The document contains 14 math word problems involving fractions, percentages, ratios, time/work problems, and other quantitative reasoning questions. It provides the questions, possible multiple choice answers, and in some cases hints or step-by-step solutions to arrive at the answers. The problems cover a range of basic math skills and concepts commonly assessed on standardized tests.
1. The document contains 17 multiple choice questions related to numbers and arithmetic concepts.
2. It tests skills such as comparing and ordering fractions, solving word problems involving ratios and remainders, and performing arithmetic operations.
3. The questions have answer options ranging from simple calculations to multi-step word problems requiring setup and solution of equations.
The document provides examples of factorizing algebraic expressions. It begins with expanding simple expressions like 3g + 4 and finding the common factors of terms like 12 and 20. The next section provides more examples of factorizing expressions like x2 + 2x by finding the highest common factor. It emphasizes factorizing completely, like writing 3abc(ab4 + 9) instead of 9abc(ab4 + 9). The document concludes with an exercise for students to practice factorizing expressions and an extension with more challenging examples. It provides the opportunity for a 10 minute practice session to reinforce the steps of factorizing algebraic expressions.
The document provides examples of non-verbal reasoning questions and their solutions. It includes number series, letter series, logical reasoning, and mathdoku puzzles. For the number series questions, the correct answer is choosing the option that continues the same pattern to fill in the missing term. The letter and logic series involve analyzing the relationship between letters or numbers to determine the missing element. The mathdoku puzzles require logically placing the numbers 1 to 5 in the grid so that each row and column uses each number, and the sums or products of the bold outlined groups equal the given hints.
This document contains 46 math homework assignments involving operations on polynomials, factoring expressions, solving equations, graphing, and working with complex numbers. The homework covers topics including adding, subtracting, multiplying and dividing polynomials; writing expressions in factored form; solving systems of equations and inequalities; graphing lines, parabolas, and other functions; simplifying radical expressions; and performing operations with complex numbers in standard form (a + bi).
Strategic Intervention Material (SIM) was provided for Grade 10 students to enhance learning and to motivate and stir up the attention and interest of the students until they master the topic. This material depicts the entire definition of learning since it concludes a systematic development of students’ comprehension on a distinct lesson in Mathematics 10.
The document describes the Vedic method for multiplying multi-digit numbers using a technique called "Vedic Mathematics". It breaks down multiplication into place-value groups and uses dots and lines to represent the digits being multiplied. It then provides examples of multiplying several pairs of numbers step-by-step using this method. The numbers are converted back to normal format after each calculation.
1. The document contains 17 multiple choice questions related to numbers and arithmetic concepts.
2. It tests skills such as comparing and ordering fractions, solving word problems involving ratios and remainders, and performing arithmetic operations.
3. The questions have answer options ranging from simple calculations to multi-step word problems requiring setup and solution of equations.
The document provides examples of factorizing algebraic expressions. It begins with expanding simple expressions like 3g + 4 and finding the common factors of terms like 12 and 20. The next section provides more examples of factorizing expressions like x2 + 2x by finding the highest common factor. It emphasizes factorizing completely, like writing 3abc(ab4 + 9) instead of 9abc(ab4 + 9). The document concludes with an exercise for students to practice factorizing expressions and an extension with more challenging examples. It provides the opportunity for a 10 minute practice session to reinforce the steps of factorizing algebraic expressions.
The document provides examples of non-verbal reasoning questions and their solutions. It includes number series, letter series, logical reasoning, and mathdoku puzzles. For the number series questions, the correct answer is choosing the option that continues the same pattern to fill in the missing term. The letter and logic series involve analyzing the relationship between letters or numbers to determine the missing element. The mathdoku puzzles require logically placing the numbers 1 to 5 in the grid so that each row and column uses each number, and the sums or products of the bold outlined groups equal the given hints.
This document contains 46 math homework assignments involving operations on polynomials, factoring expressions, solving equations, graphing, and working with complex numbers. The homework covers topics including adding, subtracting, multiplying and dividing polynomials; writing expressions in factored form; solving systems of equations and inequalities; graphing lines, parabolas, and other functions; simplifying radical expressions; and performing operations with complex numbers in standard form (a + bi).
Strategic Intervention Material (SIM) was provided for Grade 10 students to enhance learning and to motivate and stir up the attention and interest of the students until they master the topic. This material depicts the entire definition of learning since it concludes a systematic development of students’ comprehension on a distinct lesson in Mathematics 10.
The document describes the Vedic method for multiplying multi-digit numbers using a technique called "Vedic Mathematics". It breaks down multiplication into place-value groups and uses dots and lines to represent the digits being multiplied. It then provides examples of multiplying several pairs of numbers step-by-step using this method. The numbers are converted back to normal format after each calculation.
