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PublishedintheUnitedStatesbyRandomHouseLLC,NewYork,andinCanadabyRandomHouseofCanada,adivisionofPenguinRandomHouseLtd.,Toronto.

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ISBN: 9780451487841EbookISBN 9781524710316

GREisaregisteredtrademarkofEducationalTestingService,whichisnotaffiliatedwithThePrincetonReview.

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Editor:OrionMcBeanProductionEditor:LizRutzelProductionArtist:DeborahA.Silvestrini

6thEdition

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AcknowledgmentsThe Princeton Review would like to thank Kyle Fox, Rachel Suvorov, BethHollingsworth, and Kevin Kelly for their dedication, hard work, and expertise withrevisingthe6thEdition.

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Lastly,theeditorofthisbookwouldliketothankDeborahA.Silvestrini,LizRutzelandSaraKupersteinfortheirworkonthisedition.

ContentsCoverTitlePageCopyrightAcknowledgmentsRegisterYourBookOnline!

PartI:OrientationIntroductionGeneralStrategy

PartII:TenStepstoScoringHigherontheGREStep1UseScratchPaperforVerbalQuestionsStep2SlowDownforReadingComprehensionStep3CoverUptheAnswersforSentenceEquivalenceStep4FillIntheBlanksforTextCompletionStep5KnowYourMathVocabularyStep6TurningAlgebraintoArithmeticStep7FindtheMissingPiecesinGeometryStep8BallparktheEquationsStep9GetOrganizedWhenDoingArithmeticStep10PlanBeforeWritingYourEssays

PartIII:DrillsVerbalDrill1VerbalDrill2MathDrill1MathDrill2

PartIV:DrillAnswersandExplanationsVerbalDrill1VerbalDrill2MathDrill1MathDrill2

2

3

4

1

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OfflineResources

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PARTI

Orientation

Introduction

WhatIsCrashCoursefortheGRE?CrashCourse for theGRE is aquickbut thoroughguide to the fundamentalsof theGRE.It includeshelpfultechniquesfornailingasmanyquestionsaspossible,evenifyou don’t have a lot of time to prepare.CrashCourse for theGREwill give you anoverview of the test, exposure to all question types, and loads of helpful advice,including10specifictipsonhowtoimproveyourscore.Butrememberthatthisbookisnot intended tobeacomprehensivestudyguide for theGRE. Ifyouneedsignificantscore improvements or a more intensive review of any of the subject matter youencounter, try ourotherhelpfulGREbooks,Cracking theGRE,1,007GREPracticeQuestions,MathWorkout for theGRE,orVerbalWorkout for theGRE.Youcanalsoregister to takea free full-lengthGREpractice testonlineatPrincetonReview.com/grad/gre-practice-test.

WhatIstheGRE?TheGraduateRecordExam(GRE)isa3-hourand45-minuteexamintendedtorankapplicants for graduate schools. It does not measure your intelligence, nor is it arealisticmeasureofhowwell you’ll do ingraduateschool. It is safe to say theGREprovidesavalidassessmentofonlyonething:howwellyoutaketheGRE.Luckily,thisisaskillyoucanimprovewithpractice.

AfteryoutaketheGRE,youwillreceiveaAnalyticalWritingscore,aVerbalReasoningscore, and aQuantitative Reasoning score. These correspond to the three types ofsectionsyouwillseeonthetest.

Sectionbysection,here’showthetestbreaksdown:

TheAnalyticalWriting,oressaysection,alwayscomesfirst.Itconsistsoftwoback-to-backessays,with30minuteseachtowrite.Aftertheessays,youwillhavetwoofyourfivemultiple-choicesections,andthenyouwillgetyouroneandonlyproperbreakafterthethirdsection.Moststudentsseefivemulti-questionsections,eithertwoVerbalandthreeQuantitative(Math),orthreeVerbalandtwoMath.TwoVerbalsectionsandtwoMathsectionsalwayscount.Theextrasectionisanexperimentalone.ItmaybeMathor Verbal. It will look just like the other sections, but it will not count. These fivesections,includingtheexperimental,couldoccurinanyorder.Thereisnowaytoknowwhichsectionisexperimental.Youwillhaveaone-minutebreakbetweeneachofthesesections.

Youmightalsogeta researchsection inplaceof theexperimentalsection. Ifso, theresearchsectionwillcomelast,anditwillbeidentifiedasaresearchsection.Thetestwillspecificallysaythatthesectiondoesnotcounttowardyourscore.Ifyouseeoneofthese,yourtestisover,andyourfirstfourmulti-questionsectionscounted.

MathQuestionTypesQuantitative Comparison—Quant comps, for short, give you information in two

columns.Yourjobistodecideifthevaluesinthetwocolumnsarethesame,ifoneisgreater,orifitisimpossibletodetermine.

ProblemSolving—Theseare the typicalmultiple-choicequestions thatarecommononstandardizedtestssuchastheSAT.Youmustcorrectlyselectoneofthefiveanswerchoicestogetcredit.

Select All That Apply—This question type is similar to a standard multiple-choicequestionbutwithonetwist. In thiscasethereare threetoeightanswerchoices,andoneormoreiscorrect.Youmustselectallofthecorrectanswerchoicestogetcredit.

NumericEntry—Alas,thesearenotmultiplechoice.Itisyourjobtocomeupwithyour

ownanswerandtypeitintotheboxprovided.Forfractions,youaregiventwoboxes,

andyoumustfillinthetopandthebottomboxesseparately.Youdon’thavetoreduce

fractions.Thecomputerreads thesameas ,sosaveyourselfastep.

TheCalculatorThecomputer-deliveredGREprovidesanon-screencalculator.Thiscalculatorwilladd,subtract,multiply,divide,and findasquare root,plushaveadecimal functionandapositive/negative feature. It also has a transfer number button that allows you totransfer the number on the calculator screen directly to the answer box forNumericEntryquestions.Thisbuttonwillbegrayedoutformultiple-choicequestions.

Thecalculatorcanhelpyoucutdownonbasiccalculationerrorsandsaveabitoftimeonquestions that involve things likeaveragesorpercentages.TheGRE,however, isnot generally a test of your ability to do large calculations; nor is the calculator areplacement foryourbrain.The testmakerswill look forways to test youranalyticalskills, often making the calculator an unnecessary temptation, or, at times, even aliability.Beparticularlycarefulofquestionsthataskyoutoprovideanswersinaspecificformat.Aquestionmayaskyoutoprovideananswerroundedtothenearesttenth,forexample.Ifyourcalculatorgivesyouananswerof3.48,andyoutransferthatnumber,youwillgetthequestionwrong.Oraquestionmayaskyouforapercentandwillhavethepercentsymbolnext to theanswerbox. In thiscase theyare looking forawholenumber.Dependinguponhowyousolvetheproblemonyourcalculator,youmayendupwith an answer of 0.25 for 25 percent. If you enter the decimal, youwill get thequestionwrong.

