and experience. He holds an MBBS and MD in Pharmacology. His current role is as a Drug Safety Physician at APCER PHARMA INDIA LTD, where he performs medical review and safety evaluation of drugs. Previously he has worked in clinical research and medical affairs. He has over 6 years of experience in clinical research, teaching, and medical evaluation. His areas of expertise include pharmacovigilance and clinical trial conduct.
- The document discusses a group of families who were evicted from their homes in a forest area and are now living in precarious conditions in the banks of the Luri River.
- Around 12 of the 24 homes had been demolished, and 6 families are now living exposed to the elements on the river banks.
- The evicted families have submitted an application to the district administration asking for alternative housing within 5 days, but their demands have not been addressed yet.
The document outlines criteria for evaluating short answer and extended response questions in ELA based on the M.D. LOC framework. The framework examines Meaning, Development, Language use, Organization, and Conventions. Each category is further defined to evaluate if the student provided the requested information, used sufficient and relevant details, demonstrated language control, had a logical structure, and used correct mechanics.
Este documento lista 10 comportamientos digitales importantes: 1) Respeto, 2) Libertad, 3) Identidad, 4) Integridad, 5) Intimidad, 6) Autonomía, 7) Calidad de vida, 8) Cuidado y acompañamiento, 9) Respeto por la ley, y 10) Derechos de autor. Cada comportamiento incluye un enlace a un artículo o blog que ofrece más información sobre ese tema.
Psychology is the science that deals with mental processes and behavior. It emerged as an independent field in 1879 with Wilhelm Wundt establishing the first experimental psychology lab. Major schools of thought in psychology include structuralism, functionalism, psychoanalysis, behaviorism, humanism, and cognitivism. Psychology encompasses many subfields like biological, clinical, cognitive, developmental, and social psychology that study different aspects of mental processes and behavior.
1. The document provides important facts and formulas regarding numbers, including place value, types of numbers, tests for divisibility, and progressions.
2. It defines numeral, place value, face value, and types of numbers such as natural numbers, whole numbers, integers, even/odd numbers, prime/composite numbers.
3. Tests for divisibility by various numbers from 2 to 24 are explained. Shortcut methods for multiplication and basic formulas are also listed.
4. Progressions including arithmetic and geometric progressions are defined, with formulas provided for their terms and sums. Solved examples illustrate applications of the concepts.
This document contains information about important numbers and formulas. It discusses topics like place value, types of numbers (natural, whole, integers, even, odd, prime, composite), tests for divisibility, multiplication shortcuts, basic formulas, progression, and the Euclidean algorithm for division. Some key points covered are the place value system in Hindu-Arabic numerals, definitions of different types of numbers, tests for divisibility by various numbers, formulas for arithmetic and geometric progressions, and the division algorithm.
1. The document provides various shortcuts and methods for solving problems involving numbers and operations like multiplication, division, finding sums, squares, cubes etc.
2. Shortcuts are given for multiplying multi-digit numbers, finding sums of series where digits are repeated, evaluating expressions with decimals where one number is repeated, and determining properties of squares, cubes, primes and other numbers.
3. Various methods are outlined for testing divisibility by different numbers, finding highest common factors and lowest common multiples, algebraic identities and other quantitative reasoning concepts.
This document provides information on various types of numbers and formulas related to numbers. It discusses natural numbers, whole numbers, integers, even/odd numbers, prime numbers and tests for divisibility. It also covers topics like place value, numeral systems, arithmetic progressions, geometric progressions, and shortcut methods for multiplication. Key points include the definition of different types of numbers, tests for divisibility by various numbers, formulas for operations like addition, subtraction and multiplication of algebraic expressions, and the general forms of arithmetic and geometric progressions.
The document provides important facts and formulae related to numbers. It discusses the following key points:
1. The Hindu-Arabic numeral system uses 10 digits (0-9) to represent any number. A group of digits forming a number is called a numeral.
2. Types of numbers include natural numbers, whole numbers, integers, even/odd numbers, prime/composite numbers. Tests for divisibility by various numbers are outlined.
3. Shortcut methods for multiplication like distributive law are described. Basic formulae for exponents, progressions, and the division algorithm are listed.
This document provides information on numbers and numerical concepts in 3 sentences:
It defines key terms like numeral, place value, and face value. It also categorizes different types of numbers such as natural numbers, whole numbers, integers, even/odd numbers, and prime/composite numbers. Finally, it outlines tests for divisibility and formulas for operations like multiplication, progression, and division.
1. Natural numbers include counting numbers like 1, 2, 3, and continue indefinitely. Whole numbers include natural numbers plus zero. Integers include whole numbers and their opposites.
2. Rational numbers can be written as a fraction, like 1.5 = 3/2. Irrational numbers cannot be written as a fraction, like π.
3. The four basic operations are addition, subtraction, multiplication, and division. Addition and subtraction follow rules about sign and order. Multiplication and division rules depend on the signs of the factors or dividend and divisor.
I am Tim L. I am a Mathematical Statistics Assignment Expert at excelhomeworkhelp.com. I hold a Master's in Statistics, from Seletar, Singapore. I have been helping students with their assignments for the past 7 years. I solved assignments related to Mathematical Statistics.
Visit excelhomeworkhelp.com or email info@excelhomeworkhelp.com. You can also call on +1 678 648 4277 for any assistance with Mathematical Statistics Assignments.
- The document provides information on various topics related to number properties including natural numbers, whole numbers, integers, rational numbers, fractions, decimals, recurring and non-recurring decimals, prime factorization, HCF, LCM, factors, multiples, and divisibility rules.
- It includes examples of converting recurring decimals to fractions, finding the digit in the units place when a number is raised to a power, and the maximum power of a prime factor in a factorial.
- Properties of remainders when dividing numbers are discussed along with applications demonstrating the use of remainder properties and the cancellation rule. Fermat's theorem is also stated.
The document discusses various types of numbers including natural numbers, whole numbers, and integers. It provides examples and explanations related to properties of these numbers. Some key points include:
- Natural numbers start from 1 and do not include 0, negative numbers, or decimals.
- Whole numbers include all natural numbers and 0.
- Integers include whole numbers and their negatives.
- Examples are provided to illustrate properties like divisibility, perfect squares, and solving word problems involving sums and products of numbers.
- The last part discusses Donkey's stable number based on his true and false answers to questions about divisibility, being a square, and the first digit. It is determined his number must
The document outlines 9 multiplication shortcuts or tricks using properties of numbers. These include multiplying numbers by 11 by adding the digits, squaring numbers ending in 9 by placing 9s and appending other digits, squaring numbers ending in 5 by omitting the 5 and multiplying the remaining number by the next higher number and appending 25, and multiplying numbers where the ones digits sum to 10 by multiplying the tens and ones places separately and placing the products successively.
This document provides practice questions and tips in business mathematics. It contains multiple choice questions related to topics like ratios, percentages, profit and loss, time and work, averages, simple and compound interest, discounts, and permutations and combinations. The questions are intended to help students prepare for competitive exams in subjects like commerce and management.
This document provides practice questions and tips in business mathematics. It contains multiple choice questions related to topics like ratios, percentages, profit and loss, time and work, averages, simple and compound interest, discounts, and permutations and combinations. The questions are intended to help students prepare for competitive exams in subjects like commerce and management.
1. The document discusses various mathematical concepts related to number systems, divisibility tests, LCM, HCF, indices, and surds.
2. It provides definitions and examples of LCM, HCF, and properties related to indices.
3. Various problems and their step-by-step solutions related to number systems, divisibility tests, LCM, HCF, indices, and surds are presented.
This document contains a mathematics lesson on whole numbers, place value, rounding, and solving word problems. It includes examples of writing numbers in expanded and standard form, determining place values, rounding numbers, testing for divisibility, and solving multi-step word problems involving operations on whole numbers. The lesson concludes with additional challenge problems applying the concepts covered.
