PDF- Numerical Reasoning Test Formulas, Numerical -Introduction - Mechanical Aptitude Tests - How to Pass Numerical Reasoning Tests a Step by Step Guide

Pass Numerical Reasoning Tests a Step by Step Guide

Description

How to Pass Numerical Reasoning Tests

Openmirrors

THIS PAGE IS INTENTIONALLY LEFT BLANK

Openmirrors

How to Pass Numerical Reasoning Tests A step-by-step guide to learning key numeracy skills 2nd edition

Heidi Smith

Openmirrors

Publisher’s note Every possible effort has been made to ensure that the information contained in this book is accurate at the time of going to press,

and the publishers and authors cannot accept responsibility for any errors or omissions,

No responsibility for loss or damage occasioned to any person acting,

as a result of the material in this publication can be accepted by the editor,

the publisher or any of the authors

First published in Great Britain and the United States in 2003 by Kogan Page Limited Revised edition 2006 Reprinted 2007,

as permitted under the Copyright,

Designs and Patents Act 1988,

this publication may only be reproduced,

with the prior permission in writing of the publishers,

or in the case of reprographic reproduction in accordance with the terms and licences issued by the CLA

Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned addresses: 120 Pentonville Road 1518 Walnut Street,

Suite 1100 London N1 9JN Philadelphia PA 19102 United Kingdom USA www

© Heidi Smith 2003,

Designs and Patents Act 1988

ISBN E-ISBN

British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library

Library of Congress Cataloging-in-Publication Data Smith,

ISBN 978-0-7494-6172-0 – ISBN 978-0-7494-6173-7 (ebk)  1

  Mathematics– Examinations,

S654 2011 510

Hong Kong Printed and bound in India by Replika Press Pvt Ltd

Openmirrors

This book is dedicated to Dr J V Armitage

Openmirrors

THIS PAGE IS INTENTIONALLY LEFT BLANK

Openmirrors

Contents Preface to second edition  ix Introduction  1

Openmirrors

CONTENTS

Working with rates  76 Work rate problems  85 Answers to Chapter 3  88

fractions and decimals  102 Converter tables  104 Working with percentages  106 Simple interest and compound interest  117 Answers to Chapter 4  120

Openmirrors

Preface to second edition T

he success of the First Edition of How to Pass Numerical Reasoning Tests demonstrates that there are many people who,

despite a high level of experience and competence in other areas of their professional life,

are not confident about passing tests that involve numbers

However,

what is not commonly known is that with practice it is possible to improve your numerical reasoning score dramatically

This book was designed with the adult test-taker in mind – someone who is looking for some extra practice material prior to taking a test

Topics covered include:

percentages – ‘what are the three parts I have to know in order to work out the answer

decimals – ‘what was that quick way to multiply them

workrates – ‘wasn’t there something about adding the total time together and dividing by something

prime numbers and multiples – ‘I remember I can use these to help me,

but can’t quite remember how’

interest rates – ‘what were the two different types and how do I use each of them

This workbook reminds the non-mathematician what these terms are and how to work with them quickly

Openmirrors

PREFACE TO SECOND EDITION

The First Edition of How to Pass Numerical Reasoning Tests has helped thousands of applicants prepare for their test

This Second Edition will help many more

Better preparation for psychometric testing leads to increased confidence during the initial assessment and this,

gives you a better chance of getting that job

Openmirrors

Introduction Numerical reasoning tests in context Standardized testing is becoming more popular as a means to assess candidates at an early stage of the job application process,

particularly in organizations where the demand for jobs is high

If you have picked up this book and started to read this chapter,

the chances are that you are facing a numerical reasoning test in the very near future

It is likely that you know that you are perfectly capable of doing the job for which you have applied,

and that the only obstacle between you and the next round of interviews is a set of tests that includes a numerical reasoning section

It is possible that you are dreading it

Not many people like being tested under pressure,

so it is unsurprising that you are not looking forward to the experience

Take heart though

The good news is that the numerical knowledge you need to do well in these tests is the maths you learnt in school

You need now a quick refresher course and the application of some logical thinking

With practice and commitment to drilling in mental arithmetic you can improve your score

The numerical reasoning section of an aptitude test is the section where many people find they can improve their score,

so it’s worth dedicating a decent amount of test preparation time to this area

Openmirrors

How to Pass Numerical Reasoning Tests

Purpose of this workbook This is a self-study modular workbook,

and its purpose is to provide you with the necessary skills to perform well in your numerical reasoning test

There is no magic formula for improving your performance in numerical reasoning tests

performance is determined by a number of factors aside from basic intelligence

Preparation plays a large part in determining your level of success,

and the secret is to practise as much as you can

If the last time you had to work out a percentage increase was a decade ago,

it is likely that a quick reminder of the method will help you complete the calculation within the time allowed in the test