HereareafewtipsforwhentouseandwhennottouseyourcalculatorontheGRE:

UseaCalculatorWhen…

• multiplyingtwo-andthree-digitnumbers• findingpercentagesoraverages• workingquestionsinvolvingOrderofOperations(ThecalculatorwillfollowtheOrderofOperations.Ifyoutypein3+5×6,itwillknowtoprioritizemultiplicationoveraddition,forexample.)

• workingwithdecimals

DoNOTUseaCalculatorWhen…

• convertingfractionstodecimalsinordertoavoidworkingwithfractions(betterthatyouknowtherulesandarecomfortablewithfractions)

• attemptingtosolvegreatexponents,squareroots,orothercalculation-heavyoperations.Thereisalmostalwaysafasterwaytodotheproblem.

• addingorsubtractingnegativenumbersifyou’renotsureoftherules

VerbalQuestionTypesTextCompletion—Questionsmayhavebetweenoneandfivesentencesandonetothreeblanks.Aone-blankquestionwillhavefiveanswerchoices.Atwo-orthree-blankquestionwillhavethreechoicesperblank.Youmustselectthecorrectwordforeachblanktogetcreditforthequestion.

SentenceEquivalence—These have one blank and six answer choices. You mustselecttwoanswerchoicesfromthesixprovided.Thecorrectanswerswillcompletethesentenceandkeepthemeaningthesame.

Reading Comprehension—Reading Comp supplies you with a passage and thenasks you questions about the information in the passage, the author’s intent, or thestructure.

TherearethreedistinctquestiontypesintheVerbalsections:

• MultipleChoice—Youmustselectonecorrectanswerfromfivechoices.• SelectAllThatApply—Thesehavethreeanswerchoices.Youmustselectallthatarecorrecttoreceivecredit.Atleastonechoiceiscorrect.

• SelectinPassage—Youwillbeaskedtoclickonanactualsentenceinthepassage.Youmayclickonanyonewordtoselectthewholesentence.Onlyone

sentenceiscorrect.Thesequestionswilloccurprimarilyonshortpassages.Iftheyoccurforalongpassage,thequestionwillspecifyaparticularparagraph.

WhatDoesaGREScoreLookLike?Youwill receive separateVerbal andQuantitative scores, each on a scale that runsfrom130to170inone-pointincrements.YourAnalyticalWritingscoreisonascaleof0to6inhalf-pointincrements.Forexample:

YOURSCORES:163QUANT158VERBAL5.5ANALYTIC

Beforeyouseeyourscores,youwillbegiven theopportunity tocancel them. If youchoosenot to cancel, youcanmakeuseof theGREScoreSelect® service,allowingyou to select which score youwant to send to schools. Options for sending scoresdependonwhetheryouaresendingthemonthedayofyourtestorafteryourtestday.Formore information on this service, visitwww.ets.org/gre/revised_general/about/scoreselect.

WhoisETS?TheGREiscreatedandadministeredbyEducationalTestingService,(ETS),underthesponsorship of the Graduate Record Examinations Board, an organization affiliatedwiththeAssociationofGraduateSchoolsandtheCouncilofGraduateSchoolsintheUnitedStates.

ETS isalso theorganization thatbringsyou theSAT, theTestofEnglishasForeignLanguage (TOEFL), the National Teacher Examination (NTE), and licensing andcertificationexamsindozenoffields.

WhyShouldIListentoThePrincetonReview?Wemonitor theGRE.Our teachingmethods for cracking itwere developed throughexhaustiveanalysisofallavailableGREtestsandcarefulresearchintothemethodsbywhichstandardizedtestsareconstructed.Ourfocusisonthebasicconceptsthatwillenableyoutoattackanyproblem,stripitdowntoitsessentialcomponents,andsolveitinaslittletimeaspossible.

GREFactsTheGRE test fee is$205.Youcan register to takeyour testonlineorbyphone.Toregisteronline,youneedtocreateorhaveanETSAccount.Gotowww.ets.org/greandclickon“RegisterfortheTest”under“GeneralTest”tocreateanonlineaccount.Ifyouareregisteringbyphone,callthetestcenterdirectlyat(800)473-2255atleasttwobusinessdaysbeforeyouranticipatedtestdate.ETSacceptsallmajorcreditcards.

ETS’ website will answer most questions, including registering for the paper-basedGREtest,guidelinesfordisabilityaccommodationsandinternationaltesting,aswellastestcenterlocationsanddates.Foradditionalquestions,visitwww.ets.org/greorcallETSat(609)771-7670.

WhattheGRELooksLikeOnthecomputer-deliveredGRE,theproblemyou’reworkingonwillbeinthemiddleofthescreen.Ifthereisadditionalinformation,suchasachartorgraphorpassage,itwillbeonasplitscreeneitherabovethequestionortotheleftofit.Iftheentirechart(s)orpassageoradditionalinformationdoesnotfitonthesplitscreen,therewillbeascrollbar.

Questions with only a single answer will have an oval selection field. To select ananswer,justclickontheoval.Aquestionwiththepotentialformultiplecorrectanswerswillhavesquareanswerfields.Anxappearsinthesquarewhenyouselecttheanswerchoice. At the bottom of the screen, under the question, there may be some basicdirections,suchas“Clickonyourchoice.”

A read-out of the time remaining in the section will be displayed in the upper-rightcorner. Next to it is a button that allows you to hide the time. The time is alwaysdisplayedandblinksonandoffwhenyouhavefiveminutesremaininginasection.Thetopcenterofthescreenshowswhichquestionnumberyouareworkingon,outofthetotal number of questions. The top of the screen will also contain the following fivebuttons.

ExitSection—Thisbuttonindicatesthatyouaredonewithaparticularsection.Shouldyou finish a section early, you can use this button to get to the next section. Onceyou’veexitedasection,however,youcannotreturntoit.Notethatthetwoessaysareconsideredasinglesection.Ifyouusethisbuttonafteryourfirstessay,youwillhaveskippedthesecondessay.

Review—This button brings up a review screen. The review screen indicateswhichquestionsyou’veseen,whichonesyou’veanswered,andwhichonesyou’vemarked.

From the review screen you can return to the question you’ve just left, or you canreturntoanearlierquestion.

Mark—TheMarkbuttonisjustwhatitlookslike.Youcanmarkaquestionforwhateverreasonyouchoose.Markingaquestiondoesnotanswerthequestion.Youcanmarkaquestionwhetheryou’veanswered itornot.Markedquestionsappearasmarkedonthereviewscreen.

