GRE All the Quant: Effective Strategies and Practice from 99th Percentile Instructors, 6th Edition (2023)

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All The QuantGRE® is a registered trademark of Educational Testing Service (ETS), which is notaffiliated with Kaplan and was not involved in the production of, and does not endorse, thisproduct..

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GRE All The QuantRetail ISBN: 978-1-5062-8178-0Course ISBN: 978-1-5062-8180-3Retail eISBN: 978-1-5062-8179-7Course eISBN: 978-1-5062-8181-0Copyright © 2023 Kaplan, Inc.10 9 8 7 6 5 4 3 2 1All rights reserved. The text of this publication, or any part thereof, may not be reproduced in anymanner whatsoever without written permission from the publisher.GRE® is a registered trademark of Educational Testing Service (ETS), which is not affiliated withKaplan and was not involved in the production of, and does not endorse, this product.

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INSTRUCTIONAL GUIDE SERIESGRE All the QuantGRE All the Verbal5 lb. Book of GRE®Practice ProblemsSUPPLEMENTAL MATERIALS500 Essential Words: GRE®Vocabulary Flash Cards500 Advanced Words: GRE®Vocabulary Flash Cards

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May 2, 2023Hello! Welcome to theGRE®All The Quant.I hope this book provides just the guidance you need to get the most out ofyour GRE studies.If you have any questions or feedback, please do nothesitate to contact us at gre@manhattanprep.com or 212-721-7400.Also:We try to keep all of our books free of errors, but if you think we’ve goofed,please visit manhattanprep.com/GRE/errata.All of our Manhattan Prep books are based on the continuing experiences ofboth our instructors and our students. The primary authors and editors of thisedition of the book were Manhattan Prep instructors Dmitry Farber, ChrisGentry, Rina Goldfield, Tyler Johnson, Stacey Koprince, Logan Smeallie,and Ryan Starr. Project management, design, and quality assurance were ledby Deepika Devan, Mario Gambino, Marie Gugnishev, and Helen Tan. I’dlike to send particular thanks to Manhattan Prep instructors Whitney Garnerand Emily Meredith Sledge for their additional content contributions to thisedition.Finally, we are indebted to all of the Manhattan Prep students who havegiven us excellent feedback over the years. This book wouldn’t be half ofwhat it is without their voice.And now thatyouare one of our students too, please chime in! I look forwardto hearing from you. Thanks again and best of luck preparing for the GRE!Sincerely,

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Stacey KoprinceDirector of Content and CurriculumManhattan Prepwww.manhattanprep.com/gre 623 Broadway, New York, NY 10012 Tel:212-721-7400

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TABLE OF CONTENTSGetting the Most Out of Your GRE Math StudiesThe GRE ExamMath Formats in DetailUNIT ONE: Number PropertiesChapter 1:Develop Your Number SenseIntegers and Their DigitsNon-Integers and Their DigitsManipulating IntegersFactorsPrime NumbersPositives, Negatives, and ZeroCalculator UseNumber LinesCheck Your Skills Answer KeyProblem SetSolutionsChapter 2:Number PropertiesUnderstanding the UnknownPositives and NegativesAbsolute ValuesTesting Positive and Negative CasesEvens and OddsThe Sum of Two PrimesTesting Odd and Even CasesExponentsCheck Your Skills Answer KeyProblem SetSolutions

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Chapter 3:Quantitative Comparison: Pick NumbersQC StructureSimplify and Pick NumbersCheck Your Skills Answer KeyProblem SetSolutionsUNIT TWO: AlgebraChapter 4:EquationsThe Order of Operations (PEMDAS)Fraction Bars as Grouping SymbolsSolving for a Variable with One EquationSolving Absolute Value EquationsCheck Your Skills Answer KeyProblem SetSolutionsChapter 5:Exponents and RootsExponents and Roots LanguageRoots as ExponentsExponential EquationsSame BasesSame ExponentsSpecial PowersSpecial BasesRules of ExponentsCommon Exponent ErrorsExponents on QCCheck Your Skills Answer KeyProblem SetSolutionsChapter 6:Formulas and FunctionsPlug In FormulasStrange Symbol Formulas

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FunctionsCheck Your Skills Answer KeyProblem SetSolutionsChapter 7:Inequalities and Systems of EquationsInterpreting InequalitiesSolving InequalitiesManipulating Compound InequalitiesInequalities and Absolute ValuesSystems of EquationsAn Equation and an InequalitySeriously, Distribute!Two InequalitiesEquations on QCCheck Your Skills Answer KeyProblem SetSolutionsChapter 8:QC Gameplan: SimplifyThe Hidden InequalityRelative OrderPick Numbers: Part TwoCheck Your Skills Answer KeyProblem SetSolutionsUNIT THREE: FactorsChapter 9:DivisibilityDivisibility TermsDivisibility ShortcutsFactor Pair MethodPrime Factor TreeDivisibility of UnknownsCombining Givens