This workbook will explain these formulae to remind you how to complete such calculations

Test preparation and good exam technique gives you the confidence to estimate correct answers quickly

Method and practice will help you to calculate correct answers swiftly

This book will help you to prepare for your test by giving you plenty of examples,

practice questions and explanations

What this workbook doesn’t do The content of this workbook is aimed at adult test-takers who want to prepare to take a numerical reasoning test

It is assumed that you don’t necessarily want,

but you do want to relearn enough maths to help you to do well in the test

This workbook is designed to help you to prepare the required numeracy skills for the standardized aptitude tests currently on the market

This workbook will not explain why mathematical formulae work the way they do

Rather,

it explains how to apply the formula in a practical setting,

in particular in the application of maths in numeracy tests

It is likely that if you wanted to understand the theory of maths,

you would be already immersed in advanced level maths books and wouldn’t need this refresher course

Openmirrors

Introduction

Content of this workbook Each chapter first explains the concept,

works through an example and provides you with practice questions to help consolidate your learning

The emphasis throughout the book is on the practice questions and corresponding explanations

Chapter 1,

guides you through the fundamentals and gives you the opportunity to get started with numeracy questions

The worked examples in Chapter 1 demonstrate useful methods to complete calculations quickly

Chapter 2,

explains how to work with parts of whole numbers expressed either as fractions or decimals

You will practise the methods to add,

multiply and divide fractions and decimals

Chapter 3,

reminds you of the formulae to work out speed,

distance and time when you know two (or more) variables

This chapter also covers the work rate formula

Chapter 4,

covers the three variables in a typical percentage question

The part,

the whole and the per­centage are all explained

Percentage increases and decreases are also explained,

and you will practise questions involving simple and compound interest

Chapter 5,

examines ‘part to part’ and ‘part to whole’ type ratios and explains how to use ratios to find actual quantities

An explanation of the use of proportions is included

Chapter 6,

takes all the skills you have practised and combines them to allow you to practise applying your new skills to data presented in graphs,

Chapter 7,

is brand new to this edition and shows how your analytical skills are under scrutiny just as much as your numerical skills when you are presented with a word problem

The ‘Glossary of terms and formulae’ section lists all the terms and formulae you have used throughout the book and serves as a reference guide

The ‘Recommendations for further practice’ section identifies a number of useful publications and websites for you to use for further practice prior to your test

Openmirrors

How to Pass Numerical Reasoning Tests

In each chapter,

an explanation is offered to solve each of the problems

Often there are several different ways to solve a problem

You may find that your preferred method differs from the explanation offered

As you work through more and more examples,

you will discover the methods you find easiest to work with,

or to find out whether there is a quicker way to solve the problem

Remember that speed is a key indicator of success

How to use this workbook This workbook is designed to teach the foundation skills relevant to a number of numerical reasoning tests currently on the market

It is progressive and you should work through each of the chapters in order

Concepts explained in the earlier chapters are used and tested again in later chapters

It is good practice for employers and recruiters to send you sample questions prior to the test,

in order that you know what to expect on the day

Once you know the broad content of the test,

you can use this workbook to practise the areas most relevant to you if time is short

It is recommended that you work thoroughly through Chapter 1 regardless of the type of test you are taking,

as Chapter 1 provides you with the skills to build a numerical foundation relevant to subsequent chapters

Preparation and test technique Being prepared for the test If you don’t know what kind of questions to expect in your test,

there are two things you can do

call the tester or recruiter and ask for a sample practice booklet

It is good practice for recruiters to distribute practice tests to prepare you for the type of tests you will be taking

Second,

while you are waiting for the practice questions to arrive,

Many people find that part of the difficulty they experience with numeracy tests is the lack of familiarity with everyday maths skills

This book aims to help you to overcome

Openmirrors

Introduction

that lack of familiarity by providing you with the opportunity to refresh your memory through plenty of practice drills and questions

Types of question There are a wide range of questions set in a test

There are also a number of different ways you may be asked to answer the question

Typical answer formats include calculation,

multiple choice and data sufficiency answers,

where you are given pieces of information and asked whether you have enough information to answer the questions correctly

Chapters 1 to 5 require that you calculate the answers to practice questions

The reason for the adoption of this method is to ensure that you can work out correct answers confidently,

without resorting to a ‘multiple guess’ technique

In Chapter 6,

you are given a range of answers from which to choose the correct one

The answer choices include deliberate traps,

rather like those the test-writers will set for you

The accompanying explanations will help you to learn about these traps and to help you to avoid them in the test

Getting to the right answer When you are asked to calculate an exact answer,

The question will give you an indication of the level of precision that is expected from you,

‘Give the answer to 3 decimal places’