The document is a series of slides providing instruction and examples for simplifying basic radical expressions. It covers rationalizing denominators, combining like radicals, and performing basic arithmetic operations like addition, subtraction, and multiplication on radical expressions. Example problems are provided after each set of instructions to demonstrate the techniques. The goal is to teach learners how to simplify radical expressions in a step-by-step manner.
Section 3.5 inequalities involving quadratic functions Wong Hsiung
This document contains information about solving inequalities involving quadratic functions. It provides examples of solving the inequalities 5 4 0x x+ + > , 6x x≤ + , and 2 8 9 0x x− + − < and graphing the solution sets. For the inequality 5 4 0x x+ + > , the solution set is the region where the function ( ) 5 4f x x x+ + is greater than 0, which is the interval (4,1). For 6x x≤ + , the solution set is the region where the function ( ) 6f x x x− − is less than or equal to 0, which is the interval [2,3]. For 2 8 9
This document provides an overview and activities on solving quadratic equations by factoring. It begins by defining quadratic equations and their standard form. Several activities are presented to practice identifying quadratic equations, rewriting them in standard form, and factoring trinomials of the form x^2 + bx + c. The final activity involves factoring quadratic equations to determine their roots. The document aims to build mastery of skills needed to solve quadratic equations using factoring techniques.
This document provides instruction on solving quadratic equations by completing the square. It begins by defining a quadratic equation and explaining why the coefficient of the quadratic term cannot be zero. It then presents the steps to solve a quadratic equation by completing the square, which involves transforming the equation into the form (x - h)2 = k. An example problem is worked through to demonstrate the process.
This document provides examples of factorizing algebraic expressions by finding the highest common factor (HCF) of the terms. It shows expressions being factorized, such as 2a+6 being written as 2(a+3), and 8m+12 being written as 4(2m+3). The document explains that algebraic expressions can sometimes be written as the HCF multiplied by grouped terms in parentheses. It provides steps for finding the factors of each term and the HCF to factorize expressions like 9jk+4k as k(9j+4).
This document provides information on binomial and Poisson probability distributions:
- It defines the binomial distribution and gives its probability mass function and conditions for applicability, including examples. The mean and variance of the binomial are derived.
- Problems are presented to demonstrate calculating probabilities using the binomial, including the number of coin tosses needed to expect a given outcome.
- The Poisson distribution is defined and its conditions for applicability are described, with examples provided.
This document discusses exponent rules and formulas involving positive, negative, fractional and zero exponents. It provides examples of simplifying expressions using these rules. Key points covered include:
- Formula I: am×an = am+n
- Formulas II-V cover properties for negative exponents and fractional exponents
- Examples are worked through applying the exponent rules and formulas
This document provides an overview of rational numbers including:
- Integers and fractions written in the form a/b where a and b are integers and b ≠ 0
- Equivalent fractions represented by the same number
- Ordering and comparing rational numbers
- Converting between improper fractions and mixed numbers
- Basic operations of addition, subtraction, multiplication, and division of rational numbers
- Word problems involving rational numbers
The document provides 5 algebra word problems and their step-by-step solutions. It begins with a disclaimer that the document was prepared by trainees and is not an official document. It then presents 5 multi-step algebra word problems, showing the work and reasoning for arriving at each solution. The document concludes by providing contact information and a thank you.
This document discusses manipulations of rational expressions. It begins by differentiating between rational numbers and rational expressions. The objectives are to simplify, multiply, divide, add and subtract rational expressions. Examples are provided to distinguish rational numbers from expressions. Steps are outlined for simplifying expressions, including factorizing and cancelling common factors. Students work through practice problems in groups and individually. The document concludes by assigning further study on multiplying and dividing rational expressions.
1. The document contains a series of math problems involving operations with real numbers such as addition, subtraction, multiplication, division, exponents, and algebraic expressions.
2. The problems are arranged in a 5x5 grid and include steps to solve for missing quantities and expressions.
3. Key concepts covered include real numbers, operations with signed numbers, the distributive property, and simplifying algebraic expressions.
This document provides instructions for a test being administered by Sri Chaitanya IIT Academy in India. The test is 3 hours long and contains 90 questions in Mathematics, Physics, and Chemistry worth a total of 360 marks. Candidates will receive 4 marks for each correct answer and lose 1/4 marks for incorrect answers, with no penalty for unanswered questions. Only one answer per question is allowed. Calculators and other materials are prohibited during the test.
Simplifying Basic Rational Expressions Part 1DaisyListening
This document provides instructions and examples for simplifying rational expressions by factoring and canceling terms. It begins with definitions of rational expressions and undefined values. Examples shown include finding excluded values that make expressions undefined, as well as simplifying expressions by factoring numerators and denominators and canceling common factors. The goal is to either find excluded values or simplify the expressions into their lowest terms. Ten problems with step-by-step solutions are provided to demonstrate the techniques.