Help—TheHelpbuttondropsyouintotheHelptabfortheparticularquestiontypeyouareworkingon.From there, there are threeadditional tabs.Onegives you “SectionDirections.”Thisisanoverviewofthesection, includingthenumberofquestions,theamountof timeallotted,andabriefdescriptionof thefunctionofovalsversusboxes.The second is “General Directions” on timing and breaks, test information, and therepeaterpolicy.Thelastadditionaltabis“TestingTools.”Thisisanoverviewofeachofthebuttonsavailabletoyouduringasection.NotethattheHelpbuttonwillnotstoptheclock. The clock continues to run even if you are clicking around and readingdirections.

Back/Next—These two buttons take you to the next question or back to the priorquestion.Youcancontinuetoclicktheseasmanytimesasyoulikeuntilyougettothebeginningor endof the section. If you return to a question youhaveanswered, thequestionwilldisplayyouranswer.

WewilltalkmoreaboutstrategiesforpacingonthetestandwaystousetheMarkandReview buttons. You should never need theHelp button. Ideally youwill be familiarenoughwith the functionsof the test thatyoudon’thave tospendvaluable test timereadingdirections.

YoushouldneverneedtheHelpbutton.Befamiliarwiththetestingtoolsbeforeyougointothetest.

HowtheGREWorksTheGREisadaptivebysection.Yourscoreisdeterminedbythenumberofquestionsyougetcorrectandtheirdifficultylevel.OnthefirstVerbalsection,thetestgivesyouamix of mostly medium questions along with a few easy and hard questions. Baseduponthenumberofquestionsyougetcorrectonthatfirstsection,thecomputerselectsthedifficultyofyoursecondsection.Yourgoal is togetasmanyquestionscorrect inthe first section as possible. If you get enough questions correct in the first section,yoursecondsectionwillbehard,butyou’llalsohaveachanceofgettingthehighest

possiblescore.Ifyougettoomanyquestionsincorrectinthefirstsection,yoursecondsectionwillbeeasier,buttherewillalsobeacaponhowhighyourscorecanbe.

AdditionalResourcesYou boughtCrash Course for the GRE because you want the basics and probablydon’thavealotoftimetoprepare.AlthoughthisbookisagreatwaytopreparefortheGRE in a limited amount of time, you still need real GRE questions on which topractice.TheonlysourceofrealGREsisthepublisherofthetest,ETS.Therefore, ifyouhavethetime,werecommendthatyoudownloadGREPOWERPREP®II,Version2.2softwarefromwww.ets.org/gre.ThissoftwareincludestwocompleteGREpracticetests. You can also download the PDF Practice Book for the Paper-based GRE®revisedGeneralTest,2ndEdition.Whiletheformatofthepaper-basedtestisdifferentfromthecomputer-basedtest,thepracticequestionscontainedinthePDFarerelevantanduseful.Bothofthesehelpfulresourcesarementionedinthestudyplansonline,soitishighlyrecommendedthatyouusetheminadditiontothisbook.

StayUpToDateThe information in this book is accurate up to the time of publication. For themostcurrent information possible, visit www.ets.org/gre or our websitePrincetonReview.com.

GeneralStrategy

TakeontheEasyQuestionFirst!ThetypesofquestionsontheGREvaryindifficulty.Someareabreeze,whileotherswill have you pulling your hair out. The GRE is designed so that you can answerquestionsinanyorderyoulikewithinagivensection,andthedifficultyofthequestionsyougetonthesecondsectiondependsuponthenumberofquestionsyougetcorrectonthefirstsection.Youcanmaximizethatnumberbystartingwiththequestionsyoufindtheeasiest.Rememberthateveryquestioncountsequallytowardyourscore.Asyouworkthroughasection,ifyouencounteraquestionyoufinddifficult,skipit.Ifyouseeone that looksas if itwill takea long time,skip it. Ifyou lovegeometrybuthatealgebra,doallofthegeometryquestionsfirstandleavethealgebraquestionsforlast.

Unlessyouareshootingfora165orhigher,youshouldNOTattempttoworkoneverysinglequestion.

Ifyouaregoingtorunoutoftime,youmightaswellrunoutoftimeonthequestionsyou are least likely to get correct. By leaving time-consuming and difficult questionsuntil the end, youwill be able to seemore questions overall and getmore of themcorrect.Donotmarkquestionsyouskip;wewillusetheMarkfunctionforsomethingelse.Justclick“Next”andmoveontothenextquestion.Thereviewscreenwilltellyouwhichquestionsyouhaveandhavenotanswered.

Note: There is no guessing penalty on theGRE. They don’t take points away for awronganswer.Whenyougettothetwo-minutemark,therefore,stopwhatyou’redoingandjustselectarandomletterfortheunansweredquestions.

AnswerQuestionsinStagesAnytimeyoupracticeforatest,youendupgettingafewquestionswrong.Later,whenreviewing thesequestions, youendup smacking your foreheadandasking yourself,“WhatwasIthinking?”Or,youmayfindaproblemutterlyimpossibletosolvethefirsttimearound,onlytolookatitlaterandrealizethatitwasactuallyquiteeasy;youjustmisreadthequestionormissedakeypieceofinformation.

Onanapproximately four-hour test,yourbrain isgoing toget tired.Whenyourbraingets tired, you’re more likely to make mistakes. Typically these mistakes consist of

misreadings or simple calculation errors. A misread question or a calculation errorcompletely changes the way you see the problem. Unfortunately, once you see aquestionwrong,itisalmostimpossibletoseeitcorrectly.Aslongasyoustaywiththatquestion,youwillcontinuetoseeitwrongeverytime.Meanwhile, theclock istickingandyou’renotgettinganyclosertotheanswer.

On the flipside,onceyou’vespotted theerror,solving theproblemcorrectly isoftenquick work. A question that bedeviled you for minutes in the middle of a test mayappeartobeappallinglyobviouswhenviewedinthecomfortofapost-testreview.Thetrickistochangethewayyouseethequestionwhileyoustillhavetheopportunitytofixit.Rememberthefollowingthreestagestohandlingdifficultquestions.

Stage1—Recognizethatyou’restuck.

Stage2—Distractyourbrain.

Stage3—Seetheproblemwithfresheyesandfixit.