If you are asked for this level of precision,

usually you will have a calculator to assist you

If you are given a range of answers to choose from,

do a quick estimate of the correct answer first

Then eliminate all out-of-range answers or the ‘outliers’

This technique reduces the likelihood of choosing incorrectly under pressure and gives you a narrower range of answers from which to choose the correct answer

Your estimate may be accurate enough to choose the correct answer without completing any additional calculations

This will save you time and allow you to spend more time on difficult questions

Once you have eliminated some answers from the multiple-choice range,

Openmirrors

How to Pass Numerical Reasoning Tests

substitute in possible correct answers to the question and effectively solve the question using the answer as the starting point

Translating the language Part of the difficulty of aptitude tests is in understanding exactly what is being asked of you

Before you set off to answer a question,

be absolutely sure that you understand what you are being asked to do

Think carefully whether you have enough information to translate the question into an equation,

or whether you need to complete an interim step to provide you with enough information to answer the question

If you are working with graphs and charts,

read the labels accompanying the diagrams to make sure you understand whether you are being given percentages or actual values

Read the axis label in case the axes are given in different values

Typically,

once you have translated the words,

Calculators Many aptitude tests disallow the use of calculators,

so you may as well get into the habit of doing mental arithmetic without it

If you are of the GCSE generation,

maths without a calculator may seem impossible: after all,

calculators are a key tool in maths learning today

However,

all the examples and practice questions in this book have been designed so that you can work out the correct answer without the use of the calculator

Think of it as a positive

Think of it this way: if you can’t use a calculator in the test,

the maths can’t be that hard,

? If you set about the practice questions and drills with your calculator,

you will be wasting your test preparation time and practice material

By all means,

check your answers afterwards with your calculator,

but get into the habit of sitting down to take the test without it

Test timings Where timings are applied to the practice questions in this workbook,

do try to stick to the time allocated

One of the skills tested in

Openmirrors

Introduction

aptitude tests is your ability to work quickly and accurately under pressure

However,

sometimes you do not have to finish all the questions in order to do well in a test,

you must answer those questions correctly

If you find that at first you are taking longer to complete the questions than the allocated time,

work out which aspect of the problem is taking the extra time

For example,

are you wasting time reworking simple calculations or are you having difficulty in working out exactly what is being asked in the question

? Once you have identified the problem,

you can go back to the relevant section of this book to find suggestions to help overcome the difficulty

What else can you do to prepare

? If you find that you draw a complete blank with some of the mental arithmetic questions,

particularly the timed questions,

find other ways to exercise your grey matter even when you are not in study mode

Add up the bill in your head as you are grocery shopping

Work out the value of discounts offered in junk e-mail

Work out whether the deal on your current credit card is better or worse than the last one

Work out dates backwards

For example,

if today is Saturday 3 August,

what was the date last Tuesday

? If my birthday is 6 April 1972 and today is Monday,

? On the bus on the way to work,

work out roughly how many words there must be on the front page of your neighbour’s newspaper,

based on your estimate of the number of words per line and the number of lines per page

Play sudoko,

In other words,

become proficient at estimating everyday calculations

Think proactively about numbers and mental arithmetic

It will pay off enormously in the test

Getting started This introduction has explained the purpose of this workbook and has recommended a method to use it

Now roll up your sleeves and go straight on to Chapter 1

Openmirrors

THIS PAGE IS INTENTIONALLY LEFT BLANK

Openmirrors

CHAPTER 1

Review the basics Chapter topics ●●

Terms used in this chapter

Multiplication tables

Dividing and multiplying numbers

Prime numbers

Multiples

Working with large numbers

Working with signed numbers

Averages

Answers to Chapter 1

Terms used in this chapter Arithmetic mean: The amount obtained by adding two or more numbers and dividing by the number of terms

Openmirrors

How to Pass Numerical Reasoning Tests

Average: See Mode,

Median and Arithmetic mean

Dividend: The number to be divided

Divisor: The number by which another is divided

Factor: The positive integers by which an integer is evenly divisible

Find the product of …: Multiply two or more numbers together

Integer: A whole number without decimal or fraction parts

Lowest common multiple: The least quantity that is a multiple of two or more given values

Mean: See Arithmetic mean

Median: The middle number in a range of numbers when the set is arranged in ascending or descending order

Mode: The most popular value in a set of numbers

Multiple: A number that divides into another without a remainder

Prime factor: The factors of an integer that are prime numbers

Prime number: A number divisible only by itself and 1

Test-writers assume that you remember the fundamentals you learnt in school and that you can apply that knowledge and understanding to the problems in the tests

The purpose of this chapter is to remind you of the basics and to provide you with the opportunity to practise them before your test