Algebra is a branch of mathematics that studies structure, relations, and quantities. The quadratic formula provides a method for solving quadratic equations of the form ax^2 + bx + c = 0 by using the coefficients a, b, and c. There are three main methods for solving quadratic equations: factoring, completing the square, and using the quadratic formula.
The document contains 15 examples explaining how to solve various math problems involving number systems, equations, remainders, and arithmetic progressions. Each example shows the steps to find the number of possible solutions, values that satisfy the equations, or other numerical relationships implied by the given information.
1. The document discusses rules and principles for working with negative numbers and algebraic expressions involving negative numbers.
2. Key ideas include defining negative multiplication, such as -3 × 2, as -6; establishing that the order of factors does not matter in negative multiplication, similar to positive numbers; and simplifying algebraic expressions by using properties such as x - (y - z) = x - y + z.
3. General principles are stated for adding and subtracting negative numbers, and techniques are described for simplifying algebraic expressions involving negative terms.
Re call basic operations in mathematics Nadeem Uddin
The document discusses basic mathematical operations - addition, subtraction, multiplication and division. It provides examples and exercises for performing each operation on numbers and algebraic expressions. It also covers concepts like coefficients, bases and exponents of algebraic terms, polynomials, and the order of operations (BODMAS rule).
The document provides information about order of operations in math. It explains that order of operations is important to get the correct answer when a math problem contains multiple operations. It presents the mnemonic "PEMDAS" (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) as the standard order of operations. Several examples of applying order of operations to evaluate expressions are shown. The document is intended to teach students the proper order for solving expressions with multiple operations.
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 contains 17 math problems involving squares, square roots, and perfect squares. It provides the questions, possible multiple choice answers, and the key/solutions to checking the answers. Some question types include finding the square root of a number, evaluating expressions involving squares and square roots, determining the number needed to be added to a quantity to make it a perfect square, and finding unknown values based on relationships between squares.
This document discusses squares, square roots, and properties related to them. It defines a square number as the result of multiplying a number by itself. It provides examples of perfect square numbers and discusses patterns in the last digits of squares based on the last digit of the original number. The document also covers finding square roots using repeated subtraction, properties of square roots based on the last digit, and other methods for finding squares and square roots. Additionally, it discusses Pythagorean triplets, prime factorizations, and other concepts related to squares and square roots.
The document is a series of slides providing instruction and examples for simplifying basic radical expressions. It covers rationalizing denominators, combining like radicals, and performing basic arithmetic operations like addition, subtraction, and multiplication on radical expressions. Example problems are provided after each set of instructions to demonstrate the techniques. The goal is to teach learners how to simplify radical expressions in a step-by-step manner.
Section 3.5 inequalities involving quadratic functions Wong Hsiung
This document contains information about solving inequalities involving quadratic functions. It provides examples of solving the inequalities 5 4 0x x+ + > , 6x x≤ + , and 2 8 9 0x x− + − < and graphing the solution sets. For the inequality 5 4 0x x+ + > , the solution set is the region where the function ( ) 5 4f x x x+ + is greater than 0, which is the interval (4,1). For 6x x≤ + , the solution set is the region where the function ( ) 6f x x x− − is less than or equal to 0, which is the interval [2,3]. For 2 8 9
This document provides an overview and activities on solving quadratic equations by factoring. It begins by defining quadratic equations and their standard form. Several activities are presented to practice identifying quadratic equations, rewriting them in standard form, and factoring trinomials of the form x^2 + bx + c. The final activity involves factoring quadratic equations to determine their roots. The document aims to build mastery of skills needed to solve quadratic equations using factoring techniques.
This document provides instruction on solving quadratic equations by completing the square. It begins by defining a quadratic equation and explaining why the coefficient of the quadratic term cannot be zero. It then presents the steps to solve a quadratic equation by completing the square, which involves transforming the equation into the form (x - h)2 = k. An example problem is worked through to demonstrate the process.
This document provides examples of factorizing algebraic expressions by finding the highest common factor (HCF) of the terms. It shows expressions being factorized, such as 2a+6 being written as 2(a+3), and 8m+12 being written as 4(2m+3). The document explains that algebraic expressions can sometimes be written as the HCF multiplied by grouped terms in parentheses. It provides steps for finding the factors of each term and the HCF to factorize expressions like 9jk+4k as k(9j+4).
This document provides information on binomial and Poisson probability distributions:
- It defines the binomial distribution and gives its probability mass function and conditions for applicability, including examples. The mean and variance of the binomial are derived.
- Problems are presented to demonstrate calculating probabilities using the binomial, including the number of coin tosses needed to expect a given outcome.
- The Poisson distribution is defined and its conditions for applicability are described, with examples provided.
