501 CHALLENGING LOGIC AND REASONING PROBLEMS N E W Y O R K 501 CHALLENGING LOGIC AND REASONING PROBLEMS 2nd Edition ® Copyright © 2005 LearningExpress, LLC. All rights reserved under International and Pan-American Copyright Conventions. Published in the United States by LearningExpress, LLC, New York. Library of Congress Cataloging-in-Publication Data: 501 challenging logic & reasoning problems. p. cm.—(LearningExpress skill builders practice) Includes bibliographical references. ISBN 1-57685-534-1 1. Logic—Problems, exercises, etc. 2. Reasoning—Problems, exercises, etc. 3. Critical thinking—Problems, exercises, etc. I. LearningExpress (Organization) II. Title: 501 challenging logic and reasoning problems. III. Series. BC108.A15 2006 160'.76—dc22 2005057953 Printed in the United States of America 9 8 7 6 5 4 3 2 1 Second Edition ISBN 1-57685-534-1 For information or to place an order, contact LearningExpress at: 55 Broadway 8th Floor New York, NY 10006 Or visit us at: www.learnatest.com INTRODUCTION vii QUESTIONS 1 ANSWERS 99 Contents v T his book—which can be used alone, with other logic and reasoning texts of your choice, or in com- bination with LearningExpress’s Reasoning Skills Success in 20 Minutes a Day—will give you practice dealing with the types of multiple-choice questions that appear on standardized tests assessing logic, reasoning, judgment, and critical thinking. It is designed to be used by individuals working on their own and by teachers or tutors helping students learn, review, or practice basic logic and reasoning skills. Practice on 501 logic and reasoning questions will go a long way in alleviating test anxiety, too! Maybe you’re one of the millions of people who, as students in elementary or high school, never understood the necessity of having to read opinion essays and draw conclusions from the writer’s argument. Or maybe you never understood why you had to work through all those verbal analogies or number series questions. Maybe you were one of those people who could never see a “plan of attack”when working through logic games or critical think- ing puzzles. Or perhaps you could never see a connection between everyday life and analyzing evidence from a series of tedious reading passages. If you fit into one of these groups, this book is for you. First, know you are not alone. It is true that some people relate more easily than do others to number series questions, verbal analogies, logic games, and reading passages that present an argument. And that’s okay; we all have unique talents. Still, it’s a fact that for most jobs today, critical thinking skills—including analytical and log- ical reasoning—are essential. The good news is that these skills can be developed with practice. Learn by doing. It’s an old lesson, tried and true. And it’s the tool this book is designed to give you. The 501 logic and reasoning questions that follow will provide you with lots of practice. As you work through each set of questions, you’ll be gaining a solid understanding of basic analytical and logical reasoning skills—all without mem- orizing! The purpose of this book is to help you improve your critical thinking through encouragement, no frustration. Introduction vii � An Overview 501 Challenging Logic and Reasoning Problems is divided into 37 sets of questions: Sets 1–4: Number Series Sets 5–6: Letter and Symbol Series Sets 7–8: Verbal Classification Sets 9–11: Essential Part Sets 12–17: Analogies Sets 18–19: Artificial Language Set 20: Matching Definitions Set 21: Making Judgments Set 22: Verbal Reasoning Sets 23–27: Logic Problems Sets 28–31: Logic Games Sets 32–37: Analyzing Arguments Each set contains between 5–20 questions, depending on their length and difficulty. The book is specifically organized to help you build confidence as you further develop your logic and reasoning skills. 