The skills you will learn in this chapter are the fundamentals you can apply to solving many of the problems in an aptitude test,

so it is worth learning the basics thoroughly

You must be able to do simple calculations very quickly,

without expending any unnecessary brainpower

This chapter reviews the basics and includes a number of practice drills to ease you back into numerical shape

Remember,

Multiplication tables ‘Rote learning’ as a teaching method has fallen out of favour in recent years

There are good reasons for this in some academic areas but it doesn’t apply to multiplication tables

You learnt the times-tables when you first went to school,

Openmirrors

Review the basics

? Recite them to yourself quickly,

when you’re cleaning your teeth,

when you’re stirring your baked beans

Six times,

seven times and eight times are the easiest to forget,

so drill these more often than the twos and fives

Make sure that you can respond to any multiplication question without pausing even for half a second

If you know the multiplication tables inside out,

you will save yourself valuable seconds in your test and avoid needless mistakes in your calculations

Multiplication tables: practice drill 1 Practise these drills and aim to complete each set within 15 seconds

the answers are at the end of the chapter

Drill 1

Drill 2

Drill 3

Drill 4

Drill 5

7× 5=

6× 3=

11 × 11 =

4× 7=

11 × 13 =

3× 4=

8 × 15 =

8× 8=

2× 6=

7× 6=

4 × 12 =

5 × 14 =

3 × 11 =

9× 6=

Openmirrors

How to Pass Numerical Reasoning Tests

Multiplication tables: practice drill 2 Drill 1

Drill 2

Drill 3

Drill 4

Drill 5

11 × 11 =

13 × 13 =

11 × 14 =

11 × 15 =

14 × 14 =

11 × 10 =

12 × 15 =

13 × 14 =

11 × 12 =

Dividing and multiplying numbers Long multiplication Rapid multiplication of multiple numbers is easy if you know the multiplication tables inside-out and back-to-front

In a long multiplication calculation,

you break the problem down into a number of simple calculations by dividing the multiplier up into units of tens,

In Chapter 2 you will work through practice drills involving division and multiplication of decimals

Worked example Q

What is the result of 2,348 × 237

? To multiply a number by 237,

break the problem down into a number of simpler calculations

Divide the multiplier up into units of hundreds,

Openmirrors

Review the basics

For example,

to multiply by 237 you multiply by: 7 (units) 3 (tens) 2 (hundreds) (It doesn’t matter in which order you complete the calculation

) 2,348   237 × 16,436 70,440 469,600 556,476

Multiplier 2,348 × 7 2,348 × 30 2,348 × 200 16,436 + 70,440 + 469,600

Long multiplication: practice drill 1 No calculators

! This exercise is intended to help you to speed up your mental arithmetic

Set a stopwatch and aim to complete this drill in five minutes

Long multiplication: practice drill 2 Set a stopwatch and aim to complete this practice drill in five minutes

Openmirrors

How to Pass Numerical Reasoning Tests

Long division Long division calculations,

like long multiplication calculations,

can be completed quickly and easily without a calculator if you know the multiplication tables well

There are four steps in a long division calculation,

and as long as you follow these in order,

you will arrive at the right answer

Worked example Q: Divide 156 by 12 This may seem obvious,

but recognize which number you are dividing into

This is called the dividend

In this case you are dividing the dividend (156) by the divisor (12)

Be clear about which is the divisor and which is the dividend

There are four steps in a long division question

Step 1 Step 2 Step 3 Step 4

Openmirrors

Divide (D) Multiply (M) Subtract (S) Bring down (B)

Review the basics

You can remember this as D-M-S-B with any mnemonic that helps you to remember the order

Do-Mind-Slippery-Bananas

Dirty-Muddy-Salty-Bicycles

Follow the steps in order and repeat until you have worked through the whole calculation

Step 1: Divide Work from the left to the right of the whole number

so write ‘1’ on top of the division bar

1 12 156

Step 2: Multiply Multiply the result of step 1 (1) by the divisor (12): 1 × 12 = 12

Write the number 12 directly under the dividend (156)

Step 3: Subtract Subtract 12 from 15 and write the result directly under the result of Step 2

1 12 156

Step 4: Bring down Bring down the next digit of the dividend (6)

1 12 156

- 12 36

Return to Step 1 and start the four-step process again

Openmirrors

How to Pass Numerical Reasoning Tests

Step 1: Divide 12 into 36 and write the result (3) on top of the long division sign

13 12 156

Step 2: Multiply the result of Step 1 (3) by the divisor (12): 3 × 12 = 36

Write the number 36 directly below the new dividend (36)

13 12 156

-12 36 36

Step 3: Subtract 36 from 36

13 12 156

Step 4: There aren’t any more digits to Bring down,

so the calculation is complete

Openmirrors

Review the basics

Long division: practice drill 1 Set a stopwatch and aim to complete these calculations in four minutes