This document discusses exponent rules and formulas involving positive, negative, fractional and zero exponents. It provides examples of simplifying expressions using these rules. Key points covered include:
- Formula I: am×an = am+n
- Formulas II-V cover properties for negative exponents and fractional exponents
- Examples are worked through applying the exponent rules and formulas
This document provides an overview of rational numbers including:
- Integers and fractions written in the form a/b where a and b are integers and b ≠ 0
- Equivalent fractions represented by the same number
- Ordering and comparing rational numbers
- Converting between improper fractions and mixed numbers
- Basic operations of addition, subtraction, multiplication, and division of rational numbers
- Word problems involving rational numbers
The document provides 5 algebra word problems and their step-by-step solutions. It begins with a disclaimer that the document was prepared by trainees and is not an official document. It then presents 5 multi-step algebra word problems, showing the work and reasoning for arriving at each solution. The document concludes by providing contact information and a thank you.
This document discusses manipulations of rational expressions. It begins by differentiating between rational numbers and rational expressions. The objectives are to simplify, multiply, divide, add and subtract rational expressions. Examples are provided to distinguish rational numbers from expressions. Steps are outlined for simplifying expressions, including factorizing and cancelling common factors. Students work through practice problems in groups and individually. The document concludes by assigning further study on multiplying and dividing rational expressions.
1. The document contains a series of math problems involving operations with real numbers such as addition, subtraction, multiplication, division, exponents, and algebraic expressions.
2. The problems are arranged in a 5x5 grid and include steps to solve for missing quantities and expressions.
3. Key concepts covered include real numbers, operations with signed numbers, the distributive property, and simplifying algebraic expressions.
This document provides instructions for a test being administered by Sri Chaitanya IIT Academy in India. The test is 3 hours long and contains 90 questions in Mathematics, Physics, and Chemistry worth a total of 360 marks. Candidates will receive 4 marks for each correct answer and lose 1/4 marks for incorrect answers, with no penalty for unanswered questions. Only one answer per question is allowed. Calculators and other materials are prohibited during the test.
Simplifying Basic Rational Expressions Part 1DaisyListening
This document provides instructions and examples for simplifying rational expressions by factoring and canceling terms. It begins with definitions of rational expressions and undefined values. Examples shown include finding excluded values that make expressions undefined, as well as simplifying expressions by factoring numerators and denominators and canceling common factors. The goal is to either find excluded values or simplify the expressions into their lowest terms. Ten problems with step-by-step solutions are provided to demonstrate the techniques.
Algebra is a branch of mathematics that studies structure, relations, and quantities. The quadratic formula provides a method for solving quadratic equations of the form ax^2 + bx + c = 0 by using the coefficients a, b, and c. There are three main methods for solving quadratic equations: factoring, completing the square, and using the quadratic formula.
The document contains 15 examples explaining how to solve various math problems involving number systems, equations, remainders, and arithmetic progressions. Each example shows the steps to find the number of possible solutions, values that satisfy the equations, or other numerical relationships implied by the given information.
1. The document discusses rules and principles for working with negative numbers and algebraic expressions involving negative numbers.
2. Key ideas include defining negative multiplication, such as -3 × 2, as -6; establishing that the order of factors does not matter in negative multiplication, similar to positive numbers; and simplifying algebraic expressions by using properties such as x - (y - z) = x - y + z.
3. General principles are stated for adding and subtracting negative numbers, and techniques are described for simplifying algebraic expressions involving negative terms.
Re call basic operations in mathematics Nadeem Uddin
The document discusses basic mathematical operations - addition, subtraction, multiplication and division. It provides examples and exercises for performing each operation on numbers and algebraic expressions. It also covers concepts like coefficients, bases and exponents of algebraic terms, polynomials, and the order of operations (BODMAS rule).
The document provides information about order of operations in math. It explains that order of operations is important to get the correct answer when a math problem contains multiple operations. It presents the mnemonic "PEMDAS" (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) as the standard order of operations. Several examples of applying order of operations to evaluate expressions are shown. The document is intended to teach students the proper order for solving expressions with multiple operations.
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 contains 17 math problems involving squares, square roots, and perfect squares. It provides the questions, possible multiple choice answers, and the key/solutions to checking the answers. Some question types include finding the square root of a number, evaluating expressions involving squares and square roots, determining the number needed to be added to a quantity to make it a perfect square, and finding unknown values based on relationships between squares.
This document discusses squares, square roots, and properties related to them. It defines a square number as the result of multiplying a number by itself. It provides examples of perfect square numbers and discusses patterns in the last digits of squares based on the last digit of the original number. The document also covers finding square roots using repeated subtraction, properties of square roots based on the last digit, and other methods for finding squares and square roots. Additionally, it discusses Pythagorean triplets, prime factorizations, and other concepts related to squares and square roots.
