Gruber's Complete PSAT/NMSQT Guide 2015

561 Pages·2016·6.95 MB·English

by  Gruber Gary R.

Gruber’s
c o m p l e t e
PSAT/
NMSQT*
5th edition
GuIDe 2015
*
PSAT® and NMSQT® are registered trademarks of the College Entrance Examination Board
and National Merit Scholarship Corporation. Neither the College Entrance Examination
Board nor NMSC are associated with this book, nor do they endorse it.
G r. G , P D
ary ruber h
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Copyright © 2014 by Gary R. Gruber
Cover and internal design © 2014 by Sourcebooks, Inc.
Sourcebooks and the colophon are registered trademarks of Sourcebooks, Inc.
All rights reserved. No part of this book may be reproduced in any form or by any electronic or mechanical means
including information storage and retrieval systems—except in the case of brief quotations embodied in critical
articles or reviews—without permission in writing from its publisher, Sourcebooks, Inc.
This publication is designed to provide accurate and authoritative information in regard to the subject matter covered.
It is sold with the understanding that the publisher is not engaged in rendering legal, accounting, or other professional
service. If legal advice or other expert assistance is required, the services of a competent professional person should
be sought.—From a Declaration of Principles Jointly Adopted by a Committee of the American Bar Association and a
Committee of Publishers and Associations
All brand names and product names used in this book are trademarks, registered trademarks, or trade names of their
respective holders. Sourcebooks, Inc., is not associated with any product or vendor in this book.
Published by Sourcebooks, Inc.
P.O. Box 4410, Naperville, Illinois 60567-4410
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Library of Congress Cataloging-in-Publication Data is on file with the publisher.
Printed and bound in the United States of America.
DR 10 9 8 7 6 5 4 3 2 1
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Recent and Forthcoming Study Aids from
Dr. Gary Gruber Include
Gruber’s Complete SAT Guide 2015
Gruber’s Complete ACT Guide 2015
Gruber’s Complete GRE Guide 2015
Gruber’s SAT 2400
Gruber’s Complete SAT Math Workbook
Gruber’s Complete SAT Critical Reading Workbook
Gruber’s Complete SAT Writing Workbook
Gruber’s SAT Word Master
Gruber’s Essential Guide to Test Taking: Grades 3–5
Gruber’s Essential Guide to Test Taking: Grades 6–9
www.collegecountdown.com
www.sourcebooks.com
www.drgarygruber.com
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v
Welcome to Gruber’s Complete
PSAT/NMSQT Guide 2015
The PSAT is great practice for the SAT, which contains the same type of questions. You can
also compete for a National Merit Scholarship if you get really good scores on the PSAT. In
fact, there is a unique test in this book that will tell you if you have a good chance of qualifying
for the scholarship! But—please—make sure that after you take the PSAT, you get your exam
back with your answers. You can obtain the test about two months after you take it. Once you
get the test back, you can review it and make sure you used the strategies and other material
in this book. If you’re taking the SAT the year after you have taken the PSAT, get Gruber’s
Complete SAT Guide for complete preparation for the SAT. By using my Complete SAT Guide,
you’ll reinforce your knowledge of all the strategies and skills you learned from this PSAT
book, and you’ll be completely prepared for the SAT.
I want to help you to look at problems and questions in such a way that you will know
how to extract the important thing that will lead you to the answer—without any panic or
brain-racking. The material in this book should help you develop a passion for problem solving
so that you will find the test interesting, as if you were looking at puzzles rather than trying
to figure out the answers to problems you couldn’t care less about. After you learn and use
the material in this book, the hard problems should become a lot easier and the less difficult
problems should become really easy.
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vi
Important Note About This
Book and Its Author
This book is the most up-to-date and complete book on the current PSAT. Every exam is
patterned after the PSAT, and all the strategies and techniques deal with the PSAT. This PSAT
prep book incorporates all the Gruber Critical-Thinking Strategies.
This book was written by Dr. Gary Gruber, the leading authority on standardized tests
such as the SAT, PSAT, and ACT, who knows more than anyone else in the test-prep market
exactly what is being tested in the PSAT. In fact, the procedures to answer the PSAT questions
rely more heavily on the Gruber Critical-Thinking Strategies than ever before, and this is the
only book that has the exact thinking strategies you need to use to maximize your PSAT score.
Gruber’s SAT books are used by the nation’s school districts more than any other books.
Dr. Gruber has published more than 35 books with major publishers on test-taking and
critical-thinking methods, with more than 7 million copies sold. He has also authored more
than 1,000 articles on his work in scholarly journals and nationally syndicated newspapers,
has appeared on numerous television and radio shows, and has been interviewed in hundreds
of magazines and newspapers. He has developed major programs for school districts and for
city and state educational agencies for improving and restructuring curriculum, increasing
learning ability and test scores, increasing motivation and developing a “passion” for learning
and problem solving, and decreasing the student dropout rate. For example, PBS (Public
Broadcasting System) chose Dr. Gruber to train the nation’s teachers on how to prepare
students for the PSAT and SAT through a national satellite teleconference and videotape. His
results have been lauded by people throughout the country from all walks of life.