You may check your answers with a calculator only once you have finished all the questions in the drill

Q10 2,496  ÷  78

Long division: practice drill 2 Set a stopwatch and aim to complete the following practice drill within five minutes

Q10   3,591  ÷    27

Openmirrors

How to Pass Numerical Reasoning Tests

Prime numbers An integer greater than 1 is a prime number if its only positive divisors are itself and 1

All prime numbers apart from 2 are odd numbers

Even numbers are divisible by 2 and cannot be prime by definition

because it is divisible by one number only,

The following is a list of all the prime numbers below 100

It’s worth becoming familiar with these numbers so that when you come across them in your test,

you don’t waste time trying to find other numbers to divide into them

  2    3    5    7

23  29

31  37

53  59

61  67

83  89

Prime numbers: practice drill Refer to the table above to assist you with the following drill: Q1

What is the product of the first four prime numbers

What is the sum of the prime numbers between 40 and 50 minus the eleventh prime number

How many prime numbers are there

How many prime numbers are there between 1 and 100

What is the only even prime number

Openmirrors

Review the basics

Between 1 and 100,

there are five prime numbers ending in 1

What are they

What is the result of the product of the first three prime numbers minus the sum of the second three prime numbers

How many prime numbers are there between 60 and 80

How many prime numbers are there between 90 and 100

Q10 What is the sum of the second 12 prime numbers minus the sum of the first 12 prime numbers

Multiples A multiple is a number that divides by another without a remainder

For example,

Tips to find multiples An integer is divisible by: 2,

if the last digit is 0 or is an even number 3,

if the sum of its digits are a multiple of 3 4,

if the last two digits are a multiple of 4 5,

if the last digit is 0 or 5 6,

if it is divisible by 2 and 3 9,

if its digits sum to a multiple of 9 There is no consistent rule to find multiples of 7 or 8

Worked example Is 2,648 divisible by 2

because 8 is divisible by an even number

Is 91,542 divisible by 3

because 9+1+5+4+2 = 21 and 21 is a multiple of 3

Is 216 divisible by 4

Is 36,545 divisible by 5

Openmirrors

How to Pass Numerical Reasoning Tests

Is 9,918 divisible by 6

is divisible by an even number and the sum of all the digits,

Multiples: practice drill Set a stopwatch and aim to complete the following 10-question drill in five minutes

The following numbers are multiples of which of the following integers: 2,

Drill 2

Drill 3

Drill 4

989,136

240,702

161,174

Lowest common multiple The lowest common multiple is the least quantity that is a multiple of two or more given values

To find a multiple of two integers,

you can simply multiply them together,

but this will not necessarily give you the lowest common multiple of both integers

To find the lowest common multiple,

you will work with the prime numbers

This is a concept you will find useful when working with fractions

There are three steps to find the lowest common multiple of two or more numbers:

Openmirrors

Review the basics

Step 1: Express each of the integers as the product of its prime factors

Step 2: Line up common prime factors

Step 3: Find the product of the distinct prime factors

Worked example What is the lowest common multiple of 6 and 9

? Step 1: Express each of the integers as the product of its prime factors To find the prime factors of an integer,

divide that number by the prime numbers,

The product of the prime factors of an integer is called the prime factorization

Divide 6 by 2: 3 26

Now divide the remainder,

by the next prime factor after 2: 1 33

So the prime factors of 6 are 2 and 3

(Remember that 1 is not a prime number

) The product of the prime factors of an integer is called the prime factorization,

so the prime factorization of 6 = 2 × 3

Now follow the same process to work out the prime factorization of 9 by the same process

Divide 9 by the first prime number that divides without a remainder: 3 39

Now divide the result by the first prime number that divides without a remainder

The prime factorization of 9 = 3 × 3

Openmirrors

How to Pass Numerical Reasoning Tests

Step 2: Line up common prime factors Line up the prime factors of each of the given integers below each other: 6  =  2  ×  3 9  =  3  ×  3 Notice that 6 and 9 have a common prime factor (3)

Step 3: Find the product of the prime factors Multiply all the prime factors together

When you see a common prime factor,

The lowest common multiple of 6 and 9 = 18

Lowest common multiple: practice drill 1 Set a stopwatch and aim to complete the following drill in four minutes

Find the lowest common multiple of the following sets of numbers: Q1   8  and   6 Q2

Q3   3  and   5 Q4

Q5   8  and  14 Q6   9  and  18 Q7   4  and   7 Q8

Q10   7  and  15

Openmirrors

Review the basics

Lowest common multiple: practice drill 2 Set a stopwatch and aim to complete the following drill in four minutes

Find the lowest common multiple of the following sets of numbers: Q1

Q10 4  and  6  and   7

Working with large numbers Test-writers sometimes set questions that ask you to perform an operation on very large or very small numbers

