i TEST YOUR NUMERICAL APTITUDE ii This page intentionally left blank iii TEST YOUR NUMERICAL APTITUDE How to assess your numeracy skills and plan your career JIM BARRETT London and Philadelphia iv 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, however caused. No responsibility for loss or damage occasioned to any person acting, or refraining from action, as a result of the material in this publication can be accepted by the editor, the publisher or the author. First published in Great Britain and the United States in 2007 by Kogan Page Limited Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of repro- graphic 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 525 South 4th Street, #241 London N1 9JN Philadelphia PA 19147 United Kingdom USA www.kogan-page.co.uk © Jim Barrett, 2007 The right of Jim Barrett to be identified as the author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. ISBN 978 0 7494 5064 9 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 Barrett, James. Test your numerical aptitude / Jim Barrett. p. cm. Includes bibliographical references. ISBN-13: 978-0-7494-5064-9 ISBN-10: 0-7494-5064-9 1. Numeracy--Problems, exercises, etc. 2. Ability--Testing. I. Title. QA141.B34 2007 513.076--dc22 2007022036 Typeset by Saxon Graphics Ltd, Derby Printed and bound in Great Britain by Creative Print and Design (Wales), Ebbw Vale v Contents Introduction 1 Part 1 Number tutor 7 Number usage 8 Applying numbers 16 Part 2 Applied tests 31 Test 1: Number usage 31 Test 2: Proportion 35 Test 3: Money 39 Test 4: Graphs and tables 43 Test 5: Space 50 Test 6: Accuracy 58 Test 7: Multiple choice 69 Relative strength of applied test scores 75 Career guidance 75 Part 3 Abstract tests 79 Test 8: Deduction 79 Test 9: Concept formation 86 Test 10: Sequential logic 105 Test 11: Construct analysis 110 Test 12: Power synthesis 128 vi Contents Comparison between applied and abstract tests 133 Career guidance 135 Level of scores and IQ 137 Part 4 Numerical motivation test 139 Test 13: Numerical motivation test 139 Motivation chart 145 Interpreting your results 146 Career guidance 147 Part 5 Work style personality test 153 Test 14: Work style personality test 153 Interpreting your results 157 Understanding your personality style 159 The 16 styles 161 Your contribution to an organization 162 Your contribution to the people you work with 163 Your possible weaknesses 164 Matching your personal style to a career 165 Careers list 169 Further reading 177 1 Introduction It is surprising how many people, including those who are highly intelligent and well educated, even to degree and professional level, suffer from apprehension about numerical tests. All too often, lack of confidence, not aptitude, is the reason for their failure pass a test or an exam, obtain a job or be selected for a training course. Because people are unsure of what may be expected of them they may underperform on tests and assessments, even though they have the innate potential to do well and make appropriate career progression. Unfortunately, they may even hold back from applying for a job or course in the first place. What a waste of talent! At the same time, the requirement to work with some form of numbers at work is growing. And there are always more oppor- tunities for people who are willing to use their numerical aptitude. It is strange that as demand for numerical aptitude from employers is increasing, the supply, or aptitude, does not appear to keep up with it. For this reason, many employers, as well as universities, do not trust exam results and may prefer to search out the talent themselves. Thus, more organizations are setting their own tests of key aptitudes, numbers being one of the high priority areas. Yet, numbers have not changed: although numbers 2 Test your numerical aptitude may be used in different ways as new patterns of work are created, the basic ways of using numbers have always been the same. This book intends to reassure you of the ways numbers are used and applied, and suggest how you can succeed with your underlying aptitude for numbers. When you know what you are capable of and what to expect, there is little need for fear; it makes sense to provide yourself with the means to take advantage of the opportunities that are available to you. I know of professional people who have worked through the numerical tests in my earlier books as preparation before an assessment for a new job or because a new role demanded greater familiarity and use of numbers. This book is distinct because it is designed to concentrate many different types of numerical tests in a single volume. It intends to provide comprehensive coverage of what can be expected in many real life working, exam and test situations. Additionally, there are exercises that investigate your personality and motivation, thus enabling you to think how your particular type of numerical aptitude might suit different careers. This book looks at numerical aptitude, that is, the underlying talent a person possesses in order to understand and use numbers. It does not look at acquired skills, for example the level of ability that is the product of educational courses at school or college in mathematics, business studies, economics, accounts or computer science. However, if a person has the underlying ability, it may help to point them in one of these directions or even ‘brush them up’ in areas in which they feel they may be lacking. This book makes every attempt to be ‘fair’ by trying to establish a ‘level playing field’ for everybody who takes each test. This is important because it is true that familiarity in working with numbers will allow someone to develop specific numerical skills. But, to be ‘fair’ everyone should have an equal chance at the start. Therefore, Part 1 is a preparation containing plenty of examples and explanation in order that there will be no unex- pected or surprising problem that confronts you. Parts 1 and 2 Introduction 3 present you with a range of tests that are similar to those commonly used by organizations for aptitude testing. This book hopes to reassure you that there will be no test about which you say, ‘I just couldn’t do it; it was too difficult’, or, ‘It caught me out’, so that you may in the future be confident about numerical aptitude tests. Timed and power tests Of course, most of the tests are deliberately designed to get harder as you proceed, but all the skills required to solve the problems are provided before you start. There may well be a limit to what you can do in the time allowed by each test. It is essential to know what your ‘timed limit’ is because this gives an indication of level by which there can be some basis of comparison with everybody else. Your limit may also have another purpose in suggesting where you may need to work harder in your course of study, before an assessment or in your work. Naturally, people work at different rates and in different ways on the same task. Therefore, a timed test may not fully reveal a person’s top limit of aptitude since they may not have had suffi- cient time to get to the harder problems and thus demonstrate the full range of their proficiency. Speed is not necessarily everything: some people spend more time checking through their answer than others; some people are relating the problem they are working on to other problems or possibilities, an imaginative process not always measured by the test. Yet aspects such as these may be important in the ‘real world of work’ in which their numerical aptitudes are applied, if not in the test situation itself. Therefore, the ‘power’ test looks at what a person is capable of doing where the timed element is taken out. This ensures that you encounter the full range of problems at all levels of difficulty in the type of aptitude being tested. The basis of comparison is with what you are capable of doing as opposed to how quickly you are 4 Test your numerical aptitude capable of doing it. Achieving above average marks on either ‘time’ or ‘power’ indicates possible career opportunity. When taking each test it is possible to take it as a timed or power test, or both, by noting your progress after the timed period, then going on to complete the entire test. Making sense of the aptitude tests There are two questions: 1) What does my score mean? and 2) What can my score guide me towards? Firstly, at the end of each test your score or scores can be compared with an assumed average. This compares you with everyone else or ‘the general population’, as it is known statisti- cally. This allows you some insight as to whether you have a talent greater than that of most other people. Admittedly, the average is no more than a guideline, since it does not reflect any real statistical or measured average in relation to a specific group. But the more you are above average, the more likely it is that you have an aptitude that has a special value because it is compara- tively rare and therefore provides you with more career oppor- tunity than most. Then, your scores on each test can be compared to indicate where your strengths probably lie. These scores can also be related to an intelligence quotient (IQ) scale, which is a quick way to compare your aptitude with a level at which people achieve awards, such as degrees or professional qualifications, or work in senior jobs in which it is essential to possess some form of numerical aptitude. With regard to the answer to the second question, there are also some suggestions as to the type of work that proficiency on the test might lead to. These are not intended to be specific or exclusive simply because, in the real world, activities can assume a different character due to the manner of working or the nature of the work undertaken in an organization. It is not always