The document contains a math problem involving sequences, geometry transformations, simultaneous equations, and other algebra topics. It provides the steps to solve various math problems, including listing the first three terms of a sequence, describing a geometric reflection, solving simultaneous equations algebraically, and estimating the median from a histogram.
Lovely Professional University UNIT 1 NUMBER SYSTEM.pdfkhabarkus234
This document provides information on various number theory concepts including:
- Types of numbers such as positive integers, rational numbers, and irrational numbers.
- Converting decimals to fractions and using divisibility rules.
- Finding factors, multiples, and applying the remainder theorem.
- Understanding prime numbers, composite numbers, and perfect squares.
- Working with concepts like least common multiples, greatest common factors, arithmetic and geometric progressions.
More companies in the process of recruitment, play more emphasis in the topic of numbers in numerical aptitude. Especially for AMCAT aspirants this is very much useful.
The document provides information on various number system concepts in Vedic maths including:
1. Methods for multiplying numbers with 11, 9, 99, and 999 using place value concepts.
2. Methods for multiplying two-digit and three-digit numbers using the "criss-cross" method.
3. Shortcuts for finding squares and square roots of numbers.
4. Divisibility rules and their applications.
5. Concepts like remainder theorem, power cycles, and unit digit patterns that are useful for solving problems involving remainders and exponents.
6. Information on factors, multiples, and their properties like total number of factors and sum of factors.
Unlocking Productivity: Leveraging the Potential of Copilot in Microsoft 365, a presentation by Christoforos Vlachos, Senior Solutions Manager – Modern Workplace, Uni Systems
Ocean lotus Threat actors project by John Sitima 2024 (1).pptxSitimaJohn
Ocean Lotus cyber threat actors represent a sophisticated, persistent, and politically motivated group that poses a significant risk to organizations and individuals in the Southeast Asian region. Their continuous evolution and adaptability underscore the need for robust cybersecurity measures and international cooperation to identify and mitigate the threats posed by such advanced persistent threat groups.
AI 101: An Introduction to the Basics and Impact of Artificial IntelligenceIndexBug
Imagine a world where machines not only perform tasks but also learn, adapt, and make decisions. This is the promise of Artificial Intelligence (AI), a technology that's not just enhancing our lives but revolutionizing entire industries.
In his public lecture, Christian Timmerer provides insights into the fascinating history of video streaming, starting from its humble beginnings before YouTube to the groundbreaking technologies that now dominate platforms like Netflix and ORF ON. Timmerer also presents provocative contributions of his own that have significantly influenced the industry. He concludes by looking at future challenges and invites the audience to join in a discussion.
Things to Consider When Choosing a Website Developer for your Website | FODUUFODUU
Choosing the right website developer is crucial for your business. This article covers essential factors to consider, including experience, portfolio, technical skills, communication, pricing, reputation & reviews, cost and budget considerations and post-launch support. Make an informed decision to ensure your website meets your business goals.
Ivanti’s Patch Tuesday breakdown goes beyond patching your applications and brings you the intelligence and guidance needed to prioritize where to focus your attention first. Catch early analysis on our Ivanti blog, then join industry expert Chris Goettl for the Patch Tuesday Webinar Event. There we’ll do a deep dive into each of the bulletins and give guidance on the risks associated with the newly-identified vulnerabilities.
Driving Business Innovation: Latest Generative AI Advancements & Success StorySafe Software
Are you ready to revolutionize how you handle data? Join us for a webinar where we’ll bring you up to speed with the latest advancements in Generative AI technology and discover how leveraging FME with tools from giants like Google Gemini, Amazon, and Microsoft OpenAI can supercharge your workflow efficiency.
During the hour, we’ll take you through:
Guest Speaker Segment with Hannah Barrington: Dive into the world of dynamic real estate marketing with Hannah, the Marketing Manager at Workspace Group. Hear firsthand how their team generates engaging descriptions for thousands of office units by integrating diverse data sources—from PDF floorplans to web pages—using FME transformers, like OpenAIVisionConnector and AnthropicVisionConnector. This use case will show you how GenAI can streamline content creation for marketing across the board.
Ollama Use Case: Learn how Scenario Specialist Dmitri Bagh has utilized Ollama within FME to input data, create custom models, and enhance security protocols. This segment will include demos to illustrate the full capabilities of FME in AI-driven processes.
Custom AI Models: Discover how to leverage FME to build personalized AI models using your data. Whether it’s populating a model with local data for added security or integrating public AI tools, find out how FME facilitates a versatile and secure approach to AI.
We’ll wrap up with a live Q&A session where you can engage with our experts on your specific use cases, and learn more about optimizing your data workflows with AI.
This webinar is ideal for professionals seeking to harness the power of AI within their data management systems while ensuring high levels of customization and security. Whether you're a novice or an expert, gain actionable insights and strategies to elevate your data processes. Join us to see how FME and AI can revolutionize how you work with data!
Cosa hanno in comune un mattoncino Lego e la backdoor XZ?Speck&Tech
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Partecipate alla presentazione per immergervi in una storia di interoperabilità, standard e formati aperti, per poi discutere del ruolo importante che i contributori hanno in una comunità open source sostenibile.
BIO: Sostenitrice del software libero e dei formati standard e aperti. È stata un membro attivo dei progetti Fedora e openSUSE e ha co-fondato l'Associazione LibreItalia dove è stata coinvolta in diversi eventi, migrazioni e formazione relativi a LibreOffice. In precedenza ha lavorato a migrazioni e corsi di formazione su LibreOffice per diverse amministrazioni pubbliche e privati. Da gennaio 2020 lavora in SUSE come Software Release Engineer per Uyuni e SUSE Manager e quando non segue la sua passione per i computer e per Geeko coltiva la sua curiosità per l'astronomia (da cui deriva il suo nickname deneb_alpha).
Have you ever been confused by the myriad of choices offered by AWS for hosting a website or an API?
Lambda, Elastic Beanstalk, Lightsail, Amplify, S3 (and more!) can each host websites + APIs. But which one should we choose?
Which one is cheapest? Which one is fastest? Which one will scale to meet our needs?
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Overview
Dive into the world of anomaly detection on edge devices with our comprehensive hands-on tutorial. This SlideShare presentation will guide you through the entire process, from data collection and model training to edge deployment and real-time monitoring. Perfect for those looking to implement robust anomaly detection systems on resource-constrained IoT/edge devices.
Key Topics Covered
1. Introduction to Anomaly Detection
- Understand the fundamentals of anomaly detection and its importance in identifying unusual behavior or failures in systems.
2. Understanding Edge (IoT)
- Learn about edge computing and IoT, and how they enable real-time data processing and decision-making at the source.
3. What is ArgoCD?
- Discover ArgoCD, a declarative, GitOps continuous delivery tool for Kubernetes, and its role in deploying applications on edge devices.
4. Deployment Using ArgoCD for Edge Devices
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5. Introduction to Apache Kafka and S3
- Explore Apache Kafka for real-time data streaming and Amazon S3 for scalable storage solutions.
6. Viewing Kafka Messages in the Data Lake
- Learn how to view and analyze Kafka messages stored in a data lake for better insights.
7. What is Prometheus?
- Get to know Prometheus, an open-source monitoring and alerting toolkit, and its application in monitoring edge devices.
8. Monitoring Application Metrics with Prometheus
- Detailed instructions on setting up Prometheus to monitor the performance and health of your anomaly detection system.
9. What is Camel K?
- Introduction to Camel K, a lightweight integration framework built on Apache Camel, designed for Kubernetes.
10. Configuring Camel K Integrations for Data Pipelines
- Learn how to configure Camel K for seamless data pipeline integrations in your anomaly detection workflow.
