...501 CHALLENGING LOGIC AND REASONING PROBLEMS 501 CHALLENGING LOGIC AND REASONING PROBLEMS 2nd Edition ® NEW YORK 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 Contents INTRODUCTION QUESTIONS ANSWERS vii 1 99 v Introduction his book—which can be used alone, with other logic and reasoning texts of your choice, or in combination 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...
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...Mathematics Classes 9-10 Chapter One Real Number Mathematics is originated from the process of expressing quantities in symbols or numbers. The history of numbers is as ancient as the history of human civilization. Greek Philosopher Aristotle According to the formal inauguration of mathematics occurs in the practice of mathematics by the sect of priest in ancient Egypt. So, the number based mathematics is the creation of about two thousand years before the birth of Christ. After that, moving from many nations and civilization, numbers and principles of numbers have gained an universal form at present. The mathematicians in India first introduce zero (0) and 10 based place value system for counting natural numbers, which is considered a milestone in describing numbers. Chinese and Indian mathematicians extended the idea zero, real numbers, negative number, integer and fractional numbers which the Arabian mathematicians accepted in the middle age. But the credit of expressing number through decimal fraction is awarded to the Muslim Mathematicians. Again they introduce first the irrational numbers in square root form as a solution of the quadratic equation in algebra in the 11th century. According to the historians, very near to 50 BC the Greek Philosophers also felt the necessity of irrational number for drawing geometric figures, especially for the square root of 2. In the 19th century European Mathematicians gave the real numbers a complete shape...
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