Dr. Gruber is recognized nationally as the leading expert on standardized tests. It is said
that no one in the nation is better at assessing the thinking patterns of how a person answers
questions and providing the mechanism to improve faulty thinking approaches. Gruber’s
unique methods have been and are being used by PBS, by the nation’s learning centers,
by international encyclopedias, by school districts throughout the country, in homes and
workplaces across the nation, and by a host of other entities.
His goal and mission is to get people’s potential realized and the nation impassioned with
learning and problem solving so that they don’t merely try to get a fast uncritical answer, but
actually enjoy and look forward to solving the problem and learning.
For more information on Gruber courses and additional Gruber products, visit:
www.drgarygruber.com.
Important: Many books do not reflect the current PSAT questions. Don’t practice with ques-
tions that misrepresent the actual questions on the PSAT. For example, the math questions
created by the test makers are oriented to allow someone to solve many problems without a
calculator as fast as he or she could with one, and some can be solved faster without a calcu-
lator. This book reflects the PSAT more accurately than any other commercial book, and the
strategies contained in it are exactly those needed for taking the PSAT. It is said that only Dr.
Gruber has the expertise and ability to reflect the exam far more closely than any competitor!
Don’t trust your future with less than the best material.
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vii
The Author Has Something
Important to Tell You
About How to Raise
Your PSAT Score
What Are Critical-Thinking Skills?
First of all, I believe that intelligence can be taught. Intelligence, simply defined, is the aptitude
or ability to reason things out. I am convinced that you can learn to think logically and figure
things out better and faster, particularly in regard to PSAT Math and Verbal problems. But
someone must give you the tools. Let us call these tools strategies. And that’s what Critical-
Thinking Skills are all about—strategies.
Learn the Strategies to Get More Points
The Critical-Thinking Skills (beginning on page 41) will sharpen your reasoning ability so that
you can increase your score dramatically on each part of the PSAT.
These Critical-Thinking Skills—5 General Strategies, 19 Math Strategies, and 13 Critical
Reading Strategies—course right through this book. The Explanatory Answers for the 3
Practice Tests in the book direct you to those strategies that may be used to answer specific
types of PSAT questions. The strategies in Part 3 of this book are usable for more than 90
percent of the questions that will appear on the PSAT. Each additional correct answer gives
you approximately 1 point. It is obvious, then, that your learning and using the 37 easy-to-
understand strategies in this book will very likely raise your PSAT score substantially.
Are the Practice Tests in This Book Like
an Actual PSAT?
If you compare any one of the 3 Practice Tests in this book with an actual PSAT, you will find
the book test very much like the actual test in regard to format, question types, and level of
difficulty. Compare our book tests with any one of the official PSAT tests.
Building Your Vocabulary Can Make a
Big Difference on Your Test
Although antonyms no longer appear on the PSAT, Vocabulary will still be tested, especially on
Sentence Completions and Reading Comprehension. This book includes three vital sections to
build your vocabulary:
1. The Vocabulary Strategies, page 105
2. The Hot Prefixes and Roots, page 108
3. The Most Important/Frequently Used PSAT Words, page 116
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viii  •  Gruber’S cOMPLeTe PSAT/NMSQT GuIDe 2015
Study the Hot Prefixes and Roots
We have developed a list of hot roots and prefixes that can help you determine the meaning
of more than 110,000 words. Learning all of them will increase your vocabulary immensely.
Study the Most Important/Frequently used 
PSAT Words
We have developed a list of the most frequently used words and their opposites related to
specific categories for easy memorization. Study these words.
Study the Mini-Math Refresher
If you believe you are weak in basic math skills, study the Mini-Math Refresher. The material
in this section is keyed to the Complete Math Refresher section for more thorough instruction.
Take the 101 Most Important Math Questions Test
To determine your weak basic math skills areas, take the 101 Most Important Math Questions
Test and look at the solutions to the questions. The questions are keyed to the Complete Math
Refresher so you can further brush up on your weak areas by referring to those pages in the
Complete Math Refresher that are relevant for any questions you missed.
The explanatory Answers to Questions Are Keyed to 
Specific Strategies and Basic Skills
The Explanatory Answers in this book are far from skimpy—unlike those of other PSAT
books. Our detailed answers will direct you to the strategy that will help you arrive at a correct
answer quickly. In addition, the Math solutions in the book refer directly to the Complete Math
Refresher section, particularly useful in case your Math skills are rusty.
Lift That PSAT Score
By using the material in this book—that is, by taking the tests, learning the specific strate-
gies, and refreshing your basic skills, as described above—you should increase your PSAT
score substantially.