11. What is a Jupyter Notebook?
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12. Jupyter Notebooks with Code Examples
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Presented at the CAiSE 2024 Forum, Intelligent Information Systems, June 6th, Limassol, Cyprus.
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Paper: https://doi.org/10.1007/978-3-031-61000-4_16
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We will explore the capabilities of AI in understanding XML markup languages and autonomously creating structured XML content. Additionally, we will examine the capacity of AI to enrich plain text with appropriate XML markup. Practical examples and methodological guidelines will be provided to elucidate how AI can be effectively prompted to interpret and generate accurate XML markup.
Further emphasis will be placed on the role of AI in developing XSLT, or schemas such as XSD and Schematron. We will address the techniques and strategies adopted to create prompts for generating code, explaining code, or refactoring the code, and the results achieved.
The discussion will extend to how AI can be used to transform XML content. In particular, the focus will be on the use of AI XPath extension functions in XSLT, Schematron, Schematron Quick Fixes, or for XML content refactoring.
The presentation aims to deliver a comprehensive overview of AI usage in XML development, providing attendees with the necessary knowledge to make informed decisions. Whether you’re at the early stages of adopting AI or considering integrating it in advanced XML development, this presentation will cover all levels of expertise.
By highlighting the potential advantages and challenges of integrating AI with XML development tools and languages, the presentation seeks to inspire thoughtful conversation around the future of XML development. We’ll not only delve into the technical aspects of AI-powered XML development but also discuss practical implications and possible future directions.
1. BASIC CALCULATION
(i) Square nearest to 50 (+) or 50 (-).
For numbernearestto50 we will take the base as 25 and forcomparisonwe will compare
the numberwith50.
50
50 – 18 =32
(32)
(a) (32)² = 25 - 18/(18)² = 7 /324.
We needonlytwodigitnumberinthe secondhalf.Sowe will addthe remainingdigitinto
the firsthalf.
So,7 + 3 /24 =1024.
(b) (47)²
Compare the numberwith50.Since itis 3 lessthan 50 .sowe will subtract3 fromitsbase
and take the square of 3 in the secondhalf.
25 – 3 / (3)²= 22/9.
We getonlyone digitinsecondhalf,we have toget a two digitnumbersowe make 9 as 09.
22/09 = 2209.
(ii) Square nearest to 100 (+) or 100 (-).
For numbernearestto100 we will take the base asnumberonlyandfor comparisonwe will
compare the numberwith100.
100
100 + 7 =107
107
(a) (107)² = 107 +7 /(7)²
=114 /49
=11449
2. (b) (97)² = 97 -3 /(3)²= 94 /9
We getonlyone digitinsecondhalf,we have toget a two digitnumbersowe make 9 as 09.
94/09 = 9409.
(iii) Square nearest to 200 (+) or 200 (-)
For numbernearestto200 we will take the base asnumberonlyandfor comparisonwe
will compare the numberwith200.
200
200 + 8 =208
208
(a) (208)² = 208 + 8 /(8)²
= 216/64 (Incase of numbernearestto200 ,we have to multiply2infirsthalf)
= 2 x 216 / 64
=43264.
200
(b) (197)² = 197 – 3 /(-3)² 200 – 3 =197
= 194 / 9 197
=2 x 194/09 (make secondhalf twodigitnumber)
= 38809.
(iv) Square nearest to 300 (+) or 300 (-)
For numbernearestto300 we will take the base asnumberonlyandfor comparisonwe
will compare the numberwith300.
(a) (309)² = 309 +9/ (9)²
=318/81 (Incase of numbernearestto300, we have to multiply3infirsthalf)
= 3 x 318 /81
=95481
(v) Square nearest to 400 (+) or 400 (-)
For numbernearestto400 we will take the base asnumberonlyandfor comparisonwe
will compare the numberwith400.
(a) (404)² = 404 +4/ (4)²
=416/16 (Incase of numbernearestto400, we have to multiply4infirsthalf)
= 4 x 416 /16
3. = 163216
(vi) Square nearest to 1000 (+) or 1000 (-)
For numbernearestto1000 we will take the base as numberonlyand forcomparisonwe
will compare the numberwith1000.
(a) (1004)² = 1004 +4/ (4)²
= 1008/16 (Incase of numbernearestto1000, we have to multiply10in first
half)
= 10 x 1008 /16 = 1008016
(vii) Square nearest to 1100 (+) or 1100 (-)
For numbernearestto1000 we will take the base as numberonlyandforcomparisonwe
will compare the numberwith1000.
(a) (1108)² = 1108 +8 / (8)²
= 1116/64 (Incase of numbernearestto1100, we have to multiply11in first
part)
= 11 x 1116 /16 = 1227664
(viii) ENDING WITH 5 (SQUARE)
(i) (35)² = 35 x 35 = 3 x (3 + 1 ) / 5 x 5
= 3 x 4 / 25
= 1225
(ii) (105)² = 105 x 105 = 10 x (10 + 1) / 5 x 5
= 10 x 11 / 25
11025.
(ix) UNIT DIGIT SUM = 10
In thiscase the othernumbernumbershouldbe same,andthe sumof digitsatunit
place mustbe = 10
(i) 76 x 74 = 7 x (7 +1) / 6 x 4
= 7 x 8 /24
=5624
(ii) 23 x 27 = 2 x (2 + 1) / 3 x 7
= 2 x 3 /21
= 621.
(x) SQUARE ROOT :-
NUMBERS LAST DIGIT
(i) 1, 9 1
(ii) 2, 8 4
4. (iii) 3, 7 9
(iv) 4, 6 6
(v) 5 5
(a) Findthe square root of 6084.
60 / 84 (We divide the numberintotwohalves,startingfromthe lefthandside)
60 / 84
7 / 2 7 / 8
7 x 8 = 56 ( lessthan60 ) ,so the square root is78.
(xi) CUBE ROOT :-
NUMBERS LAST DIGIT
(i) 1 1
(ii) 2 8
(iii) 3 7
(iv) 4 4
(v) 5 5
(vi) 6 6
(vii) 7 3
(viii) 8 2
(ix) 9 9
(a) Findthe Cube root of 912673
Steps:-
i) We divide the numberintotwohalves.
ii) From the lefthandside take the pairof three numbers,whichmakesone half
and remainingnumberformsthe other.
5. 912 / 673
9 (Cube of the number(9) is nearestto912) / 7.
Cube root is97
To multiply any two digit number by 11:
• For this example we will use 54.
• Separate the two digits in your mind (5 4).
• Add the 5 and the 4 together (5+4=9)
• Put the resulting 9 in the gap 594.
11 x 54=594
11 x 57 ... 57 ... 5+7=12 ... put the 2 in the hole and add the 1 from the 12 to the 5 in to get 6 for a result
of 627
6. NUMBER SYSTEM
Natural numbers: - The numberswhichwe use tocount anynumberof things.
Example:-1,2,3, 4, 5 ---- etc.
Whole number:- Whenzeroisincludedinnatural number,itbecomeswholenumber.
Example:-0,1,2, 3, 4, 5 ---- etc.
Integers:- Integersare whole numbers,whichare eitherpositiveornegative.
Example:-0,-1, -2,3, 4 --- etc.
Prime number: - All the numberswhichare divisibleby1 anditself onlyare prime numbers.
Example:-2,3,5, 7, 11 ---- etc.
Composite Number:- It isthe product of two or more than twodistinctor same prime number.
Example:- 4, 6, 8 ------ etc.
Even Number:- Anyintegerthatisa multipleof 2 isEven.
Example:-2,4,6, 8, 10 --- etc.
Odd Number:- Anyintegerthatis nota multipleof 2 isOdd.
Example:- 1, 3, 5, 7, 9 ----- etc.