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Divisibility and Addition/SubtractionDivisibility and Consecutive IntegersRemaindersCheck Your Skills Answer KeyProblem SetSolutionsChapter 10:Common FactorsDistributing and FactoringExponents and FactorsRoots and FactorsFractions and FactorsCheck Your Skills Answer KeyProblem SetSolutionsChapter 11:FractionsImproper Fractions and Mixed NumbersMultiplying and Dividing FractionsAdding and Subtracting FractionsNEVER Split the Denominator!Fractions and EquationsComparing FractionsComparing Complex FractionsCheck Your Skills Answer KeyProblem SetSolutionsChapter 12:Quadratic EquationsEquivalent FormsSolving Quadratic EquationsUsing FOIL with Square RootsOne-Solution QuadraticsThe Three Special ProductsQuadratics in QCQuadratics and Fractions

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Check Your Skills Answer KeyProblem SetSolutionsChapter 13:QC Gameplan: CompareCompare, Don’t ComputeProblem SetSolutionsUNIT FOUR: Stories, Percents, Ratios, Stats, and DataChapter 14:Algebraic TranslationsCommon TranslationsComplex GRE TranslationsCommon Translation ErrorsHidden ConstraintsCheck Your Skills Answer KeyProblem SetSolutionsChapter 15:PercentsPercents as FractionsPercents as Word ProblemsPercent ChangePercent of OriginalSuccessive PercentsPick 100 for Unspecified AmountsCheck Your Skills Answer KeyProblem SetSolutionsChapter 16:RatiosLabel A Ratio with UnitsRatios and FractionsProportionsThe Unknown Multiplier

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Multiple Ratios: Make a Common TermRatios in QCCheck Your Skills Answer KeyProblem SetSolutionsChapter 17:Fractions, Decimals, Percents, and RatiosConverting FormsPowers of 10: Shifting the DecimalCommon FDP EquivalentsWhen to Use Which FormPut It All TogetherCheck Your Skills Answer KeyProblem SetSolutionsChapter 18:StatisticsAveragesUsing the Average FormulaSpecial Cases: Weighted AveragesMedian: The Middle NumberRangeQuartiles and PercentilesStandard DeviationThe Normal DistributionCheck Your Skills Answer KeyProblem SetSolutionsChapter 19:Data InterpretationThe Basic DI ProcessTypes of ChartsPie ChartsColumn ChartsLine ChartsBar Charts

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TablesOther DiagramsCheck Your Skills Answer KeyProblem SetSolutionsUNIT FIVE: GeometryChapter 20:Geometry on the GREGeometry FormulasUsing Geometry EquationsCheck Your Skills Answer KeyProblem SetSolutionsChapter 21:Triangles and DiagonalsThe Basic Properties of a TrianglePerimeter and AreaRight TrianglesPythagorean TriplesIsosceles Triangles and the 45–45–90 TriangleEquilateral Triangles and the 30–60–90 TriangleDiagonals of Other PolygonsCheck Your Skills Answer KeyProblem SetSolutionsChapter 22:PolygonsPolygons and Interior AnglesPolygons and PerimeterPolygons and Area3 Dimensions: Surface Area3 Dimensions: Volume3 Dimensions: Diagonal of CubeQuadrilaterals: An OverviewQuadrilaterals

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Check Your Skills Answer KeyProblem SetSolutionsChapter 23:Circles and CylindersThe Basic Elements of a CircleSectorsInscribed vs. Central AnglesInscribed TrianglesCylinders and Surface AreaCylinders and VolumeCheck Your Skills Answer KeyProblem SetSolutionsChapter 24:Lines and AnglesLine SegmentsIntersecting LinesExterior AnglesParallel LinesCheck Your Skills Answer KeyProblem SetSolutionsChapter 25:The Coordinate PlaneCreating the Coordinate PlaneKnowing Just One CoordinateKnowing RangesReading a GraphPlotting a RelationshipLines in the PlaneThe Intercepts of a LineThe Intersection of Two LinesThe Distance Between Two PointsCheck Your Skills Answer KeyProblem Set

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SolutionsChapter 26:QC GeometryShape GeometryVariable CreationWord GeometryPick NumbersProblem SetSolutionsUNIT SIX: Advanced TopicsChapter 27:RatesRate FormulaBasic Motion: The RTD ChartMatching Units in the RTD ChartMultiple RatesAverage Rate: Don’t Just Add and DivideWorking Together: Add the RatesPopulation ProblemsCheck Your Skills Answer KeyProblem SetSolutionsChapter 28:Sequences and PatternsSequence FormulasLogical SequencingProperties of TermsDigit ProblemsEvenly Spaced SequencesDefining Evenly Spaced SequencesVisualizing Evenly Spaced SetsProperties of Evenly Spaced SequencesEvenly Spaced Sets on QCCheck Your Skills Answer KeyProblem Set

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