501 Challenging Logic and Reasoning Problems begins with basic number and letter series questions, and then moves on to verbal classification, artificial language, and matching definition items. The last sets contain logic problems, logic games, and logical reasoning questions. By the time you reach the last question, you’ll feel confident that you’ve improved your critical thinking and logical reasoning abilities. � How to Use This Book Whether you’re working alone or helping someone brush up his or her critical thinking and reasoning skills, this book will give you the opportunity to prac- tice, practice, practice! Working on Your Own If you are working alone to improve your logic skills or prepare for a test in connection with a job or school, you will probably want to use this book in combination with its companion text, Reasoning Skills Success in 20 Minutes a Day, 2nd Edition, or with some other basic reasoning skills text. If you’re fairly sure of your basic logic and reasoning abilities, however, you can use 501 Challenging Logic and Reasoning Problems by itself. Use the answer key at the end of the book not only to find out if you got the right answer, but also to learn how to tackle similar kinds of questions next time. Every answer is explained. Make sure you under- stand the explanations—usually by going back to the questions—before moving on to the next set. Tutoring Others This book will work well in combination with almost any analytical reasoning or logic text. You will proba- bly find it most helpful to give students a brief lesson in the particular operation they’ll be learning— number series, verbal classification, artificial language, logic problems, analyzing arguments—and then have them spend the remainder of the session actually answering the questions in the sets. You will want to stress the importance of learning by doing and of checking their answers and reading the explanations carefully. Make sure they understand a particular set of questions before you assign the next one. � Additional Resources Answering the 501 logic and reasoning questions in this book will give you lots of practice. Another way to improve your reasoning ability is to read and study on your own and devise your own unique methods of attacking logic problems. Following is a list of logic and reasoning books you may want to buy or take out of the library: –INTRODUCTION– viii REASONING Reasoning Skills Success in 20 Minutes a Day (2nd Edition) by LearningExpress Critical Reasoning: A Practical Introduction by Anne Thomson (Routledge) Attacking Faulty Reasoning: A Practical Guide to Fallacy-Free Arguments by T. Edward Damer (Wadsworth) Thinking Critically: Techniques for Logical Rea- soning by James H. Kiersky and Nicholas J. Caste (Wadsworth) LOGIC Essential Logic: Basic Reasoning Skills for the Twenty-First Century by Ronald C. Pine (Oxford University Press) Increase Your Puzzle IQ: Tips and Tricks for Building Your Logic Power by Marcel Danesi (Wiley) Amazing Logic Puzzles by Norman D. Willis (Sterling) Challenging Logic Puzzles by Barry R. Clarke (Sterling) CRITICAL THINKING Critical Thinking by Alec Fisher (Cambridge University Press) Brainplay: Challenging Puzzles & Thinking Games by Tom Werneck (Sterling) Challenging Critical Thinking Puzzles by Michael A. Dispezio and Myron Miller (Sterling) Becoming a Critical Thinker: A User-Friendly Manual by Sherry Diestler (Prentice Hall) ANALOGIES 501 Word Analogy Questions by Learning- Express Analogies for Beginners by Lynne Chatham (Dandy Lion Publications) Cracking the MAT (3rd Edition) by Marcia Lerner (Princeton Review) –INTRODUCTION– ix R eady to test your mental abilities? Your 501 challenging logic and reasoning problems begin on the next page. They’re grouped together in sets of 5–20 questions with a common theme. You can work through the sets in order or jump around, whichever you choose. When you finish a set, check your answers beginning on page 99. Questions 1 � Set 1 (Answers begin on page 99.) Start off with these simple series of numbers. Number series questions measure your ability to reason without words. To answer these questions, you must determine the pattern of the numbers in each series before you will be able to choose which number comes next. These questions involve only simple arithmetic. Although most number series items progress by adding or sub- tracting, some questions involve simple multiplication or division. In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much? 1. Look at this series: 2, 4, 