L.C.M (Least CommonMultiple):- Itisa multiple of twoormore than twonumber.
H.C.F (HighestCommonFactor):- It is the highestvalue whichcandivide the givennumber.
For any 2 givennumbers HCFx LCM = Product of the 2 numbers.
HCF of fractions = HCF of numerators of all the givenfractions/LCM ofthe denominatorsof all the
fractions.
LCM of fractions = LCM ofnumerators of all the fractions/HCF ofthe denominatorsof all the fractions.
NumberSystem (Sumof differentnatural numbers):-
(i) Sum of first n natural number:-
1+2+3+4+5+------+n = n (n+1)/2.
7. (ii) Sum of square of first n natural number:-
1²+2²+3²+4²+5²+ ------ +n²= n (n+1)(2n+1)/6.
(iii) Sum of cube offirst n natural number:-
1³+2³+3³+4³+5³+ ------ +n³= {n(n+1)/2}².
(iv) Sum of first n evennatural number:-
2+4+6+8+10+ ----- +n = n(n+1).
(v) Sum of first n odd natural number:-
1+3+5+7+9+ ----- +n= (n) ².
DIVISIBILITY RULES:-
1) For 2:- Unit digitof any numberis0, 2, 4, 6, 8.
2) For 3:- Sum of all digitof anynumberisdivisibleby3.
3) For 4(2²):- If last twodigitof a numberisdivisible by4,thenthat numberisdivisibleby
4.
4) For 5:- If lastdigitof the numberis5 or 0, thennumberisdivisible by5.
5) For 6(2x3):- Last digitof any numberisdivisible by2 andsum total of all digitof a
numberisdivisible by3.
6) For 7:- Multiplyunitdigitby2, and subtract the numberwiththem. If itisdivisible
Example:- 795 is divisible by7or not check?
Unit digit5x2 = 10.
Remaining79 – 10 = 69.
Nowdivide 69 by7, resultisnotdivisibleby7.
7) For 8(2³):- Checkthe last three digit,whetheritisdivisibleby8 or not.
8) For 9:- Sum of all digitsmustbe divisibleby9.
9) For 10(2x5):- Checkthe divisibilityof 2and 5 or unitdigitmusthave zeroat the end.
8. 10) For 11:- A numberisdivisible by11,if difference betweensum of evenplace andthe
sumof digitof odd placesisdivisible by11.(Zeroisdivisibleby11).
11) For 12(3x4):- Checkdivisibilityof 3& 4.
12) For 13:- Multiplyunitdigitby4 and addthe value tothe remainingdigit.
Example:- Check1404 isdivisible by13 or not?
Unit digit4 x 4 =16
Now,addi.e.140+16 =156 /13. Thisnumberisdivisibleby13.
13) For 14:- Checkdivisibilityof 2& 7.
14) For 17:-Multiplyunitdigitby5 andsubtract withthe remainingdigit,checkif nowthe
numberisdivisible.
15) For 19:- Multiplyunitdigitby2 and addwiththe remainingdigit,checkif now the
numberisdivisible.
16) For 23:- Multiplyunitdigitby7 and addwiththe remainingdigit,checkif now the
numberisdivisible.
17) For 29:- Multiplyunitdigitby3 and addwiththe remainingdigit,checkif now the
numberisdivisible.
18) For 31:- Multiplyunitdigitby3 and subtractwiththe remainingdigit,checkif nowthe
numberisdivisible.
19) For 39:- Multiplyunitdigitby4 and addwith the remainingdigit,checkif now the
numberisdivisible.
NUMBER OF DIVISORS:-
N = aᴾ x bᴿx cᵀ
Numberof divisors:- (P+1)(R+1)(T+1).
9. N = aᴾ x bᴿx cᵀ
Sum of divisor:-
How to determine if a number is Prime?
The easiest& simplestmethodistodivide the numberuptothe closetsquare rootof thatnumber.
Example. Let’sconsider53. Numberclose to53 havinga perfectsquare is64 and itssquare root is8.
Nowstart dividing53from 2 to 8. There isno such numberbetween2to 8 whichdivides53so 53 isa
prime number.
Recurring decimal intoFractionConversion:
Convertthe decimal
intoa fraction.
Start withthe equation:
There are twodigitsinthe repeatingblock,somultiplybothsidesby102
= 100.
Nowsubtract N from bothsides.Notice thatthe repeatingpartcancelsout.
Divide bothsidesby99, multiplynumeratoranddenominatorbya powerof 10 to get ridof the decimal
point,andsimplify.
CYCLICITYMETHOD: - It isa methoduse tofindoutthe remainderof anyexpression.
Example:Findthe remainderwhen 4⁹⁶ isdividedby 6.
(aᴾ⁺¹-1)(bᴿ⁺¹-1)(cᵀ⁺¹ - 1) /(a-1)(b-1)(c-1).
10. Number/6 4¹ 4² 4³ 4⁴ 4⁵ 4⁶ 4⁷ 4⁸
Remainder 4 4 4 4 4 4 4 4.
Remainderinall casesis4, so final remainderwill be 4.
REMAINDER THEOREM:- Product of any twoor more thantwo natural numberhasthe same numberas
the product of theirremainder.
FERMAT’S REMAINDER THEOREM:-
Let P be a prime numberandN be a numbernotdivisible byP.ThenremainderobtainedwhenAᴾ⁻¹/P
=1, If H.C.F (A,P) is1.
(i) (A+1)ᴿwill alwaysgive 1as remainderforall valuesof A and N.
(ii) (A) ᴿwheneven,remainderis1 andwhenN isodd,remainderisA itself.
(iii) (aⁿ+ bⁿ) is divisiblebya+ b, if n isodd.
(iv) (aⁿ - bⁿ) is divisible bya+ b , if n is even.
(vi) (aⁿ - bⁿ) isdivisible bya- b , if n iseven.
Number of a’s (a prime factor) in N!
Number of a’s in N! = [N/a] + [N/a²] + [N/aᶟ] + …….
Q1) For example howmany2’sare in12!
Ans:It‘s [12/2] + [12/4] + [12/8] + [12/16]
= 6 + 3 + 1 + 0 = 10
Q2) 45! Ends withhowmanyzeros?
Numberzerosdependuponnumberof 5’s and2’s.
Numberof 5’s: 9 + 1 = 10
Numberof 2’s: 22 + 11 + 5 + 2 + 1 = 41
So numberof zero’s= 10
11. MIXTURES AND ALLIGATION
Alligation:Itisthe rule thatenablesustofindthe ratio inwhichtwoor more ingredientsatthe
givenprice mustbe mixedtoproduce a mixture of desiredprice.
Mean Price: The cost of a unitquantityof the mixture iscalledthe meanprice.
1. Rule of Alligation:If twoingredientsare mixed,then Quantityof cheaper = C.P.of dearer -
Mean Price
Quantity of dearerMean price - C.P. of cheaper
C.P.of a unitquantityof cheaper(c) C.P.of a unitquantityof dearer(d)
Mean Price (m)
(d- m) (m - c)
(Cheaperquantity) : (Dearer quantity) = (d - m) : (m - c).
2. Suppose acontainercontainsx of liquidfromwhichyunitsare takenoutand replacedbywater.
Afternoperations,the quantityof pure liquid=x{1 – (y/x)}ⁿ units.
12. PERCENTAGE
PERCENTAGE CHART:
1 2 3 4
1 100% 200 300 400
2 50 100 150 200
3 33.33 66.66 100 133.33
4 25 50 75 100
5 20 40 60 80
6 16.66 33.33 50 66.66
7 14.24 28.56 42.85 57.14
8 12.5 25 37.5 50
9 11.11 22.22 33.33 44.44
10 10 20 30 40
PERCENTAGE BASICS:-
1) Percentage increase = increase x 100 / Base Value. 100 120
2) Percentage decrease = decrease x 100 / Base Value. 120 100
3) Percentage = Value attainedx 100/ Total value.