Stage1—Recognizethatyou’restuck.Thisisoftenthehardestpartoftheprocess.Themoreworkyou’veput intoaproblem,themoredifficult it istowalkawayfromit.Onceyougetoff trackonaproblem,however,anyadditionalworkyou invest in thatsamequestioniswasted.Ifyouunderstandwhat’sbeingasked,noneofthequestionsontheGREshouldever takemorethanafewminutestosolve. Ifyougoover threeminutes, you’re stuck. Move on. If you find yourself working too hard, or plowingthrough reamsofcalculations,youareoff track.Moveon.Herearea fewsigns thatyou’restuckandneedtomoveon:

• you’vefoundananswer,butitisnotoneofthechoicesthey’vegivenyou• youhavehalfapageofcalculationsbutarenoclosertoananswer• you’vespentmorethanthreeminutesonaproblem• yourhandisnotmoving• you’redowntotwoanswerchoices,andyouareconvincedthatbotharecorrect• you’rebeginningtowonderiftheymadeamistakewhentheywrotethequestion

Ifyoufindyourselfinanyofthesesituations,youaredefinitelystuckandneedtomoveon. You’ve got better things to dowith your time than sit aroundwrestlingwith onequestion.

Stage2—Distractyourbrain.Thinkof it thisway:Youcouldspendmorethanthreeminutesonaquestionevenwhenyouknowyou’restuck,oryoucouldwalkawayandspend those sameminutes on two or three other easier questions and get them all

correct.Whythrowgoodminutesawayafterabadquestion?Whethertheyrealizeitornot,ETShasactuallydesignedthetesttofacilitatethisprocess.ThisiswheretheMarkbuttoncomes intoplay. Ifyoudon’t likeaproblemordon’tknowhowtosolve it, justskip it. If you start a problem and get stuck,mark it andmove to the next questionbeforeyouwastetoomuchtime.Dotwoorthreeotherproblemsandthenreturntotheproblemthatwasgivingyoutrouble.

Whenyou “walkaway” fromaproblem, you’renotwalkingawayentirely; you’re justmovingittothebackburner.Yourbrainisstillchewingonit,butit’sprocessinginthebackgroundwhile youwork on something else. Sometimes your best insights occurwhenyourattentionispointedelsewhere.Don’tbeafraidtowalkawayfromaproblemandreturntoitlater.It’sevenokaytotaketwoorthreerunsatahardproblem.

Stage 3—See the problemwith fresh eyes and fix it. You use other problems todistractyourbrainso thatwhenyou returnyoucanseea troublesomeproblemwithfresh eyes. You can help this process by reading the question differently when youreturntoit.Useyourfingeronthescreentoforceyourselftoreadtheproblemwordforword.Are there differentways to express the information?Can you use the answerchoices tohelp?Canyouparaphrase theanswerchoicesaswell? If thepath to thecorrectanswer isnot clearona secondviewing,walkawayagain.Whystickwithaproblemyoudon’tknowhowtosolve?

ThePowerofPOEThereareroughlyfourtimesasmanywronganswersastherearecorrectanswers;it’soften easier to identify the wrong answers than it is to identify the right ones. POEstands forProcessofElimination.Ondifficult questions, spendyour time looking forandeliminatingwronganswers.Theyareeasierandquickertofind.

The simple act of eliminating wrong answers will raise your score. Why? Becauseeverytimeyou’reabletoeliminateanincorrectchoiceonaGREquestion,youimproveyouroddsof findingtheanswer.Themoreincorrectchoicesyoueliminate, thebetteryourodds.Don’tbeafraidtoarriveatthecorrectanswerindirectly.You’llbeavoidingthetrapslaidinyourpathbythetestwriters—trapsthataredesignedtocatchunwarytesttakerswhotrytoapproachtheproblemsdirectly.

Ifyouguessedblindlyonafive-choiceGREproblem,youwouldhaveonechance infiveofpickingETS’sanswer.Eliminateoneincorrectchoice,andyourchancesimprovetoone in four.Eliminate three,andyouhavea fifty-fifty chanceofearningpointsbyguessing. Eliminating answer choices improves your odds of getting the questioncorrect!

Note:EspeciallyonVerbalquestions,ifyou’renotsurewhatawordinananswerchoicemeans,don’teliminatethatchoice.Itmightbetheanswer!Eliminateonlythe

answersyouknowarewrong.

The“Best”AnswerTheinstructionsontheGREtellyoutoselectthe“best”answertoeachquestion.ETScallsthem“best”answers,orthe“creditedresponses,”insteadof“correct”answers,toprotect itself from thecomplaintsof test takerswhomightbe tempted toquarrelwithETS’sjudgment.YouhavetopickfromthechoicesETSgivesyou,andsometimesyoumight not like any of them. Your job is to find the one answer for which ETS givescredit.

UseYourScratchPaper!ForPOEtowork,it’scrucialthatyoukeeptrackofwhichchoicesyou’reeliminating.Bycrossingoutaclearlyincorrectchoice,youpermanentlyeliminateitfromconsideration.Ifyoudon’tcross itout,you’llkeepconsidering it.Crossingout incorrectchoicescanmakeitmucheasiertofindthecreditedresponsebecausetherewillbefewerplaceswhereitcanhide.Buthowcanyoucrossanythingoutonacomputerscreen?

Byusing your scratchpaper!On theGRE, theanswer choiceshaveempty bubblesnext to them,but in thisbook,we’ll refer to themas (A), (B), (C), (D),and (E).Eachtimeyouseeaquestion,getinthehabitofimmediatelywritingdownA,B,C,D,Eonyourscratchpaper.Bythetimeyou’vedoneafewquestions,yourscratchpaperwillbeorganizedlikethis:

Thenyoucanphysicallycrossoutchoicesthatyoueliminate.Doiteverytimeyouworkthrough aGREquestion,whether in this book or elsewhere.Get used towriting onscratchpaperinsteadofnearthequestion,becauseyouwon’tbeabletowritenearthequestionontestday.

Don’tDoAnythinginYourHeadBesideseliminatingincorrectanswers,therearemanyotherwaystousescratchpaperto solve questions; you’re going to learn them all. Just remember: Even if you’retempted to try to solve questions in your head, even if you think that writing thingsdownonyourscratchpaper isawasteof time,you’rewrong.Trustus.Alwayswriteeverythingdown.

ReadandCopyCarefullyYoucandoallthecalculationsrightandstillgetaquestionwrong.How?Whatifyousolveforxbutthequestionwas“Whatisthevalueofx+3?”Becauseofthis,alwaysrereadthequestion.Takeyourtimeanddon’tbecareless.Thequestionwillstayonthescreen;it’snotgoinganywhere.

Or,howaboutthis?Theradiusofthecircleis6,butwhenyoucopiedthepictureonto

your scratchpaper, youaccidentally labeled the radius5!Manyof themistakes youmakeat firstmight stem from copying information down incorrectly. Learn from yourmistakesandbeextracarefulwhencopyingdowninformation.

