501 Quantitative Comparison Questions

1 501. Quantitative Comparison Questions 501. Quantitative Comparison Questions NEW YORK. The LearningExpress Skill Builder in Focus Writing Team is com- prised of experts in test preparation, as well as educators and teachers who specialize in language arts and math. LearningExpress Skill Builder in Focus Writing Team Lara Bohlke Middle School Math Teacher, Grade 8. Dodd Middle School Cheshire, Connecticut Brigit Dermott Project Editor English Tutor, New York Cares New York, New York Sandy Gade Project Editor LearningExpress New York, New York Melinda Grove Adjunct Professor, Quinnipiac University and Naugatuck Valley Community College Middle School Math Teacher, Grade 8. Dodd Middle School Cheshire, Connecticut Noah Kravitz Educational Specialist New York, New York Kerry McLean Project Editor Math Tutor Shirley, New York Meg Moyer High School Math Teacher Vestal Central High School Vestal, New York (continued on next page).

2 William Recco Middle School Math Teacher, Grade 8. New York Shoreham/Wading River School District Math Tutor St. James, New York Colleen Schultz Middle School Math Teacher, Grade 8. Vestal Central School District Math Tutor Vestal, New York Contents Introduction ix 1 Arithmetic Questions 1. Answers and Explanations 11. 2 Algebra Questions 25. Answers and Explanations 42. 3 Geometry Questions 59. Answers and Explanations 85. 4 Data Analysis Questions 113. Answers and Explanations 129. Introduction Welcome to 501 quantitative comparison questions ! This book is designed to help you prepare for a specialized math section of a select few of the most important assessment exams. By completing the exer- cises in this book, you will also increase your math knowledge and re ne your logic and analytical skills.

3 Key academic aptitude tests produced by the Educational Testing Service (ETS) for the College Board the Preliminary Scholastic Aptitude Test/National Merit Scholarship Qualifying Test (PSAT/NMSQT) exam, the Scholastic Aptitude Test (SAT) assessment, and the Graduate Records Examination (GRE) test include a Quantitative Comparison section within the math portion of the exam, so for college-bound students and many graduate students, mastering this question type is essential for getting into their school of choice. What makes this book different than other math practice books? It's sim- ple this math practice book contains only Questions that ask you which column contains the item of greater value, if the values are the same, or if the value cannot be determined by the information given.

4 Gaining famil- iarity with this specialized question type is a proven technique for increas- ing test scores. ix 501 quantitative comparison questions In order to solve a Quantitative Comparison problem, you must rst com- pare the quantities in the two columns and then decide whether: one quantity is greater than the other the two quantities are equal the relationship cannot be determined from the information given On the PSAT exam, SAT assessment, or GRE test, your answer always should be: a if the value in Column A is greater b if the value in Column B is greater c if the two values are equal, or d if the relationship cannot be determined from the information given in the question Math Topics The book is divided into four content sections. Math topics included in this volume are arithmetic, algebra, geometry, and data analysis.

5 These cate- gories are further divided to include the following concepts: Arithmetic Absolute Value Decimals Exponents and Square Roots Fractions Integers Ordering and the Real Number Line Percent Ratio Algebra Applications Coordinate Geometry Inequalities Operations with Algebraic Expressions Rules of Exponents x 501 quantitative comparison questions Solving Linear Equations Solving Quadratic Equations in One Variable Translating Words into Algebraic Expressions Geometry Circles Lines and Angles Polygons Quadrilaterals Three-Dimensional Figures Triangles Data Analysis Counting Sequences Data Representation and Interpretation Frequency Distributions Measures of Central Tendency Measures of Dispersion Probability A Note about the PSAT/NMSQT Exam On the PSAT/NMSQT exam, there are two 25-minute math sections, for a total of 40 Questions .

6 Of these Questions , 12 are Quantitative comparisons. This math section requires a basic knowledge of arithmetic, algebra, and geometry, so practicing with this book is ideal, as you will improve your PSAT/NMSQT exam score and start getting familiar with the SAT exam that you will encounter in the next school year. A Note about the SAT Assessment On the SAT exam, there are two 30-minute math sections, for a total of 60. Questions . Of these Questions , 30 are Quantitative Comparison Questions . (There is also a 15-minute section of 5-choice math Questions .) Math concepts tested include arithmetic, algebra, geometry, and other topics, such as log- ical reasoning, probability, and counting. This book focuses on each of xi 501 quantitative comparison questions these areas of math so that you can get the targeted practice necessary to ace the Quantitative Comparison sections in the SAT exam.

7 In addition, each SAT exam contains a 30-minute experimental verbal or math section, used for equating, that does not count toward your score, so there may be 15 more Quantitative comparisons on your exam (though you will only be scored for 30 of the potential 45 Questions ). Since you don't know which section is experimental, it's best to be prepared to answer many of these question types. You are allowed to use a calculator to answer math Questions on the exam, if you wish. A Note about the GRE Test You will be given 45 minutes to complete the 28 Quantitative Comparison Questions on the computer-based GRE test. However, there are 60 quan- titative Comparison Questions on the paper-based exam. Overall, the per- centage of Questions on the GRE test that are Quantitative Comparison are the same for both versions of the test: approximately 30% of both tests are Quantitative Comparison Questions .

8 The content areas included in the quan- titative sections of the test are arithmetic, algebra, geometry, and data analy- sis. These are math concepts usually studied in high school, and this book speci cally targets these areas. Calculators are not permitted. Questions , Questions , Questions You have just read about the math topics covered in this book. To mimic a real test environment, math concepts are mixed within each section. For example, in the arithmetic section, you may nd a question or two on expo- nents, then three Questions on square roots, followed by three Questions involving decimals and fractions. Then the next question is about square roots. This way, you are preparing for any type of arithmetic question that you could encounter on the real exam. This helps you to be prepared for whatever Questions the College Board/ETS throws your way.

9 Each chap- ter begins with an information and instruction overview describing the mathematical concepts covered in that particular section. Then you are pre- sented with a variety of problems awaiting your solutions. If you are practicing for the PSAT assessment or SAT exam, you should have a calculator on hand as you work through some of the chapters, xii 501 quantitative comparison questions because calculators are allowed in the testing center. Even if you don't use it to arrive at solutions, it's a good idea to use it to check your calculations. This goes for everyone even GRE test-takers. If you have dif culty fac- toring numbers, a multiplication chart may help you. And if you are unfa- miliar with prime numbers, use a list of them so you won't waste time trying to factor numbers that can't be factored.

10 Don't forget to keep lots of scrap paper on hand for working out complex problems. Practice Makes Perfect Because this book is designed for many levels of test takers, you may nd that some of the more advanced Questions are beyond your ability. If you are using this book to study for the PSAT assessment or SAT exam, there is a chance that you may get a few of the toughest Questions wrong. Don't worry! If you are getting most of the Questions correct, you are probably in good shape for your test. However, if you are studying for the GRE test, the full range of Questions presented is appropriate for your level. The Questions in this book can help you prepare for your test in many ways. First, completing these practice exercises will make you familiar with the question format.