This is a cruel test trap,

as it is easy to be confused by a large number of decimal places or zeros

Operations on small and large numbers are dealt with in Chapter 2

This section reminds you of some commonly used terms and their equivalents

Millions,

billions and trillions The meaning of notations such as millions,

billions and trillions is ambiguous

The terms vary and the UK definition of these terms is different from the US definition

If you are taking a test developed in the United States (such as the GMAT or GRE),

make sure you know the difference

Openmirrors

How to Pass Numerical Reasoning Tests

US definition Million: 1,000,000 or ‘a thousand thousand’ (same as UK definition) Billion: 1,000,000,000 or ‘a thousand million’ Trillion: 1,000,000,000,000 or ‘a thousand billion’

UK definition Million: 1,000,000 or ‘a thousand thousand’ (same as US definition) Billion: 1,000,000,000,000 or ‘a million million’ Trillion: 1,000,000,000,000,000,000 or ‘a million million million’ The US definitions are more commonly used now

If you are in doubt and do not have the means to clarify which notation is being used,

Multiplying large numbers To multiply large numbers containing enough zeros to make you go cross-eyed,

follow these three steps: Step 1: Multiply the digits greater than 0 together

Step 2: Count up the number of zeros in each number

Step 3: Add that number of zeros to the result of Step 1

Worked example What is the result of 2,000,000 × 2,000

? Step 1: Multiply the digits greater than 0 together 2×2=4 Step 2: Count up the number of zeros in each number 2,000,000 × 2,000 = nine zeros

Openmirrors

Review the basics

Step 3: Add that number of zeros to the right of the result of Step 1 Result of Step 1 = 4 nine zeros = 000,000,000 Answer = 4,000,000,000 (4 billion,

US definition)

Multiplying large numbers: practice drill Use the US definition of billion and trillion to complete this practice drill

Set a stopwatch and aim to complete the following drill in three minutes

Q10 14 billion × 6 thousand

Dividing large numbers Divide large numbers in exactly the same way as you would smaller numbers,

but cancel out equivalent zeros before you start

Worked example 4,000,000 ÷ 2,000 Cancel out equivalent zeros: 4,

000 ÷ 2,

Openmirrors

How to Pass Numerical Reasoning Tests

Now you are left with an easier calculation: 4,000 ÷ 2 Answer = 2,000

Dividing large numbers: practice drill Set a stopwatch and aim to complete the following drill in four minutes

240,000

6,720,000

475,000

19,500,000

23,800,000

9,890,000

15,540,000

Working with signed numbers Multiplication of signed numbers There are a few simple rules to remember when multiplying signed numbers

Positive × positive = positive Negative × negative = positive Negative × positive = negative Positive × negative = negative

Openmirrors

P×P=P N×N=P N×P=N P×N=N

Review the basics

Tip: note that it doesn’t matter which sign is presented first in a multiplication calculation

The product of an odd number of negatives = negative N×N×N=N The product of an even number of negatives = positive N×N×N×N=P

Worked example P × P = P   2 × 2 = 4 N × N = P

-2 × 2 =

-2 = 16

Division of signed numbers Positive ÷ positive = positive Negative ÷ negative = positive Negative ÷ positive = negative Positive ÷ negative = negative

Worked example P ÷ P = P   2 ÷ 2 = 1 N ÷ N = P

-2 ÷ 2 =

Openmirrors

P÷P=P N÷N=P N÷P=N P÷N=N

How to Pass Numerical Reasoning Tests

Multiplication and division of signed numbers: practice drill I Set a stopwatch and aim to complete each drill within five minutes

Multiplication and division of signed numbers: practice drill 2 Q1

Openmirrors

Review the basics

Averages One way to compare sets of numbers presented in tables,

graphs or charts is by working out the average

This is a technique used in statistical analysis to analyse data and to draw conclusions about the content of the data set

The three types of averages are the arithmetic mean,

Arithmetic mean The arithmetic mean (also known simply as the average) is a term you are probably familiar with

To find the mean,

simply add up all the numbers in the set and divide by the number of terms

Arithmetic mean =

Sum of values Number of values

Worked example In her aptitude test,

Emma scores 77,

What is her average (arithmetic mean) score

Arithmetic mean = 80

Worked example What is the arithmetic mean of the following set of numbers: 0,

The arithmetic mean of the set is 36 ÷ 4 = 9

Openmirrors

How to Pass Numerical Reasoning Tests

Tip: remember to include the zero as a value in your sum of the number of values

Worked example What is the value of q if the arithmetic mean of 3,

? Step 1: Rearrange the formula to help you to find the sum of values Sum of values = arithmetic mean × number of values Step 2: Now plug in the numbers Sum of values