AccuracyVersusSpeedYoudon’tgetpointsforspeed;theonlythingthatmattersisaccuracy.Takethetimetoworkthrougheachproblemcarefully(aslongasyouleavesometimeattheendofthesection to select an answer for any question you didn’t work on). If you’re makingcareless errors, youwon’t even realize you’re getting questions wrong.Get into thehabitofdouble-checkingallofyouranswersbeforeyouchoosethem.However,don’tspendtoomuchtimeonaquestion.Whenyougetstuck,markthequestion,moveon,andreturnafteryou’veansweredafewotherquestions.

AttheTestingCenterWhengoingtotakeyourtest,youareencouragedtobringtwoformsofidentification;onemust be a recent photo ID and have your signature. Acceptable ID documentsdepend on where you’re taking your test, so we recommend you confirm yourdocumentationontheETSwebsitebeforeyourtestday.

Thenwhenyouridentificationisverified,atestadministratorwilltakeyourphotobeforetaking you to the computer station where you will take the test. You get a desk, acomputer, a keyboard, amouse,about sixpiecesof scratchpaper, and twopencils.Beforethetestbegins,makesureyourdeskissturdyandyouhaveenoughlight,anddon’tbeafraidtospeakupifyouwanttomove.

Ifthereareotherpeopleintheroom,theymightnotbetakingtheGRE.Theycouldbetakinganursing testora licensingexam forarchitects.And theywillnotnecessarilyhavestartedtheirexamsatthesametime.Thetestingcenteremployeewillgetyousetupatyourcomputer,butfromthenon,thecomputeritselfwillactasyourproctor.It’lltellyouhowmuchtimeyouhaveleftinasection,whentimeisup,andwhentomoveontothenextsection.

Thetestcenteradministratorswillbemonitoringthetestingroomforsecuritypurposeswithclosed-circuit television. Ifyouhaveaquestion,orneedtorequestextrascratchpaperduringthetest,trytodosobetweenthetimedsectionsorduringyourbreak.

LetPastQuestionsGo

Whenyoubeginanewsection,focusonthatsectionandputthelastonebehindyou.Don’t thinkabout thatpesky text completionquestion fromanearlier sectionwhileageometryquestionisonyourscreen.Youcan’tgoback,andbesides,yourimpressionofhowyoudidonasectionisprobablymuchworsethanreality.

AttheEndoftheTestWhenyou’redonewiththetest,thecomputerwillaskyoutwiceifyouwantthistesttocount.Ifyouselect“no,”thecomputerwillnotrecordyourscore,noschoolswillseeit,andyouwon’tseeiteither.Youcan’tlookatyourscoreandthendecidewhetheryouwant to keep it or not. Once your score is canceled, it can not be retrieved. If youchoose to keep your scores, the computer will give you your unofficial Verbal andQuantitativescoresrightthereonthescreen.Afewweekslater,yourofficialscoreswillbeavailableinyourETSaccountandwillincludeyouranalyticalscore.

TestDayChecklist

• Dress in layers so that you’ll be comfortable regardless ofwhethertheroomiscoolorwarm.

• Besuretohavebreakfastorlunch,dependingonthetimeforwhichyourtest isscheduled.Andgoeasyonthe liquidsandcaffeine.

• DoafewGREpracticeproblemstowarmupyourbrain.Don’ttrytotackledifficultnewquestions,butreviewafewquestionsthatyou’vedonebeforetohelpyoureviewtheproblem-solvingstrategiesforeachsectionoftheGRE.Thiswillalsohelpyouputyour“gameface”onandgetyouintotestmode.

• Make sure to bring two forms of identification (one with arecent photograph and your signature) to the test center.Acceptable forms of identification generally include driver’slicenses,StateandMilitaryIDsandvalidpassports.ChecktheETSwebsitetoconfirmyourcountry’sIDrequirementsbeforetestday.

PARTII

TenStepstoScoringHigherontheGRE

STEP1

UseScratchPaperforVerbalQuestions

UseScratchPaperforVerbalQuestionsFor the Verbal Reasoning Section of the GRE, most people answer the TextCompletionandSentenceEquivalentquestionsintheirheads.Thisisnotagoodidea!When you answer these types of questions in your head, you are really doing twothingsatonce.Thefirstisevaluatingeachanswerchoice,onebyone,andthesecondiskeepingtrackofwhichanswerchoicesareinandwhichareout.Studiesshowthatmultitaskingcannotbedoneverywell.Thebrainissimplynotequippedtodotoomanythings correctly and efficiently at once. What most people call multitasking is reallyjumping back and forth between multiple tasks. People who attempt to multitaskinevitably end up doing both tasks poorly. People who try to multitask make moremistakes because they are constantly distracting their brains from the task at hand.Therefore, try not to multitask and do Text Completion or Sentence Equivalencequestions in your head. It leads to careless and avoidable mistakes that could becatastrophictoyourscore.

Thesolutionistoengagewiththequestion.Thismeansusingscratchpaper.ScratchpaperisasimportantontheVerbalportionofthetestasitisontheMathportionofthetest.Ifyourhandisnotmoving,youarestuckthinking.Thinkingdoesnotgetyouanyclosertotheanswer.Youshouldbedoing,notthinking,whiletakingtheGRE.

Here is what your scratch paper for Text Completion and Sentence Equivalencequestionscouldlooklike:

Scratchpaperallowsyoutoparkyourthinkingonpaper.OntheVerbalsectionofthetest,it’sverypossiblethattherewillbewordsoranswersyoudon’tknow.Lookingforthecorrectanswer,therefore,willworkonlypartofthetime.Fortunately,themajorityoftheVerbalsectionismultiplechoice.They’veactuallygivenyoutheanswers,andoneof those answers is correct. If you can’t identify the correct answer, you can alwaysidentifysomewrongones.You’reprobablydoingthisalready;you’rejustnotcapturingtheresultsonthepage.

Onceyoustartparkingyour thoughtsonpaper,however,a fewgood thingshappen.Thefirst is thatyouavoidredundantwork.Onceyoueliminateananswerchoice, it’sgone.Youdon’thavetolookatitagain.Next,yousavetimebecauseyouaren’tgoingbackovergroundyou’vealreadycovered.Andthelastbenefitisthatyousaveyourselfa lotofmentaleffort. It’shardkeepingtrackofdecisionsinyourhead.Duringafour-hourtest,yourbrainisgoingtogettired.Savingmentaleffortmakesadifference.

Usethesesymbolsonyourscratchpapertocaptureyourprogress:

Check:Thismeansyouknowtheanswerchoice,anditlooksright.Itdoesn’tmeanthatyouaredone.Youstillmustcheckeveryanswerchoice,butyou’vegotonethatlooksgood.Giveitacheckandmoveontothenextone.