Q 1) Salary of Ram increasesby30% in monthof January .If hismonthlysalary isRs 7000/-.Findthe
salaryof Ram inthe respective month.
Solution:- Assume Original salary=100
Salaryafterincrease = 130
100 7000
130 13 x 70 = 9100
Q2) A salaryis 20% lessthanB, thenby how much % B salarymore than A?
Solution: - Use Direct Formula 20 x 100/80 = 25%.
R x 100 /100 – R.
13. Q3) Price of Sugar increasesby 40%, familyreducesitsconsumptionsothattheirexpense remainsame.
Findthe reductioninpercentage of sugar.
Solution:- Use DirectFormula
40 x 100/140 = 28.56%
Q4) In a Companyprice of penincreasesby10% anddue to thisthe sale reducesby20%. What wouldbe
the neteffectdue tothis change?
Solution:- Use DirectFormula
A = increase by10% = +10 % {increases positive}
B = decrease by20% = - 20% {decrease negative}
10 – 20 + (-10 x 20/100) = 10 – 20 – 2 = -12 = 12 % decrease.
Q5) If side of square increase by10%, whatisthe netchange inthe area of the square?
Solution:- Use DirectFormula here,x = + 10% (increase)
2 x 10 + (10 x 10 /100) = 21%.
Q6) Ram donate 40% of hissalaryto charity organization,fromthe remaininghe put50% to hisbank
account ,fromthe remainingbalance he make aninvestmentof 30% ina companyand now he isleft
withRs 1470/-.FindRam’s monthlysalary.
Solution:- Use DirectFormula
Were p1, p2 andp3 are three percentagesgiven.
p1 = 40% p2 = 50% p3 =30%
R x 100 /100 + R.
A + B + (AB/100)
2x + (x²/100)
Salary = Saving x 100 x 100 x 100 /(100-p1)(100-p2)(100-p3)
14. Another Approach: - Total Salary(Assume) = 100
Donated(40%) = Rs 40
Left amount= 60
Bankaccount (50%) =Rs 50.
Leftamount=30
Investment(30%) =Rs30
LeftAmount=21
Here LeftAmount21 1470 (21 x 70)
AssumedSalary100 100 x 70 = Rs 7000/-
15. PROFITAND LOSS
C.P = COST PRICE OF AN ARTICLE
S.P = SELLING PRICE OF ANARTICLE
M.P = MARKED PRICE OF AN ARTICLE
L.P (LIST PRICE) = MARKED PRICE
1) PROFIT = S.P – C.P
(a) PROFIT % = PROFIT x 100 /C.P.
2) LOSS = C.P – S.P
(b) LOSS % = LOSS x 100 /C.P.
3) GENERAL FORMULA: C.P = S.P X 100 /100 + P%. (P% = PROFIT%)
Or
C.P = S.P X100/100 – L%. (L% = LOSS%)
4) SUCCESSIVEDISCOUNT: - It is a discountgivenonalreadydiscountedproduct.
A + B – (AB/100) where A and B both are discounts.
5) MARKED PRICE (M.P) – DISCOUNT = SELLING PRICE.
6) DISHONEST SHOPKEEPER (CASE ):-
PROFIT % = ERROR VALUE x 100/ORIGINAL – ERROR VALUE.
Q1) A man buysan article forRs 700/- and sellsitata gainof 20% .Findthe sellingprice of the
article.
Solution:C.P = 700, Gain % = 20
C.P=S.P x 100/100 + P%.
S.P= C.Px (100 +P %) /100 = 700 x 120/100 =Rs 840
Quick Approach: Letus assume C.P= 100, for 20% gain S.P=120
C.P:S.P=100:120
100 700 (100 x 7)
16. 120 840 (120 x 7).
Q2) Ram soldan article forRs 1500/- at a profitof 25%. Atwhat cost will she have tosell itto
geta profitof 30% ?
Solution:Assume C.P=100
At 25% profitS.P= 125
At 30% profitS.P= 130
125 1500 (125 x 12)
130 130 x12 = 1560.
Q3) The costof 12 pensisequal to sellingprice of 15 pens.Whatis the profitor loss% incurred?
Solution:C.P OF12 PEN = S.POF 15 PEN
C.P/S.P = 15/12 =5/4.
LOSS OF1 PEN (LOSS = C.P – S.P)
LOSS %= LOSS x 100/C.P = 1 x 100/5 =20%.
Q4) By selling35Orangesa vendorlosesthe sellingprice of 5 Oranges.Hisloss% is:
Solution:LOSS = C.P of 35 Orange – S.P of 35 Orange
LOSS = S.P of 5 Orange
S.P of 5 Orange = C.P of 35 Orange – S.P OF35 Orange
S.Pof 40 Orange = C.Pof 35 Orange
C.P/S.P= 40/35 = 8/7 LOSS of I Orange
LOSS %= 1 x 100/8 = 12.5%
Q5) A solda watch to B at a gainof 20% and B soldit to C at a lossof 10% .If C broughtthe
watch forRs 216,at whatprice didA buy?
Solution:In thisCase A B C
Use formula:
C.P = S.P x 100 x 100/ (100 – P %)( 100 – L %)
Q6) Successive discountof 10%,20% and 15% is:
Solution:Use formula:
A + B – (AB/100) =10 + 20 - (10 x 20/100) = 28%
Againuse same formula= 28 + 15 - (28 x 15/100) = 38.8%
Q7) A shopkeepersoldtwoitemsof Rs400 each. Onone he gain10% & on otherhe losses10%
.Findhisgain/losspercent.
Solution:Since S.Pis same forboth the items.
GAIN%=LOSS%= 10%. = x.
LOSS% = (x/10)²
= (10/10)² = 1% loss.
17. RATIO AND PROPORTION
1) A : B = 1 : 2 Here 1 = Antecedent, 2 = consequent
2) (a) A : B =1 : 2 DUPLICATE is A² : B² = 1 : 4
(b) A:B =1: 2 SUB- DUPLICATE is (A) ⅟₂: (B) ⅟₂ = 1: (2) ⅟₂
(c) A: B =1: 2 TRIPLICATE is Aᶟ: Bᶟ = 1: 8
(d) A:B =1: 2 SUB- TRIPLICATE is (A) ⅓: (B) ⅓ = 1: (2) ⅓
3) A: B:: C: D Here B and C are Means (mean values) and A and D are Extremes(extreme values).
4) MEAN PROPORTION: - Here b = Mean proportion
5) CONTINUED PROPORTION: -If a, b,c, d are in continuedproportionthen,
Q1) A:B = 1 : 3 , B:C = 5 : 7 and C:D = 9 : 7 thenA : B : C : D ?
Solution: A : B : C : D
1 3 ③ ③ fill vacantspace by puttingtheirnearestnumberi.e.(3)
⑤ 5 7 ⑦ fill vacantspace byputtingtheirnearestnumberi.e.(5,7)
⑨ ⑨ 9 7 fill vacantspace byputtingtheirnearestnumberi.e.(9)
_______________________________________________
A = 1 x 5 X 9 = 45
B = 3 x 5 x9 = 135
A/B = C/D (Basic Proportion)
b² = a x c
a/b = b/c =c/d
18. C = 3 x 7 x 9 = 108
D = 3 x 7 x 7 = 147
Q2) The monthlyincome of A & B are inratio 2: 3 and theirmonthlyexpenseare inratio5: 9.If each of
themsavesRs 600 per monththentheirmonthlyincomesare:
Solution:Let the income be intheirratio2x: 3x
Expense ratioof A & B is5y:9y
Income – Expense = Saving
2x -5y = 600 ------①
3x – 9y =600 ------②solvingboth,we getx =800.