= arithmetic mean × number of values

Sum of values

(Don’t forget to count the fourth value q in the number of values

) Sum of values = 22 Step 3: Subtract the sum of known values from the sum of values Sum of values

Answer: q = 4

The mode The mode is the number (or numbers) that appear(s) the most frequently in a set of numbers

There may be more than one mode in a given set of numbers

Openmirrors

Review the basics

Worked example What is the mode in the following set of numbers

? 21,  22,  23,  22,  22,  25,  25,  22,  21 21 appears twice

So the mode is 22 as it appears most frequently

Worked example What is the mode in the following set of numbers

So the mode numbers are 0

The median The median is the value of the middle number in a set of numbers,

when the numbers are put in ascending or descending order

Worked example What is the median in the following set of numbers

Openmirrors

How to Pass Numerical Reasoning Tests

As there are nine numbers in the set,

the fifth number in the series is the median

Worked example What is the median in the following set of numbers

Draw a line in the middle of the set: 1 0

The median of the series is the average of the two numbers on either side of the dividing line

Therefore,

the median number in the series is the arithmetic mean of 2 and 4: (2 + 4) ÷ 2 = 3

Openmirrors

Review the basics

Averages: practice drill Set a stopwatch and aim to complete the following drill in 60 seconds

What is the arithmetic mean of the following sets of numbers

What is the median of the following sets of numbers

Q10 36,

-2 Q13 0,

Openmirrors

How to Pass Numerical Reasoning Tests

Answers to Chapter 1 Multiplication tables: practice drill 1 Drill 1

Drill 2

Drill 3

Drill 4

Drill 5

Multiplication tables: practice drill 2 Drill 1

Drill 2

Drill 3

Drill 4

Drill 5

Openmirrors

Review the basics

Long multiplication: practice drill 1 Q1

Q10 4,174,236

Long multiplication: practice drill 2 Q1      162 Q2      209 Q3      252 Q4      437 Q5      494 Q6    3,587 Q7    4,121 Q8    4,576 Q9

Q10 73,225

Openmirrors

How to Pass Numerical Reasoning Tests

Long division practice: drill 1 Q1     9 Q2     7 Q3     9 Q4   13 Q5   12 Q6

Q7   85 Q8   12 Q9

Q10   32

Long division practice: drill 2 Q1   23 Q2   23 Q3

Q4   45 Q5

Q6   56 Q7   46 Q8   26 Q9   85 Q10 133

Openmirrors

Review the basics

Prime numbers: practice drill Q1

An infinite number

Q10 569

Multiples: practice drill Drill 1

Drill 2

Drill 3

Drill 4

2,3,4,6,9

2,3,4,6

2,3,4,6

2,4 [8]

2,3,6 [7]

2,4 [8]

2,3,4,6

2,4 [8]

2,4 [8]

2,4 [8]

2,4 [8]

Where the integer is also a multiple of 7 or 8,

this is indicated in the answer table with [7] or [8]

Openmirrors

How to Pass Numerical Reasoning Tests

Lowest common multiple: practice drill 1 Q1

Prime factorization = 2 × 2 × 2 × 3 Q2

Prime factorization = 2 × 2 × 3 × 3 Q3

Prime factorization = (1 × ) 3 × 5 Q4

Prime factorization = 2 × 2 × 3 × 5 Q5

Prime factorization = 2 × 2 × 2 × 7

Openmirrors

Review the basics

Prime factorization = 2 × 3 × 3 Q7

Prime factorization = (1 ×) 13 × 7 Q9

Prime factorization = 2 × 2 × 3 × 13 Q10 7 and 15 Answer = 105   7   =   1   ×   7 15   =   3   ×   5 Prime factorization = (1 ×) 3 × 5 × 7

Openmirrors

How to Pass Numerical Reasoning Tests

Lowest common multiple: practice drill 2 Q1   10 Q2   20 Q3   45 Q4   30 Q5   42 Q6   30 Q7   42 Q8

Q9   66 Q10   84

Multiplying large numbers: practice drill Q1

1 million,

6 trillion

48 billion

36 billion

26 billion

6 billion,

Openmirrors

Review the basics

Dividing large numbers: practice drill Q1

170,000

Multiplication and division of signed numbers: practice drill 1 Q1

Openmirrors

How to Pass Numerical Reasoning Tests

Multiplication and division of signed numbers: practice drill 2 Q1

Averages: practice drill Arithmetic mean:

Median:

Mode: Q11

1 4  

1 and 0

Openmirrors

CHAPTER 2

Fractions and decimals Chapter topics ●●

Terms used in this chapter

What a fraction is

Working with fractions

Fraction operations

Decimal operations

Answers to Chapter 2

Terms used in this chapter Denominator: The number below the line in a vulgar fraction