The document discusses various properties of squares and square roots. It defines a square number as the result of multiplying a number by itself. Some key points made include:
- Numbers ending in 2, 3, 7, or 8 cannot be perfect squares, while numbers ending in 1, 4, 5, 6, or 9 may be squares
- The units digit of a square number depends on the units digit of the original number
- Odd squares are odd numbers and even squares are even numbers
- A number is not a perfect square if it ends in an odd number of zeros
- The Pythagorean theorem relates the squares of the sides of a right triangle
- Square roots can be estimated and found using repeated subtraction
Numbers - Divisibility, Unit digit, Number of zeros.pptxVishnuS502135
The document discusses various concepts related to numbers including positive integers, prime numbers, composite numbers, and divisibility tests. It provides definitions and examples of prime numbers, composite numbers, and tests for divisibility by numbers from 2 to 18. The divisibility tests covered include divisibility by sums of digits, last digits, and performing operations on digits. Examples are provided to demonstrate the divisibility tests.
This document provides an index and overview of topics related to basic mathematics calculations. It includes definitions and methods for operations like square roots, cube roots, percentages, ratios, proportions, and more. For square roots, it discusses prime factorization and division methods. For cube roots, it discusses factorization and finding roots of exact cubes up to 6 digits. It also provides an example of order of operations (VBODMAS) and solved problems for various calculations.
Vedic maths is the ancient India secret before the calculator to fast calucation with short cuts and tricks for fast easy accurate answers. GRE exam and other competative exam test students on theability to solve the complex numercials problems with efficiently and within time limits. Vedic maths helps with tricks just for same.
GREKing helping students in basic concepts.
GREking the best GRE preparation classes in Mumbai. (www.greking.com)
This document discusses various topics related to numbers including:
1) Classification of numbers and converting decimals to fractions through examples such as converting 6.424242 to 636/99.
2) Power cycles and unit digits, explaining concepts like finding the unit digit of expressions through examples.
3) Factors and multiples, covering topics like finding the number of factors of a number and the sum of factors through examples.
4) Factorials and finding the maximum power of a prime number in a factorial.
5) Divisibility rules and the remainder theorem, exemplified through practice questions.
* Let A's age be x and B's age be y
* Then average of A and B is (x + y)/2 = 20
* So, x + y = 40
* If C replaces A, average is (y + c)/2 = 19
* So, y + c = 38
* If C replaces B, average is (x + c)/2 = 21
* So, x + c = 42
* Solving the three equations, we get:
x = 22, y = 18, c = 20
The ages are:
A = 22
B = 18
C = 20
The answer is option 1.
The document discusses integers and rational numbers including:
- All integers are rational numbers because they can be written as fractions.
- Negative numbers are expressed with a negative sign such as -77 feet below sea level.
- When multiplying integers, a positive result occurs with an even number of negatives and a negative result with an odd number.
- Coordinates are plotted on a coordinate plane and basic operations are performed with integers and rational numbers.
Factors n multiple hcf and lcm remaindderTamojit Das
This document contains multiple questions about number systems and number theory concepts including factors, factor sums, highest common factors (HCF), least common multiples (LCM), remainders, and factorials. Specifically, it asks the reader to find factors, factor sums, HCFs, LCMs, remainders when dividing numbers, unit digits of numbers and expressions, and values related to factorials and their properties. The questions cover a wide range of number theory topics and require calculating various properties of numbers.
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.
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.
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This document discusses factors, division, and prime numbers. It provides examples of dividing numbers and determining factors. A number is prime if it has only two factors - 1 and itself. The document also introduces the concepts of greatest common divisor (GCD) and least common multiple (LCM), providing examples of finding the GCD and LCM of pairs of numbers. Exercises are included for readers to find the GCD and LCM of additional number pairs.
The document contains a series of maths questions divided into categories of number, algebra, shape and space, and handling data. The questions include things like solving simultaneous equations, factorizing quadratics, calculating probabilities, and drawing box plots from data sets.
This document contains a math lesson on Roman numerals, addition, subtraction, multiplication and division of whole numbers and decimals. It includes word problems, examples worked out step-by-step and answers for students to check their work. The lesson recaps working with negative numbers and compares ordering numbers in ascending and descending order.
- 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 contains 30 multiple choice questions related to calculating averages. Some questions involve calculating the average of groups with different numbers or weights. Other questions involve identifying average values based on additional information provided, such as if a number was incorrectly recorded. The average is a common concept tested in quantitative reasoning questions involving sums, groups, and data analysis.
The document provides 30 multiple choice questions testing mathematical skills. It addresses topics like simplification, percentages, exponents, and operations with fractions, decimals, and integers. The questions range in difficulty from straightforward calculations to multi-step word problems. An answer grid is included for test-takers to fill in their responses.