Hence A = 2x = 2 x 800 = 1600 and B = 3x = 3 x 800 = 2400.
Q3) FindThirdproportionof 6, 24.
Solution:6: 24:: 24: x
6/24 = 24/x 6x = 24 x 24 => x = 24 x 24 /6 => 96.
Q4) FindFourthproportion8, 24, and36.
Solution:8:24:: 36: x.
8/24 =36/x 8x = 36 x 24 => x = 108.
A: B: C: D = 15: 45: 63: 49.
19. TIME AND DISTANCE
(i) Speed= Distance / time
Distance ismeasuredinkilometer,meterormiles.
Time ismeasuredinHour,minutesorseconds.
SpeedismeasuredinKilometer/hour,meter/sec,miles/hour.
(ii) CONVERSION:-
1 km= 1000 meter
1 hour= 3600 seconds
54 km/h= 54 x 1000/3600 = 15 m/s.(km/hto m/s multiplyby5/18).
1 meter= 1/1000 meter.
1 second= 1/3600 hour.
15 m/s = 15 x 3600/1000 = 54 km/h (m/stokm/h multiplyby18/5)
(iii) Average Speed=Total distance travelled/Total time taken.
o For twovariables= 2ab/a+b ( a & b are speed )
o For three variables=3abc/ab +bc +ca (a, b & c are speed)
(iv) Time takenafter meeting(same distance):- If 2 personsstartsjourneyfromA & B and move
towards each otherandmeetat C, aftermeetingtheyreachopposite pointsinx & y hrs
respectively.
Then speedbefore theymeetis √y : √x
TRAINS CONCEPT:-
1) Same Direction:- Whentwotrains are goingin same directionandone traincrossesthe other.
Sa, La (TrainA) Sa = Speedof trainA,La = Lengthof trainA.
Sb, Lb (TrainB) Sb = Speedof trainB, Lb = lengthof trainB.
Relative Speed= Sa - Sb, Total distance = La + Lb
20. So, Sa – Sb = La + Lb / T.
2) Train andplatformcase :-
Sa, La (TrainA)
PLATFORM ( (P) Sa = La + P/ Time.
3) Opposite Direction:-
Sa, La (TrainA)
Sb,Lb (TrainB)
Relative Speed=Sa + Sb.
Total distance =La + Lb
Sa + Sb = La + Lb / Time
Boats and streams Concept :
Let the speedof boatupstream= x km/h (upstream=againstthe currentor flow of water)
Let the speedof boatdownstream= y km/h (downstream=withthe current or flow of water)
(i) Speedof boatin Still Water= ½ (x + y) km/h.
(ii) Speedof Stream(current) = ½ (y – x) km/h.
Let the Speedof boatin Still Water= a km/h
Let the Speedof Stream(current) = b km/h
(i) Speedof boatupstream= (a –b) km/h.
(ii) Speedof boatdownstream= (a + b) km/h.
21. TIME AND WORK
TIME AND WORKEQUIVALENCE:- Essence liesinthe facthasit exhibitsthe mostfundamental
relationshipbetweenthe three factorsi.e.work,time andthe agentcompletingthe work.
Work done = Number of Days x Number of Men (W = D x M)
Condition1:- Work(w) is constant.(Mx D = Constant)
Mα1/D (If work done isconstant,thenthe numberof personsisinverselyproportional to
the numberof days.)
Condition2:- D isconstant.
WαM (More workwill be done if we employmore men&vice versa.)
Condition3:-Mis constant
WαD (More workis done if we have more numberof days.)
In general,we summarizethat
M₁D₁/W₁ =M₂D₂/W₂
Individual Work & Individual Efficiency:-
Individual Work: - If A can do a certainworkin 10 days,thenhe will finish1/10th of
the workinone day.
Individual Efficiency:- Efficiencyisalsoknownasworkrate.
General expressioncorrelatingtime taken& efficiency:-
If efficiencyof A isx percent more than efficiencyof Band B takes‘B’ daysto complete the
work,thenA will take (Bx 100/100+X ) daysto complete same work.
If efficiencyof A isx percent lessthanefficiencyof Band B takes‘B’ daysto complete the work,
thenA will take (Bx 100 /100-X) daysto complete same work.
22. If A doesthe work inx daysand B doesthe same work iny days,
Work done by A = 1/x
Work done by B = 1/y
Work done by A and B together= (1/x)+(1/y)
Days to finishthe worktogether=1/(workdone together) =(x*y)/(x+y)
If A and B togethercan do a piece of workinx days,B and C togethercan do itin y daysand C
and A togethercando itin `z` days, thennumberof days requiredtodothe same work:If A,B,
and C workingtogether=(2xyz) / (xy+ yz + zx)
A,B, C can do a piece of workinx, y,z days respectively.The ratioinwhichthe amountearned
shouldbe sharedis1/x : 1/y : 1/z = yz:zx:xy
Extension of the concept of time & work:-
1. Pipesand Cistern:- It isan applicationof conceptof time andwork.We see positive workbeing
done innormal casesof time andwork,in case of pipesandcisternnegative workisalso
possible.
Pipe A can fill a tankin 20 hours Positive workisdone.
Pipe B can emptya tankin 25 hours Negative workisdone.
2. Variable Work: - Thisconceptcomesfrom the possibilitythatthe rate of workingcan be
different,canbe dependentuponsome external agent.
Work done α external factor.
3. Alternate Work: -Thisconceptisanalogoustothe conceptof man-days.Aswe have seenin
the conceptof man-hourthatif 20 mencan do a workin 10 days,thenthisworkis equivalentto
200 man-days.
23. SIMPLE AND COMPOUND INTEREST
1. Principal:The moneyborrowedorlentoutfora certainperiodiscalledthe principal orthe sum.
2. Interest:Extramoneypaidforusingother'smoneyis calledinterest.
3. Simple Interest(S.I.): If the interestonasum borrowedforcertainperiodisreckoneduniformly,
thenit iscalled simple interest.
4. Amount(A) = Principal +Simple Interest(S.I)
Let Principal =P, Rate = R% perannum(p.a.) andTime = T years.Then
Simple Interest=P x T x R / 100.
ADDITIONAL FORMULA:
(i) AmountA₁ becomes afterTime T₁ year andAmountA₂ becomesafterTime T₂years.
(a) Principal =A₁T₂ – A₂T₁ /T₂ - T₁
(b) Rate of Interest=> R/100 = A₂ – A₁ / A₁T₂ – A₂T₁
(ii) A sumof moneybecomesntimes afterT years,Thento findrate of interestper
annum
R/100 = n – 1 /T
(iii) The annual installmentthatwill dischargeadebtof D due inT years at R % simple
interestperannum= 100 x D / 100T + {RT(T - 1) / 2}
Note:Simple interestshouldbe same foreveryyear.
COMPOUND INTEREST
Principal:The moneyborrowedorlentoutfor a certainperiodiscalledthe principal orthe sum.
Interest:Extra moneypaidforusingother'smoneyiscalled interest.
Let Principal =P, Rate = R% perannum, Time = n years.
1. Wheninterestiscompound Annually:
24. Amount = P { 1 + R /100}ⁿ
2. Wheninterestiscompounded Half-yearly:
Amount = p { 1 + (R/2)/100}²ⁿ
3. Wheninterestiscompounded Quarterly:
Amount = { 1 + (R/4)/100}⁴ⁿ
4. Wheninterestiscompounded Annuallybuttime isinfraction,say3 years.
Amount = p {1 + R/100}ᶟ x {1 + 2/5 x R/100}
5. WhenRatesare differentfordifferentyears,sayR1%,R2%,R3% for1st
, 2nd
and 3rd
year
respectively.