Dividend: The number to be divided

Divisor: The number by which another is divided

Equivalent fractions: Fractions with equivalent denominators and numerators

Fraction: A part of a whole number

Openmirrors

How to Pass Numerical Reasoning Tests

Fraction bar: The line that separates the numerator and denominator in a vulgar fraction

Improper fraction: A fraction in which the numerator is greater than or equal to the denominator

Lowest common denominator: The lowest common multiple of the denominators of several fractions

Lowest common multiple: The least quantity that is a multiple of two or more given values

Mixed fractions: A number consisting of an integer and a fraction

Numerator: The number above the line in a vulgar fraction

Prime factorization: The expression of a number as the product of its prime numbers

Proper fraction: A fraction less than one,

with the numerator less than the denominator

Vulgar fraction: A fraction expressed by numerator and denomi­ nator,

In Chapter 1,

you practised operations with whole numbers

In this chapter you will practise number operations on parts of numbers

The same principles apply to decimals and fractions as to whole numbers

Additionally,

there are a few extra tricks you can learn to complete these puzzles quickly and accurately

What a fraction is Proper and improper fractions A fraction is a part of a whole number,

or a value expressed as one number divided by another

For example: 1 2 2 3 7 5

Openmirrors

Part = 1 and whole = 2

Part = 2 and whole = 3

Part = 7 and whole = 5

Fractions and decimals

To write a fract

How to Perform Strong Man Stunts by Ottley R. Coulter

The Creative Fire Myths And Stories On The Cycles Of

s3 eu west 1 amazonaws oz8shu9n3i56rao How download How to Perform Strongman Stunts odf free International Money Postwar Trends and Theories djvu free download Pilot Charts of Mediterranean Mediterranean Sailing Bible odf free download The Doll Graveyard (a Hauntings novel) azw free download It's Okay to

How to Plan MAIO and HSN

Simulation of GSM Mobile Networks Planning Using ATOLL

PDF 4 5 Frequency Hoppi cosconor 4 5 20 20Frequency 20Hopping 20Parameters pdf PDF Frequency Planning Guidelines codelooker codelooker 8048frequencyplanningguidelines frequencyplanning guidelines pdf PDF Analyzing the Signal Flow and RF

How To Play Against Stronger Players- Vol 1

Defending against Speed - Kentucky Youth Soccer

usgo files pdf StrongerPlayer2 pdf Ver 1 2 jcs 23 NOV 2001 How To Play Against Stronger Players Vol 2 Illustrative Teaching Games SAKAI Michiharu Professional 8 Dan English Language usgo files pdf StrongerPlayer1 pdf Ver

How to Play Autumn Leaves -- Notated swing rhythm and shell voicings

The Beginner's Guide to Jazz Guitar - Jazz Guitar Online

PDF Autumn Leaves Jazz Piano Sheet Music Free Free Algavenicealgavenice it echlab it autumn leaves jazz piano sheet music free free pdf PDF Autumn Leaves Jazz Piano Sheet Music Free Free LIPImta1 lipi go id autumn leaves jazz piano sheet music free free

How to play bebop vol 1 - David Baker.pdf

How To Play Bebop Vol 1 - Ebook List - wqwlcjsgrw

PDF David Baker BS GSS Букинист bs gss ru David 20Baker 20 20Vol 203 20 20Techniques 20for 20Learning 20and 20Utilizing 20Bebop 20T PDF David baker how to play bebop vol 1 3 files Manual Book adm mantishost

How to play bebop vol 2 - David Baker .pdf

How To Play Bebop Vol 2 PDF - TorontoCriminalLawTeamCa

PDF Download How To Play Bebop Volume 2 PDFnew legislation securite tn how to play bebop volume 2 pdf PDF David Baker BS GSS Букинист bs gss ru David 20Baker 20 20Vol 203 20 20Techniques 20for 20Learning 20and 20Utilizing 20Bebop

How to Play From a Fake Book

How To Play From A Fake Book Keyboard Edition - APESEG

PDF How to Play from a Fake Book without Gettin' the Blues pianochord sample fake book preview chapters pdf PDF How To Play From A Fake Book Keyboard Edition Maestrus test maestrus how to play from a

How to play JAZZ BASS LINES.pdf

walking bass - MIGU MUSIC

PDF Basslines chapter Geib Musik geibmusik 2016 20asta 20presentation 20handout pdf PDF comping bass linesreloadsanear education teach bass comp pdf PDF WALKING BASSLINES How To Play Bass how to play bass wp content

How to Play Killer Blues Solos on the Saxophone

Lead Guitar Solos - Esyes

PDF How To Play Killer Blues And Rockin Sax Solos With 7 Cie4slnetcie4slnet cf how to play killer blues and rockin sax solos with 7 notes or less pdf PDF How To Play Killer Blues And Rockin Sax Solos With 7

Home back Next
<