The document contains 6 math word problems involving cube and cube root operations. It then provides the answers and some working steps for each problem:
1) Evaluates an expression to be 4913
2) Finds that 19 must be added to 710 to make it a perfect cube
3) Determines that 1323 must be multiplied by 7 to make it a perfect cube
4) Calculates that the sum of digits of the number that makes 1440 a perfect cube is 6
5) Identifies the number satisfying the given cube and square operation is 4
6) Establishes the relationship between x and y is x3 = y2
1. The document discusses the topic of work and provides definitions, formulas, solved examples, and exercise problems related to calculating time taken to complete work based on the number of workers and their efficiency.
2. Formulas are provided to calculate time taken based on number of workers, ratio of efficiencies, and time taken when workers work together.
3. Several word problems are solved as examples using the formulas, such as calculating time taken for part of the work or remaining work based on number of days already worked.
The document contains 27 math word problems related to concepts of LCM (least common multiple) and HCF (highest common factor). It asks the reader to solve each problem and select the correct answer among the four options provided. Some key details provided in the problems include ratios between numbers, products of numbers, remainders when dividing numbers, and the relationships between LCM, HCF and the given numbers. The document tests readers' understanding and ability to apply concepts of LCM and HCF to solve word problems involving various numerical relationships.
The document contains 25 math word problems with multiple choice answers. It provides the questions, possible answers for each question, and a key with the answer for each question. The questions cover a range of math topics including percentages, ratios, proportions, averages, and algebra. An additional section provides hints and solutions for each question to explain the steps to arrive at the correct answer.
5 Common Mistakes to Avoid During the Job Application Process.pdfAlliance Jobs
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Resumes, Cover Letters, and Applying OnlineBruce Bennett
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Joyce M Sullivan, Founder & CEO of SocMediaFin, Inc. shares her "Five Questions - The Story of You", "Reflections - What Matters to You?" and "The Three Circle Exercise" to guide those evaluating what their next move may be in their careers.
IT Career Hacks Navigate the Tech Jungle with a RoadmapBase Camp
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A Guide to a Winning Interview June 2024Bruce Bennett
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1. Number System
1. In a three digit number, the digit in the unit’s place is twice
the digit in the ten’s place and 1.5 times the digit in the
hundred’s place. If the sum of all the three digits of the
number is 13, what is the number ?
(1) 364 (2) 436
(3) 238 (4) 634
(5) None of these
2. By how much is
6
11
th of 506 lesser than
3
5
th of 895 ?
(1) 178 (2) 219
(3) 143 (4) 261
(5) None of these
3. In the fractions
5 6 7 8
, , ,
14 11 9 13
and
9
10
are arranged in
ascending order of their values, which one will be the
fourth ?
(1)
7
9
(2)
5
14
(3)
8
13
(4)
9
10
(5) None of these
4. If the numerator of a fraction is increased by 300% and
the denominator is increased by 500%, the resulatant
fraction is
5
12
. What was the original fraction ?
(1)
8
5
(2)
5
11
(3)
12
5
(4)
5
7
(5) None of these
5. One-fifth of a number is 62. What will 73% of that number
be ?
(1) 198.7 (2) 212.5
(3) 226.3 (4) 234.8
(5) None of these
6. What is 348 times 265 ?
(1) 88740 (2) 89570
(3) 95700 (4) 92220
(5) None of these
7. a, b, c, d and e are five consecutive even numbers. If the
sum of ‘a’and ‘d’is 162. What is the sum ofall the number?
(1) 400 (2) 380
(3) 420 (4) Cannot be determined
(5) None of these
8. Two numbers are such that the sum of twice the first
number and thrice the second number is 36 and the sum
of thrice the first number and twice the second number is
39. Which is the smaller number ?
(1) 9 (2) 5
(3) 7 (4) 3
(5) None of these
9. What is the greater of two numbers whose product is 1092
and the sum of two number exceeds their difference by 42?
(1) 48 (2) 44
(3) 52 (4) 54
(5) None of these
10. Which of the following smallest numbers should be added
to 6659 to make it a perfect square ?
(1) 230 (2) 65
(3) 98 (4) 56
(5) None of these
11. There are 7 dozen candles kept in a box. If there are 14
such boxes. How many candles are there in all the boxes
together ?
(1) 1176 (2) 98
(3) 1216 (4) 168
(5) None of these
12. The sum of the two digits of a two digit number is 12 and
the digit number is 12 and the difference between the two
digits of the two digit number is 6. What is the two-digit
number ?
(1) 39 (2) 84
(3) 93 (4) Cannot be determined
(5) None of these
13.
3
4
th of
2
9
th of
1
5
th of a number is 249.6. What is 50%
of that number ?
(1) 3794 (2) 3749
(3) 3734 (4) 3739
(5) None of these
14. If the numerator of a fraction is increased by 200% and
the denominator of the fraction is increased by 120% , the
resultant fraction is
4
11
. What is the original fraction ?