Maybe:Onyourfirstpassthroughtheanswerchoices,it’simportanttokeepmoving.Don’tgetstalledonasingleanswerchoice.Whenyou’renotsureaboutananswerchoice,it’sveryeasytogetstuck.Butrememberthatit’seasiertolookforwronganswersthanrightones.So,ifyoufindyourselfstartingtostallonananswerchoice,giveitthe“maybe”andmoveon.Itisentirelypossiblethattheotherfouranswerchoicesareclearlywrong,orthatyou’vecomeacrossonethatisclearlycorrect.Ineithercase,timespentagonizingoverananswerchoiceaboutwhichyou’renotsureistimewasted.

A Cross-out:Welovethisone.Whenyouknowsomethingiswrong,getridofit.Youneverwanttospendtimeonthatanswerchoiceeveragain.Evenifyouhavetoguess,youwanttoguessfromasfewanswerchoicesaspossible.ThereareaboutfourtimesasmanywronganswersontheGREastherearerightones.Thewrongonesaremucheasiertofind.Identifythemandeliminatethem.Keeptrackwithyourhand.

? QuestionMark:Ifyoudon’tknowaword,don’teliminateit.Behonestwithyourself.Ifyoudon’tliketheword,youdon’thavetopickit,butdon’tbequicktoeliminateitbecauseitcanpossiblybetheanswer.Ifyou’reunsureofaword,giveitaquestionmarkandmoveontothenextanswerchoice.

Inallcases,theplacetoinvestyourtimeisinthequestionstemandincomingupwithyourownanswer.Theanswerchoicesaredesignedtotemptandmisleadyou.Bythetimeyougettotheanswerchoices,yourfirstpassthroughshouldbefairlyquick.Eitheryouknowthewordoranswerchoiceanditworks,youknowitanditdoesn’twork,oryoudon’tknowit. Ifyoufindyourselfstartingtostall,givetheanswera“maybe”andmoveon.Butdon’tusethe“maybe”asawayofavoidingmakingadecision!

Withyourevaluationsmarkedon thepage,yourscratchpapercanoftenanswer thequestionforyou.Considerthesefivecommonscenarios:

1. A,B,C, ,EIfyouhaveananswerchoiceanditworks,gowithit.Lookatthisscratchpaper.Yourdecisionismade.

2. A,B,C,?,EWhatmoredoyouneedtoknow?Youhavefourwronganswersandoneyoudon’tknow.Iftheotherfourarewrong,they’rewrong.Youhavenochoice.Thereisonlyonepossibleanswerchoice.

3. A, ,C, ,EIfyouneedtospendmoretimeonananswerchoice,youalwayscan,butdon’tdoituntilyouhaveto.Inthiscase,you’redowntotwo.Dowhatyoucantoinformyourguess,butdon’tgocrazy.Pickoneandmoveonorskipandcomeback.

4. A,B,C,D,EYou’veeliminatedallfive.Something’sgonewrong.Mostlikely,you’vemisreadsomethinginthequestionorsomethingintheanswerchoices.You’llneverseeyourmistakeunlessyoudistractyourbrain.Markthequestion,

moveon,andcomebackafteryou’vedoneafewothers.5. A,?,C,?,EYou’redowntotwo.Youdon’tknowthewords.You’veeliminatedallthatyoucan.Don’tspendanymoretime.Pickananswerandmoveon.

Usingscratchpaperwiththesetypesofquestionsisagoodhabit.Startpracticingnowand forceyourself touse it.Themoreyouuse it, themore itwilleaseyourdecisionmaking.Eventually,youwon’tbeabletodoitanyotherway.Thisisthegoal.It’shardworkatfirst,butgoodtechniquesshouldbecomeautomaticwithenoughpractice.

STEP2

SlowDownforReadingComprehension

SlowDownforReadingComprehensionFor the Reading Comprehension questions of the Verbal Reasoning section, theanswersareinthepassagesgiventoyou.TherearethreewaysyoucangiveyourselfmoretimeonReadingComprehensionquestions:

• ThefirstwayistogetsogoodatTextCompletionsandSentenceEquivalencethatyouhaveplentyoftimeleftoverforReadingComp,wheretimeequalspoints.

• Thesecondwaytopickuptimeistopickyourbattles.Takeonfewerpassages,dofewerquestions,butgetmorecorrect.RushingthroughReadingCompguaranteeswronganswers.Slowdownandmakesurethatthetimeyouspendyieldspoints.

• ThelastwaytogiveyourselfmoretimeonReadingCompistobesmartaboutwhereyouspendyourtime.Thereisalotofinformationinthepassages,butyouwillbetestedononlyatinyportionofthatinformation.Asmartandefficientstrategyforworkingwiththepassageswillpaydividendsintheformofmoretimeandlessstress.

ThePassagesIfyouarelikemanystudents,ReadingComprehensionpassagesontheGREarenotsomething you’d read for fun on a Saturday afternoon. There is noway around thesimplefactthatmostGREReadingComprehensionpassagesaremundaneincontentandtediousinstructure.Whileitistruethatthepassagesare,forthemostpart,boring,thegoodnewsisthatallthequestionscanbeansweredbytheinformationpresentedinthetext.MostoftheReadingComprehensionpassagesyou’llseeontheGREareonlyoneparagraphlong,butoneortwopassagesareseveralparagraphslong.You’lltypicallyseetenpassages,eachofwhichwillbefollowedbyonetosixquestions.Thetopics covered include physical sciences, biological sciences, social sciences,business, and humanities, but no specialized knowledge of any of these fields isnecessary.

TheBasicApproachtoReadingComprehensionTosuccessfullyanswerReadingComprehensionquestionsontheGRE,itisimportanttogainagoodunderstandingofthepassage,thequestion,andtheanswerchoices.Bydoingso,youwillbeabletograspthemeaningofthepassage, locateinformationtoanswer questions quickly and efficiently, and spot incorrect answers. The Basic

Approach is a four-step process that will help you feel confident in your abilities tohandleanyGREReadingComprehensionpassage.

HerearethestepsoftheBasicApproach.

Step1:WorkthePassageWorking thepassage is the first step towardsuccessfullyapproachingGREReadingComprehensionquestions.ManystudentswillseeaReadingComprehensionquestionandskipstraighttothequestion.Otherswillreadthepassage,butdosoasquicklyasthey can so they can startworking through the question. If you have found yourselfdoing either of these things, you’re not alone. However, these strategies are notefficientbecausetheycanleadtotimewastedrereadingsentences,pullinginformationoutofcontext,orinaccuratelyansweringthequestions.