ADDITIONAL FORMULA:
(I) Difference betweenCompoundinterestandSimple interestfortime =2 yearsat R % rate of
interestis…….C.I – S.I = P x (R/100)²
(II) Difference between CompoundinterestandSimple interestfortime =3 yearsat R % rate of
interestis…….C.I – S.I = P(R/100)²(R/100 + 3)
(III) If a loanof Rs D at R% compoundinterestperannumistobe repaidinn equal yearly
installments,thenthe valueof eachinstallmentcanbe givenby
D / (100/100 + R) +(100/100 + R)² + (100/100 + R)ᶟ + ….
Then, Amount = P 1 +
R1
1 +
R2
1 +
R3
.
100 100 100
25. PERMUTATION AND COMBINATION
PERMUTATION:- Implies“arrangement”where“orderof the things”isimportant.
Permutationof nthingstakingr at a time isdenotedby ⁿPᵣ.
ⁿPᵣ = n! / (n-r)! Note 0! =1.
COMBINATION:- Implies“selection”where “orderof the things”isnotimportant.
Combinationof nthingstakingr at a time isdenotedby ⁿCᵣ.
ⁿCᵣ = n! / (n-r)! x (r)!
SOME IMPORTANT DERIVATIONS:-
1) Numberof arrangementsof nthingsof whichp are of one type,qare of secondtype and rest
are distinct …….. n! /p! x q! x r!
2) Numberof arrangementsof nthingstakingr at a time wheneachof the thingsmay be repeated
once,twice--- uptortimesinanyarrangementis…….nʳ.
CIRCULAR PERMUTATION:
1) The Numberof CircularPermutation(arrangement) of ndifferentarticles= (n-1)! .
2) The Numberof Circulararrangementsof n differentarticleswhenclockwise and
anticlockwisearrangementsare notdifferent.
I.e.whenobservationcanbe made fromboth the sides= (n-1)!/2.
COMBINATION:-
1) Out of n things,the numberof waysof selectingone ormore things: - 2ⁿ - 1, where n=
numberof things.
2) Distributingthe giventhings (r+n)intwogroupswhere one groupishaving r thingsand
otherone n things.
ʳ⁺ⁿCᵣ = (r + n)!/r! x n! .
If r=n , then²ʳCᵣ = (2r)!/r! x r!
27. PROBABILITY
Probability:-Probabilityisanexpectationof the happeningof some events.Itisthe measure of
uncertainty.
Sample Space: - It isthe total numberof all the possible outcomes.
CompoundEvents: - Eventsobtainedbycombiningtwoormore elementaryevents.A compoundevent
issaid to occur if one of the elementaryeventsassociated withitoccurs.
Exhaustive Events: - The total numberof possible outcomesof arandomexperimentinatrial.
MutuallyExclusive Events: - If the occurrence of anyone of the two or more eventspreventsthe
occurrence of all othersi.e.if notwoor more eventsoccursimultaneously.
Pointsto Remember:-
(i)0≤P(E)≤1
(ii) P(E)+P(E)’=1 where P(E)’=Probabilityof nothappeningof eventE.
Odds in favour & Odds against:-
Conditional Probability: -LetA and B be two eventsassociatedwitharandomexperiment.Then
probabilityof occurrence of A underthe conditionthatB has alreadyoccurredandP (B) is not equal to
0.
Thus P (A/B) = Probabilityof occurrence of A giventhat B has happened.
P (B/A) = Probabilityof occurrence of B giventhat A has happened.
Probabilityof an Event (E) = Number offavorable outcomesof E / Total numberof possible outcomes.
Oddsin Favour:- Numberof Favourable Cases/Numberof unfavourableCases.
Oddsin Against:- Numberof unfavourable Cases/Numberof favourable Cases.
28. Addition Theorem:-
1. P(AUB) = P(A)+P(B) –P(AПB)
Let A={2,4,6} and B={3,6}.
P(AUB)={2,3,4,6} Means any one of the outcomesof A or B.
P(AПB) = {6} Means occurrence of both A and B.
2. If events are mutually exclusive then
P(AUB)=P(A)+P(B)
29. DATE INTERPRETATION
Data interpretationisthe act of transformingdatawiththe objectiveof extractinguseful information&
facilitatingconclusionsonthe basicof the givendata.
Data is a meansto representfacts,conceptsorinstructionsinaformalizedmannersuitablefor
communicationinterpretationorprocessingbyhumansorotherautomaticmodes.
Differentwaysof Datarepresentation:-
(i) Narration based: - Questioninvolvestoriesthatdefine asituationandgive detailsof various
parametersinvolved.
(ii) Pictorial: - In such a formdata is presentedinvariouspictorial formssuchasline graphs,bar
diagrams,line chartsetc.
(iii) Table: - Tabularmethodisthe mostfundamental wayof representingdata.Mostof
differentkindsof datapresentationformatlike barcharts,line chartsetc originate fromthe
table.
(iv) Pie Chart: - Pie Chart istypical type of data representationwhere dataisrepresentedasa
part of a circle.The circle representsthe total value (100%) anddifferentpartrepresents
certainproportionsof the total.
There are twoapproachesconstructinga pie chart fromany givendata:-
(A) Degree Approach: - In thiscentral angle ina circle represents360◦. So anypart or a segmentin
pie-chartiscalculatedasa proportionof 360◦.
(B) Percentage Approach: - In thiscase,any part or segmentina pie-chartiscalculatedasa part of
100%.
RADAR DIAGRAM:-
In thisdiagrameveryvalue isrepresentedwithrespecttoacentral point.All the changesinthe values
are expressedinthe formof distance fromthiscenterpoint.
30. CLOCKS
A clock is an example of circular motion where length of track is equal to 60km.
Assume (1 minute = 1 km)
Now on this track, two runner i.e. hour hand and minute hand are running with a speed 5 km/h
and 60 km/h. Since their direction is same, so relative velocity (speed) = 60-5 =55 km/h.
Speed = Distance / Speed.
Or
Time = Distance / Speed. Time = 60 /55 = 12/11 hour.
DEGREE CONCEPT:-
Total Angle subtended at the centre of a clock = 360˚.
Angle made by hour hand at the centre per hour =30˚ (per minute = 0.5˚).
Angle made by minute hand at the centre per hour =360˚. (per minute = 6˚).
IMPORTANT DERIVATION:-
The number of times hand of a clock are in straight line (either at 0˚ or at 180˚) in 24
hour = 44.
The number of times hand of a clock are at right angle (90˚) in 24 hour = 44.
Both the hands of a clock are together after every 65 5/11 minutes.
31. CUBES
A cube is a three dimensional figure of square in which all the sides are equal.
Number of Faces in the cube= 6
Number of Vertices in the cube= 8
Number of Edges in the cube= 12
General cases for Cubes:-
A cube was cut into 64 cubelets. (n×n×n)
So, n³= 64, n =4.
(i) Cubelets with 1 face painted = 6(n-2)².
(ii) Cubelets with 2 face painted = 12(n-2).
(iii) Cubelets with 3 face painted = 8 .
(iv) Cubelets with no face painted = (n-2)³.
Total n³=6(n-2)²+ 12(n-2) + 8+ (n-2)³.
32. SERIES
TYPE 1:- Number Series
(i) Prime number Series:- Prime numbershave onlytwodistinctfactorslike 2,3, 5, 7, 11, 13,
17….. Theiroccurrence doesnotfollow anyparticularrule.
(a) Examples:-
(i) 3, 5, 7, 11, 13, 17, ____
Rule --- Seriescontainaprime numberserieswill have the nextnumberas 19.
(ii) 5, 7, 10, 15, 22, _____
Rule --- Seriescontaindifference betweentwosuccessivenumberis2,3,5,7and so
on,whichare prime numbers.