(1)
4
15
(2)
3
11
(3)
5
12
(4)
6
11
(5) None ot these
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2. 2
CAREER POWER
CAREER POWER, G-7, Roots Tower, Laxmi Nagar, District Centre, Delhi-92, www.careerpower.in
Chapterwise Bank PO Quantitative Aptitude
.ANSWER KEY.
1. (2) 2. (4) 3. (1) 4. (5) 5. (3) 6. (4)
7. (5) 8. (5) 9. (3) 10. (2) 11. (1) 12. (4)
13. (5) 14. (1) 15. (1) 16. (5) 17. (2) 18. (2)
19. (4) 20. (4) 21. (4) 22. (5) 23. (2) 24. (1)
25. (5)
15. The product of three consecutive even numbers is 4032.
The product of the first and the third number is 252. What
is five times the second number ?
(1) 80 (2) 100
(3) 60 (4) 70
(5) 90
16. The sum of nine consecutive odd numbers of set-A is 621.
What is the sum of different set of six consecutive even
numbers whose lowest number is 15 more than the lowest
number of set-A ?
(1) 498 (2) 468
(3) 478 (4) 488
(5) None of these
17. The sum of six consecutive even numbers of set-A is 402.
What is the sum of another set-B of four consecutive
numbers whose lowest number is 15 less than double the
lowest number of set-A ?
(1) 444 (2) 442
(3) 440 (4) 446
(5) None of these
18. The difference between the sum of four consecutive odd
numbers and three consecutive even numbers together is
20. Also, the largest even number is 5 more than the largest
odd number. What is the sum of the smallest odd number
and the smallest even number ?
(1) 75 (2) 77
(3) 85
(4) Cannot be determined
(5) None of these
19. What is the least number that can be added to the number
1020 to make it a perfect square ?
(1) 65 (2) 12
(3) 59 (4) 4
(5) None of these
20. The sum of the five consecutive even numbers of set-A is
280. What is the sum of different set of five consecutive
numbers whose lowest number is 71 less than double the
lowest number of set-A ?
(1) 182 (2) 165
(3) 172 (4) 175
(5) None of these
21. The sum of the squares of two consecutive even numbers
is 6500. Which is the smaller number ?
(1) 54 (2) 52
(3) 48 (4) 56
(5) None of these
22. The sum of the digits of a two digit number is 15 and the
difference between the two digits of the two digit number
is 3. What is the product of the two digits of the two-digit
number ?
(1) 56 (2) 63
(3) 42
(4) Cannot be determined
(5) None of these
23. The digit in the unit’s place of a three digit number is thrice
the digit in the ten’s place and the digit in the hundred’s
place is two-third of the digit in the ten’s place. If the sum
of the three digits of the number is 14, what is the three
digit number ?
(1) 932 (2) 239
(2) 326
(4) Cannot be determined
(5) None of these
24. Two-third of the first number is equal to the cube of the
seconds number. If the second number is equal to twelve
percent of 50, what is the sum of the first and the second
number ?
(1) 330 (2) 360
(2) 390 (4) 372
(5) None of these
25. The sum of three consecutive odd numbers and three
consecutive even numbers together is 231. Also, the
smallest odd number is 11 less than the smallest even
number. What is the sum of the largest odd number and
the largest even number ?
(1) 82 (2) 83
(3) 74 (4) Cannot be determined
(5) None of these
HINTS & SOLUTIONS
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3. 3
CAREER POWER
CAREER POWER, G-7, Roots Tower, Laxmi Nagar, District Centre, Delhi-92, www.careerpower.in
Chapterwise Bank PO Quantitative Aptitude
1. (2) Let the ten’s digit = x.
Unit’s digit = 2x and hundred’s digits =
2
15
x
According to the question,
x + 2x +
2
15
x
= 13 Þ
15 3 2
1.5
+ +x x x
= 13
Þ 6.5x = 13 × 1.5 Þ x =
13 15
6.5
´
= 3
Unit’s digit = 6 and hundred’s digit =
6
1.5
= 4
Number = 436
2. (4) Required difference =
3
5
× 895 –
6
11
× 506
= 537 – 276 = 261
3. (1) The decimal equivalent of fractions :
5
14
= 0.36 ;
6
11
= 0.545 ;
7
9
= 0.78 ;
8
13
= 0.62 ;
9
10
= 0.9
Clearty, 0.36 < 0.545 < 0.62 < 0.78 < 0.9
i. e.
5 6 8 7 9
14 11 13 9 10
< < < <
4. (5) Let the original fraction be =
x
y
.
According to the question,
400
600
´
´
x
y
=
5
12
Þ
x
y
=
5 6
12 4
´ =
5
8
5. (3) Let the number be x.
According to the question,
5
x
= 62 Þ x = 62 × 5 = 310
73% of 310 =
73
100
× 310 = 226.3
6. (4) 265 × 348 = 92220
7. (5) Let the five consecutive even number be x, x + 2 x + 4
x + 6 and x + 8 respectively.