Workingthepassageappropriatelyenablesyoutoavoidmanyofthosemistakesso,bythetimeyou’refinishedreading,youwillhaveaclearunderstandingofthepassagetoapply to thequestions.Youshouldwork through thepassageby identifying themainidea,thestructure,andtheauthor’sviewpoint.

Toworkthepassage,separateeachsentenceindividuallyintooneofthreecategories:claim,evidence/objections,andbackground.

• Claimsaresentencesinthepassagethatgiveyousomeinsightastothemainpointofthepassageortheauthor’sviewpoint.MostGREauthorshaveapointofview.However,mostGREauthorsareacademicswhoexpresstheirpointofviewintentativeways.Ifthesentencegivesyouanyinsightintowhattheauthorthinksoristryingtoconvinceyouof,itisaclaim.

• Evidence/objectionsaresentencesinthepassagethatprovideinformationthatsupportorarguewiththeclaimsinthepassage.

• Backgroundsentencesprovideinformationaboutthetopicofdiscussions.Backgroundsentencestypicallyprovidecontextforthediscussionsothatthereaderhasabetterunderstandingofwhytheauthoriswritingthepassageinthefirstplace.

When you work the passage, assign each sentence in the passage one of thecategories and write it down on your scratch paper so it’s easy to keep track. Byassigningeachsentenceacategory,youwilleasilybeable to identify themainpointandstructureofthepassage,aswellastheauthor’sviewpoint.

Step2:UnderstandtheQuestionAfterworkingthepassage,it’stimetotakealookatthequestion.Thisstepmightseemalittleobvioustoyou.Ofcourse,youneedtounderstandthequestion.But,breaking

thequestiondownintoitsmaincomponentsallowsyoutofocusontheinformationinthepassageyou’llneedtoanswerthequestion.Themaincomponentsofthequestionarethesubjectandthetask.

Everyquestionhasasubjectandatask.Thesubjectofthequestionisthetopicofthequestion.Ifyouidentifythesubjectofthequestion,thenyouwillknowtheinformationfromthepassageyouneedtofind.

The taskof thequestion iswhat information thequestion isaskingyou to find in thepassage about the subject. Understanding the task will help you evaluate theinformationyoufindaboutthesubject.

Checkoutthefollowingquestionstem:

ItcanbeinferredthattheauthorofthepassagewouldmostlikelyagreewithwhichofthefollowingclaimsabouttheorganizersoftheHaymarketprotest?

Now, find thesubjectandthetaskof thequestion.Thesubjectof thequestion is thetopicthatthequestionisaskingabout.Therefore,thesubject is theorganizersoftheHaymarketprotest.The taskof thequestion is the informationabout thesubject thatwillanswerthequestion.Thetaskistheauthorofthepassagewouldmostlikelyagreewith.

Lookatanotherquestion:

Thepassageisprimarilyconcernedwithdiscussingwhichofthefollowing?

Thesubjectof thequestion is thepassage.Thesubject isgeneral,as it isabout theentirepassage,solookforthetasktoprovidesomecontextabouthowtoanswerthequestion.Thetaskisprimarilyconcernedwithdiscussing.Therefore,youknowthattheanswertothequestionwillbethemainideaofthepassage.

Step3:FindtheInformationinthePassageThatAddressestheTaskoftheQuestionNowthatyouhaveworkedthepassageandyouunderstandthequestion, it’stimetofind the information in thepassagethataddresses the taskof thequestion.Findandreadacoupleofsentencesbeforeandaftertheportionofthepassagethatdiscussesthesubject.

Allof thequestionsfortheGREmustbeanswerablebasedontheinformationinthepassage.IfETSwroteaquestionthatwasnotanswerablebasedontheinformationinthepassage,theywouldhavenowaytojustifytheirchoicesandwouldbesubjecttochallengesandlawsuitsfromdisgruntledstudents.Withthatinmind,theinformationto

answerthequestioncanalwaysbefoundinthepassage.Allyouhavetodoisfindit.

This is part of what makes successfully completing Step 1 so important. If you’vecreatedagoodoutlineofthepassagefollowingthoseguidelines,youmaynothavetoreturntoactuallyreadingthepassage.Instead,youmightbeabletoquicklynotetheinformation based on the claims, evidence/objections, and background. At the veryleast,youwillknowwhereto findthe information.Atbest, theoutlinewillprovidetheappropriateinformationtoyou.

Whenyoufindtheinformationinthepassage,resisttheurgetoparaphrasewhatthepassagesays.Instead,usetheinformationfromthepassageexactlyasitisstated.Ifyou paraphrase information, you will be susceptible to assumptions and filling ininformationthattheauthorofthepassagedidnotintend.ETSquestionwritersexpectyou to do this and will write answer choices designed to trap test takers whoparaphrasewhatthepassagesays.Avoidthistrapandquotethepassageexactlyasitisstated.

Step4:UsePOEtoFindtheAnswerOnceyou’vecompletedalltheabovesteps,useProcessofElimination(POE)toattackthe answer choices. If you successfully completed steps 1–3, you will know exactlywhat the passage says about the subject and task of the question.Now that you’relookingat theanswerchoices,you’llnotice that,atanygivenpoint,chancesareyouare readingan incorrectanswerchoice.Afterall,mostof theanswerchoiceson theGREarewrong!Lookforsignsthattheanswerchoiceis incorrect,suchassoundingtoomuchlikethepassageortakingwordsfromthepassageoutofcontext.Eliminateanswerchoicesthatdon’tmatchwhatyoureadaboutthesubjectinthepassage,anddon’tbeafraidtosimplyselecttheonlyanswerchoicethatremainsifyouhaveagoodreasontoeliminatetheotheranswerchoices.

Whentestwritersmakeincorrectanswerchoices,theyuseahandfuloftoolstomakethemseemappealingtotesttakers.Thesetoolsaredesignedtotrickthetesttakerintopicking certain incorrect answer choices. Having a full understanding of what thepassagesaysabout thesubjectandtaskof thequestionwillhelpyoutoavoid theseanswerchoices,but that isnot theonlymethodatyourdisposal.Beingawareof thewaysinwhichincorrectanswerchoicesarecommonlycreatedisjustasvaluable.

Herearethesixmostcommonwaystestwriterscreatewronganswers.

1.RecycledLanguageandMemoryTraps Oneof theeasiestandmostcommonwaysthattestwriterscreateawronganswerchoiceisbyrepeatingmemorablewordsorphrasesfromthepassage.ThecorrectanswersforGREReadingComprehensionquestionsaregenerallyparaphrasesofthepassage.Therefore,thepresenceofwords

orphrasesthatareveryreminiscentof thepassageisareasontobeskepticalofananswerchoice.Anyanswerchoicethatevokesastrongmemoryofthepassageshouldcausesuspicion,as itcouldbeaRecycledLanguageorMemoryTrapanswer. Ifyoufindananswerchoicethatfeelsfamiliar,doublechecktomakesuretheinformationinthe passage supports the statement. If the information in the passage does notexplicitlysupportthisstatement,eliminatetheanswerchoice.