—Gary Gruber
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Contents
INTrODucTION  xv
Important Facts About the PSAT / xvi A 4-Hour Study Program for the PSAT / xxix
The Inside Track on How PSAT Questions Are Longer-Range Study Program and Helpful Steps for
Developed and How They Vary from Test Using This Book / xxx
to Test / xxiii
Format of the PSAT / xxxi
What Are Critical-Thinking Skills? / xxiv
Multi-Level Approaches to the Solution of
Problems / xxvi
PArT 1
DO YOu HAVe A GOOD cHANce OF WINNING 
A NATIONAL MerIT ScHOLArSHIP?  1
Critical Reading / 2 Answers / 6
Math / 4 Scoring / 7
Writing Skills / 5 Explanatory Answers for the National Merit
Scholarship Diagnostic Test / 8
PArT 2
THe 101 MOST IMPOrTANT MATH QueSTIONS
YOu NeeD TO KNOW HOW TO SOLVe  13
101 Math Questions Answer Sheet / 14 101 Math Questions: Answers / 28
101 Math Questions Test / 16 Basic Skills Math Diagnosis / 30
101 Math Questions: Answers, Diagnoses, Solutions, Solutions, Generalizations, and Rules / 31
Generalizations, and Rules / 27
PART 3
STrATeGY SecTION  41
5 General Strategies / 42 Practice with Grids / 47
32 Easy-to-Learn Strategies / 44 Answers / 48
How to Learn the Strategies / 44 Use of a Calculator in the Grid-Type Question / 49
Important Note on the Allowed Use of Calculators on 19 Math Strategies / 51
the PSAT / 44
Math Strategy 1: Cancel Quantities to Make the
Important Note on Math Questions on the PSAT / 45 Problem Simpler / 51
The Grid-Type Math Question / 45 Math Strategy 2: Translate English Words into
Mathematical Expressions / 52
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Math Strategy 3: Know How to Find Unknown Sentence Completion Strategy 1: For a Sentence
Quantities from Known Quantities (The Whole with Only One Blank, Fill in the Blank with Each
Equals the Sum of Its Parts) / 56 Choice to See the Best Fit / 81
Math Strategy 4: Remember Classic Expressions / 57 Sentence Completion Strategy 2: For a Sentence with
Two Blanks, Begin by Eliminating the Initial Words
Math Strategy 5: Know How to Manipulate
That Don’t Make Sense in the Sentence / 82
Averages / 58
Sentence Completion Strategy 3: Try to Complete
Math Strategy 6: Know How to Manipulate
the Sentence in Your Own Words Before Looking
Inequalities / 59
at the Choices / 84
Math Strategy 7: Use Specific Numerical Examples
Sentence Completion Strategy 4: Pay Close Attention
to Prove or Disprove Your Guess / 61
to the Key Words in the Sentence / 85
Math Strategy 8: When Each Choice Must Be Tested,
Introduction to Passage Reading / 87
Start with Choice E and Work Backward / 62
Summary / 94
Math Strategy 9: Know How to Solve Problems
Using the Formula R  T  D / 64 6 Reading Comprehension Strategies / 95
Math Strategy 10: Know How to Use Units of Time, Reading Comprehension Strategy 1: As You Read
Distance, Area, or Volume to Find or Check Your Each Question, Determine the Type: Main Idea,
Answer / 65 Detecting Details, Inference, or Tone/Mood / 95
Math Strategy 11: Use New Definitions and Reading Comprehension Strategy 2: Underline the
Functions Carefully / 66 Key Parts of the Reading Passage / 98
Math Strategy 12: Try Not to Make Tedious Reading Comprehension Strategy 3: Look Back at
Calculations Since There Is Usually an the Passage When in Doubt / 100
Easier Way / 67
Reading Comprehension Strategy 4: Get the
Math Strategy 13: Know How to Find Unknown Meanings of “Tough” Words by Using the Context
Expressions by Adding, Subtracting, Multiplying, Method / 101
or Dividing Equations or Expressions / 68
Reading Comprehension Strategy 5: Circle
Math Strategy 14: Draw or Extend Lines in a Transitional Words in the Passage / 102
Diagram to Make a Problem Easier; Label
Reading Comprehension Strategy 6: Increase
Unknown Quantities / 70
Your Vocabulary to Boost Your Reading
Math Strategy 15: Know How to Eliminate Certain Comprehension Score / 103
Choices / 72
3 Vocabulary Strategies / 105
Math Strategy 16: Watch Out for Questions That
Vocabulary Strategy 1: Use Roots, Prefixes, and
Seem Very Easy but That Can Be Tricky—Beware
Suffixes to Get the Meanings of Words / 105
of Choice A as a “Lure Choice” / 73
Vocabulary Strategy 2: Pay Attention to the Sound
Math Strategy 17: Use the Given Information
or Feeling of the Word—Whether Positive or
Effectively (and Ignore Irrelevant Information) / 74
Negative, Harsh or Mild, Big or Little, Etc. / 106
Math Strategy 18: Know and Use Facts about
Vocabulary Strategy 3: Use Word Associations
Triangles / 75
to Determine Word Meanings and Their
Math Strategy 19: When Calculating Answers, Opposites / 107
Never Multiply and/or Do Long Division If You
Hot Prefixes and Roots / 108
Can Reduce First / 78
Words Commonly Mistaken for Each Other / 113
Critical Reading Strategies / 80
The Most Important/Frequently Used PSAT Words
4 Sentence Completion Strategies / 81
and Their Opposites / 116
PArT 4
MINI-MATH reFreSHer  119
Algebra and Arithmetic / 120 Geometry / 123
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