According to the question,
x + x + 6 = 162
Þ 2x = 162 – 6 = 156
Þ x =
156
2
= 78
Sum of all numbers
= 78 + 80 + 82 + 84 + 86 = 410
8. (5) Let the number be x and y.
Accoding to the question,
2x + 3y = 36 ...(i)
3x + 2y = 39 ...(ii)
By equastion (i) × 3 – (ii) × 2,
6x + 9y – 6x – 4y = 108 – 78
Þ 5y = 30 Þ y =
30
5
= 6
From equation (i), we have,
2x + 3 × 6 = 36
Þ 2x = 36 – 18 = 18 Þ x =
18
2
= 9
The smaller number = 6
9. (3) Let the number be x and y.
Accoding to the question,
x + y – (x – y) = 42
Þ 2y = 42 Þ y =
42
2
= 21
x =
1092
21
= 52
10. (2) 81 × 81 = 6561
82 × 82 = 6724
To make 6659 a perfect square the number to be
added = 6724 – 6659 = 65
11. (1) Total number of candles
= 7 × 12 × 14 = 1176
12. (4) Let the two digit number be = 10 x + y where x > y
Accoding to the question,
x + y = 12 and x – y = 6
Adding these equations,
12
6
2 18
+ =
- =
=
x y
x y
x
Þ x =
18
2
= 9
y = 12 – 9 = 3
Number = 93
Again, let the number be 10x + y where x < y.
Then, x + y = 12 and y – x = 6
Adding these equations,
2y = 18 Þ y =
18
2
= 9
From equation (i),
x = 3
Number = 39
Thus we get two numbers. This does not satisfy the
uniqueness of answer.
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4. 4
CAREER POWER
CAREER POWER, G-7, Roots Tower, Laxmi Nagar, District Centre, Delhi-92, www.careerpower.in
Chapterwise Bank PO Quantitative Aptitude
13. (5) Let the number be x.
According to the question,
x ×
1
5
×
2
9
×
3
4
= 249.6
Þ x = 249.6 × 30 = 7488
50% of 7488 = 7488 ×
1
2
= 3744
14. (1) Let the original fraction be
x
y
.
According to the question,
300
100
220
100
x
y
´
´
=
4
11
Þ
30
20
x
y
=
4
11
Þ
x
y
=
4 22
11 30
´ =
4
15
15. (1) Second number =
4032
252
= 16
Required answer = 5 × 16 = 80
16. (5) Fifth number of set-A =
621
9
= 69
Smallest number of set-A = 61
Smallest number of set-B = 61 + 15 = 76
Required sum = 76+78+80+82+84+86 = 486
17. (2) Third even number =
402
6
– 1 = 67 – 1 = 66
Smallest even number = 62
Smallest number of set-B = 2 × 62 – 15 = 109
Required sum = 109 + 110 + 111 + 112 = 442
18. (2) Let the consecutive odd number be :
x, x + 2, x + 4 and x + 6
Largest even numbers = x + 11
Other even numbers = x + 7 and x + 9
x + x + 2 + x + 4 + x + 6 – (x+7+x+9+x+11) = 20
Þ x – 15 = 20 Þ x = 15 + 20 = 35
Required sum = x + x + 7 = 2x + 7
= 2 × 35 + 7 = 77
19. (4) 32 × 32 = 1024
Required number = 1024 – 1020 = 4
20. (4) For set-A,
x + x + 2 + x + 4 + x + 6 + x + 8 + 280
Þ 5x + 20 = 280
Þ 5x = 280 – 20 = 260
Þ x =
260
5
= 52
The lowset number of set-B = 2 × 52 – 71 = 33
Required sum = 33 + 34 + 35 + 36 + 37 = 175
21. (4) 562
+ 582
= 3136 + 3364 = 6500
Smaller number = 56
22. (5) Let the number be 10x + y and x > y.
x + y = 15 ... (i)
and, x – y = 3 ... (ii)
On adding, x = 9
From equation (i),
9 + y = 15 Þ 15 – 9 = 6
xy = 9 × 6 = 54
23. (2) Let the ten’s digit be x.
Unit’s digit = 3x
Hundred’s digit =
2
3
x
x + 3x +
2
3
x
= 14
Þ 3x + 9x + 2x = 14 × 3
Þ 14x = 14 × 3 Þ x = 3
Number = 239
24. (1) Second number =
50 12
100
´
= 6
First number =
3
6 3
2
´
= 324
Required sum = 324 + 6 = 330
25. (5) The smallest odd number = x
The smallest even number = x + 11
x + x + 2 + x + 4 + x + 11 + x + 13 + x + 15 = 231
Þ 6x + 45 = 231
Þ 6x = 231 – 45 = 186
x =
186
6
= 31
Required sum = x + 4 + x + 15
= 2x + 19 = 2 × 31 + 19 = 62 + 19 = 81
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