Nextnumber=(Last number)+(Nextprimenumber) =33.
(iii) 4,9,25,49,121,_____
Rule --- Seriesisthe square of prime numbers.Hence the nextnumberwillbe (169)
whichis(13)².
(ii) The Difference Series:- Inthistype ,patternwouldbe obtainedbyfindingthe difference
betweenthe terms.Differencesare categorizedas1st
orderdifference,2ndorder
difference, and3rdorder difference andsoon.
Order of difference:-
1st
orderdifference isdifference betweentwoconsecutivetermsof series.
Example:- 2 5 10 17 26 37
3 5 7 9 11
2nd
orderdifferenceisdifference betweenthe consecutive termsobtainedfromthe
1st
orderdifference.
Example:- 2 5 10 17 26 37
3 5 7 9 11
2 2 2 2
(iii) The product Series:- A seriesiscalledaproduct serieswhenthe termisobtainedby
multiplyingbyaconstantor anyothernumber.
Example:- 3 6 18 90 630 (630 x9).
x 2 x 3 x 5 x 7 x 9
33. (iv) The MixedSeries:- The mixedserieshasthree typesof formsinvolved,whichcanbe
classifiedas
(a) A mixedseriesmaybe formedbymixingtwodifferentseries.
Example:-3,6,24, 30, 63, 72, ______, 132.
ELEMENTARY IDEAS OF PROGRESSION:-
(1) ARITHMETIC PROGRESSION (A.P):- The progressionof the forma,a+d,a+2d---- isknownasA.Pwith
first term =a & common difference =d.
Example:-3,6,9, 12, ____ is an A.Pwitha =3 and d= 6-3= 3.
InA.P,we have nth term= a+ (n-1) d.
(2) GEOMETRIC PROGRESSION (G.P):- The progressionof the forma,ar, ar², ar³------ isknownasG.P
first term =a & common ratio =r.
Example:-1,5,25, 125, ____ is a G.P witha =3 and r= 5/1= 5.
InG.P, we have nth term= arⁿ⁻¹.
34. SYLLOGISM
Syllogismmeans‘Interference’or‘deduction’.
Types ofpropositionsin syllogism:-
(i) Positive Universal: ---Example:- All catsare dogs.(ALL)
Particular:---Example:- Some catsare dogs.(SOME)
(ii) Negative Universal:--Example:- Nocatsare dogs.(NO)
Particular:--Example:-Some catsare not dogs.(SOMENOT)
Euler’scircle or Venndiagram:-
SOME CATS ARE DOGS ( SOME) ALL CATSARE DOGS (ALL)
NO CATSARE DOGS (NO) SOME CATS ARE NOTDOGS (SOME NOT)
Standard Deductions:-
Statements DefinitelyTrue
1) All cats are dogs(ALL) Some dogsare cats.(SOME)
Or
Some cats are dogs.(SOME)
2) Some cats are dogs(SOME) Some dogsare cats.(SOME)
35. 3) No cats are dogs (NO) No dogsare cats.(NO)
Some dogsare not cats.(SOME NOT)
Or
Some cats are notdogs.(SOMENOT)
Deduction of two or more Statements:-
First Statement SecondStatement DefinitelyTrue Conclusion.
ALL
ALL SOME SOME
ALL ALL ALL/SOME
ALL NO SOME NOT/NO
SOME
SOME ALL SOME
SOME NO SOME NOT
NO
NO ALL NO/SOME NOT
NO SOME SOME NOT
NO NO NO/SOME NOT
36. BLOOD RELATION
RELATIONSHIP TABLE:-
Example1:- Amitintroduce Gautam as the son of the onlybrotherof hisfather’swife.How isGautamas
the son of the onlybrotherof hisfather’swife .How isGautam relatedtoAmit?
Solution:- Startingfrombackend.
Father’swife Mother
Onlybrotherof hisfather’swife Onlybrotherof hismother.
Maternal Uncle.
Sonof the onlybrotherof hisfather’swife Sonof maternal uncle cousin.
Gautam andAmitare Cousins.
Mother’sor father’sson Brother
Mother’sor father’sdaughter Sister
Mother’sor father’sbrother Uncle
Mother’sor father’ssister Aunt
Mother’sor father’sfather Grandfather
Mother’sor father’smother Grandmother
Son’swife Daughterinlaw
Daughter’shusband Son inlaw
Husbandor wife’ssister Sisterinlaw
Husband’sor wife’sbrother Brotherin law
Brother‘s son Nephew
Brother’sdaughter Niece
Uncle or aunt’s sonor daughter Cousin
Sister’shusband Brotherin law
Brother’swife Sisterinlaw
Grandson’sor Granddaughter’sdaughter Great Granddaughter
37. CALENDERS
ODD DAYS :- Numberof daysmore than the complete weeksare calledodddaysina givenperiod.
LEAP YEAR: - A leapyearhas 366 days.In a leapyear,the monthof February has29 days.
(a) Everyyear divisiblebyisa leapyear,if itis not a century.
(b) Every4th
centuryisa leapyearand noothercenturyis a leapyear.
ORDINARY YEAR: - The yearwhichisnot a leapyearis an ordinaryyear.Anordinaryyearhas 365 days.
COUNTING ODD DAYS AND CALCULATING THE DAY OF ANY PARTICULAR DATE
1) 1 Ordinaryyear= 365 days = (52 weeks+1 day)
Hence numberof Odd daysin1 Ordinaryyear= 1
2) 1 Leapyear = 366 = (52 weeks+ 2 days)
Hence numberof Odd daysin1 leapyear= 2
3) 100 years= (76 Ordinaryyear+ 24 leapyear)
= (76 x 1 + 24 x 2) odd days
=124 Odddays
= (17 weeks+ 5 days)
=5 Odd days.
4) Numberof Odddays in200 Years= (5 x2) =10 days
= 1 week+ 3 days
= 3 odd days.
5) Numberof Odddays in4th
centuries(400,800,1600,2400….etc) = 0
38. DATA SUFFICIENCY
Directions: The questionsbelowconsistof aquestionfollowedbytwostatementslabeledas(1) and(2).
You have to decide if these statementsare sufficienttoconclusivelyanswerthe question.
(A) If statement(1) alone issufficienttoanswerthe questionbutthe statement(2) alone isnot
sufficienttoanswerthe question.
(B) If statement(2) alone issufficienttoanswerthe questionbutthe statement(1) alone isnot
sufficienttoanswerthe question.
(C) If you getthe answerfrom(1) and (2) togetheralthoughneitherstatementbyitself suffices.
(D) If statement(1) alone issufficientandstatement(2) alone issufficient.
(E) If you cannot getthe answerfromstatements(1) and(2) togetherbutstill more dataare
needed.
Example:1) Whatis the relationof Xand Y?
(i) Y is motherof Z.
(ii) Z is brotherof A.
STEPS :-
Yes No
Yes No
No Yes
Yes No
Firstcheck statement1.Is itsufficient?
EitherB or C or E is the correct answer.EitherA or D is correct answer.
Now,checkstatement(2).Isit sufficient?
AnswerisD AnswerisA
AnswerisB
Try both the statementtogether.Are the statementtogethersufficient?
AnswerisEAnswerisC
39. SOME TYPICAL CASES:-
These casesare dividedintofollowingcategories:-
(i) Relationship
(ii) Dates
(iii) Comparison
(iv) Age
(v) Critical Analysis
(vi) Miscellaneous
Relationships:-
Checkthe genderof the personinvolved&followsthe previoussteps.
Dates:-
Check (A) The dayor the date of some earlierincidentismentioned.
(B) The numberof daysbetweenthatincidentandthe requiredday is given.
Critical Analysis:-
Revise general backgroundof argumentationtechniques,assumptionsof argumentsandinference
making.