6, 8, 10, . . . What num- ber should come next? a. 11 b. 12 c. 13 d. 14 2. Look at this series: 58, 52, 46, 40, 34, . . . What number should come next? a. 26 b. 28 c. 30 d. 32 3. Look at this series: 40, 40, 47, 47, 54, . . . What number should come next? a. 40 b. 44 c. 54 d. 61 4. Look at this series: 544, 509, 474, 439, . . . What number should come next? a. 404 b. 414 c. 420 d. 445 5. Look at this series: 201, 202, 204, 207, . . . What number should come next? a. 205 b. 208 c. 210 d. 211 6. Look at this series: 8, 22, 8, 28, 8, . . . What number should come next? a. 9 b. 29 c. 32 d. 34 7. Look at this series: 80, 10, 70, 15, 60, . . . What number should come next? a. 20 b. 25 c. 30 d. 50 8. Look at this series: 36, 34, 30, 28, 24, . . . What number should come next? a. 20 b. 22 c. 23 d. 26 9. Look at this series: 22, 21, 23, 22, 24, 23, . . . What number should come next? a. 22 b. 24 c. 25 d. 26 –QUESTIONS– 2 10. Look at this series: 3, 4, 7, 8, 11, 12, . . . What number should come next? a. 7 b. 10 c. 14 d. 15 11. Look at this series: 31, 29, 24, 22, 17, . . . What number should come next? a. 15 b. 14 c. 13 d. 12 12. Look at this series: 21, 9, 21, 11, 21, 13, . . . What number should come next? a. 14 b. 15 c. 21 d. 23 13. Look at this series: 53, 53, 40, 40, 27, 27, . . . What number should come next? a. 12 b. 14 c. 27 d. 53 14. Look at this series: 2, 6, 18, 54, . . . What num- ber should come next? a. 108 b. 148 c. 162 d. 216 15. Look at this series: 1,000, 200, 40, . . . What number should come next? a. 8 b. 10 c. 15 d. 20 16. Look at this series: 7, 10, 8, 11, 9, 12, . . . What number should come next? a. 7 b. 10 c. 12 d. 13 17. Look at this series: 14, 28, 20, 40, 32, 64, . . . What number should come next? a. 52 b. 56 c. 96 d. 128 18. Look at this series: 1.5, 2.3, 3.1, 3.9, . . . What number should come next? a. 4.2 b. 4.4 c. 4.7 d. 5.1 19. Look at this series: 5.2, 4.8, 4.4, 4, . . . What number should come next? a. 3 b. 3.3 c. 3.5 d. 3.6 20. Look at this series: 2, 1, �1 2 �, �1 4 �, . . . What number should come next? a. �1 3 � b. �1 8 � c. �2 8 � d. �1 1 6� –QUESTIONS– 3 � Set 2 (Answers begin on page 101.) This set contains additional, and sometimes more difficult, number series questions. Again, each ques- tion has a definite pattern. Some of the number series may be interrupted by a particular number that appears periodically in the pattern. For example, in the series 14, 16, 32, 18, 20, 32, 22, 24, 32, the number 32 appears as every third number. Sometimes, the pattern contains two alternating series. For example, in the series 1, 5, 3, 7, 5, 9, 7, the pattern is add 4, sub- tract 2, add 4, subtract 2, and so on. Look carefully for the pattern, and then choose which pair of numbers comes next. Note also that you will be choosing from five options instead of four. 21. 84 78 72 66 60 54 48 a. 44 34 b. 42 36 c. 42 32 d. 40 34 e. 38 32 22. 3 8 13 18 23 28 33 a. 39 44 b. 38 44 c. 38 43 d. 37 42 e. 33 38 23. 20 20 17 17 14 14 11 a. 8 8 b. 11 11 c. 11 14 d. 8 9 e. 11 8 24. 18 21 25 18 29 33 18 a. 43 18 b. 41 44 c. 37 18 d. 37 41 e. 38 41 25. 9 11 33 13 15 33 17 a. 19 33 b. 33 35 c. 33 19 d. 15 33 e. 19 21 26. 2 8 14 20 26 32 38 a. 2 46 b. 44 50 c. 42 48 d. 40 42 e. 32 26 27. 28 25 5 21 18 5 14 a. 11 5 b. 10 7 c. 11 8 d. 5 10 e. 10 5 28. 9 12 11 14 13 16 15 a. 14 13 b. 18 21 c. 14 17 d. 12 13 e. 18 17 29. 75 65 85 55 45 85 35 a. 25 15 b. 25 85 c. 35 25 d. 85 35 e. 25 75 –QUESTIONS– 4 30. 1 10 7 20 13 30 19 a. 26 40 b. 29 36 c. 40 25 d. 25 31 e. 40 50 31. 10 20 25 35 40 50 55 a. 70 65 b. 60 70 c. 60 75 d. 60 65 e. 65 70 32. 40 40 31 31 22 22 13 a. 13 4 b. 13 5 c. 4 13 d. 9 4 e. 4 4 33. 17 17 34 20 20 31 23 a. 26 23 b. 34 20 c. 23 33 d. 27 28 e. 23 28 34. 2 3 4 5 6 4 8 a. 9 10 b. 4 8 c. 10 4 d. 9 4 e. 8 9 35. 61 57 50 61 43 36 61 a. 29 61 b. 27 20 c. 31 61 d. 22 15 e. 29 22 36. 9 16 23 30 37 44 51 a. 59 66 b. 56 62 c. 58 66 d. 58 65 e. 54 61 37. 8 22 12 16 22 20 24 a. 28 32 b. 28 22 c. 22 28 d. 32 36 e. 22 26 38. 6 20 8 14 10 8 12 a. 14 10 b. 2 18 c. 4 12 d. 2 14 e. 14 14 39. 11 16 21 26 31 36 41 a. 47 52 b. 46 52 c. 45 49 d. 46 51 e. 46 52 40. 8 11 21 15 18 21 22 a. 25 18 b. 25 21 c. 25 29 d. 24 21 e. 22 26 –QUESTIONS– 5