2.ExtremeLanguage Anothercommonway tocreatewronganswerchoices isbyusing languagetoo“powerful”orovert.Commonwordssuchasmust,always,never,only,best,orverbssuchasproveorfailareways inwhichquestionwritersmakeananswer choice appealing. Always compare the language in the answer against thepassagetoseewhethertheclaimmadeisasstrongastheclaimintheanswerchoice.If the information in thepassage isnotasstrongas theclaim in theanswerchoice,eliminatetheanswerchoice.

3.NoSuchComparison Comparisonwords such asbetter,more, reconcile, less,decide, ormore than are often used by test writers to make answer choices moreappealing by drawing a comparison between two items referenced in the passage.However, these items may not have been compared in the passage. If you seecomparisonwordsinananswerchoice,youshouldbeskepticalanddoublecheckthepassage.Iftheitemsbeingcomparedintheanswerchoicewerenotcomparedinthepassage,eliminatetheanswerchoice.

4.Reversals Reversalanswerchoicesseektoconfusethetest takerbystatingtheoppositeof the information in thepassage.Finding theappropriate information in thepassage,consideringthe informationexactlyas it isphrased,andbreakingdownthepassage to find the main idea are tools that should help you spot reversal answerchoices.

5.EmotionalAppeals ThisanswerchoicetypeisfairlyrareontheGRE.However,itbearsworthmentioning.Someanswerchoicesmaytrytoappealtothebeliefsofthetesttaker.Forinstance,apoliticalpassagemaycontainananswerchoicethatvaluesonepoliticalstanceoveranotherevenifthepassagemadenosuchclaim.Ifyouseeanswerchoiceslikethis,beveryskepticalandreferbacktothepassage.Youneedtopickananswerbasedonwhatthepassagesaidratherthanyourownbeliefsaboutthetopic. If thepassagedoesnot support theanswerchoice it iswrong,nomatterhowmuchyoumayagreewiththeanswerchoice.

6. Outside Knowledge Like emotional appeal answer choices, outside knowledgeanswer choicesare fairly rareon theGRE.Correctanswer choiceson theGREwillcontaininformationthatisfoundinthepassage.However,someanswerchoicesmaycontain information that is designed to appeal to a test taker that has someindependent knowledge about the subject of the question. Remember, if the

information isn’t explicitly stated in the passage, it should not be considered whendecidingonananswerchoice.

QuestionFormatsMany of the questions are standard GRE fare: multiple-choice questions with fivepotentialanswersandasinglecorrectanswer.ReadingComprehensionquestionscanalsobeAllThatApplyquestions.Inthiscase,youwillbepresentedwiththreeanswerchoices, fromwhichyoumust chooseone, two,orall threecorrectanswers.Finally,there are somequestions thatwill ask you to find the sentence in the passage thatanswersthequestion.Answerthesequestionsbyclickingonthecorrectsentencefromthepassage.

RecognizeQuestionTypesKnowing the question typewill allow you to not only quickly identify the subject andtaskof thequestion,butalsobeonthe lookout forcommonwronganswertrapsthatareoftenfoundwithcertaintypesofquestions.

Therearethreecategoriesofcommonquestions:general,specific,andcomplex.EachofthosecategorieshasseveralquestiontypesthatarecommonlytestedontheGRE.

1.GeneralQuestionsThetypesofGeneralquestionsaremainidea,primarypurpose,tone,andstructure.

MainIdeaquestionsaskyoutoconsider themainclaimsmadebytheauthor.Thesequestions generally ask what the passage is about. The answer to a Main Ideaquestionissummarizeswhattheauthorwantsyoutorememberaboutthepassage.AMain Ideaquestioncanbe identifiedby thephrasemain ideaorany reference toanoverallclaim.

PrimaryPurposequestionsmayseemalotlikeMainIdeaquestions,buttheydifferinoneimportantway.WhileMainIdeaquestionsaskwhatthepassageisabout,PrimaryPurpose questions ask why the author wrote the passage. To answer a PrimaryPurposequestion,youneedtofigureoutwhytheauthorwrotethepassage.Ingeneral,theauthorwrote thepassagetoconvinceyouof thepassage’smain idea!APrimaryPurposequestioncanbeidentifiedbythepresenceofthephraseprimarypurpose inthequestionstem.

Tonequestionsaskyou toevaluate theauthor’sopinionandhowstrongly theauthorfeels about that opinion. Typically, the question asks about the main topic under

discussion in thepassage inwhich theauthorwill haveexpressedanopinionaboutthattopicthroughthemainidea.Askyourselfwhethertheauthoragreesordisagrees.If you have found themain idea, deciphering the tone of the passage should be amanageable task. These questions are readily identifiable, as the question stemusuallyincludesthewordtoneorattitude.

Structurequestionsaskabouttheoverallstructureofthepassage,ortheroleofcertainsentencesorphrasesinthepassage.Eachpassagewillhaveadefinablestructurethatyoushouldhaveuncoveredwhenyouworkedthepassage.Ifyouworkedthepassageappropriately,thesequestionsarerelativelyeasytoanswerastheywillaskabouttheflowandcontentofthepassage.

2.SpecificQuestionsThe types of specific questions typically found on the GRE are retrieval, inference,specificpurpose,andvocabularyincontext.

Retrieval questions, which are very common, are identified by the presence of thewords according to the passage or a similar phrase that tells you to simply findsomethingstated in thepassage.Thecorrectanswer isusually justaparaphraseofsomethingthepassagesaid,asRetrievalquestionsaskyoutogobacktothepassagetofindsomefactordetail.

Inference questions are also very common on the GRE and often give test takersunawareofthequestiontaskthemosttrouble.Thesequestionsusuallysaysomethingalong the lines ofwhat can be inferred from the passage. Inference questions willalwaysbeaboutsomethingveryspecificthatisstatedinthepassage,andbecauseofthat, are actually very similar to Retrieval questions. The answer to an Inferencequestionissomethingthatyouknowtobetruebasedintheinformationinthepassage.Inferencequestionsareeasilyidentifiedastheyusuallycontainthewordinfer,imply,orsuggestinthequestion.

Many students mistakenly believe Inference questions ask the reader to determinesomething theauthor thinksorbelieves,butdoesnotexplicitlystate in thepassage.This is not true.Asweoutlinedearlier, the correct answers are always found in thepassage.

SpecificPurposequestionsaresimilartoPrimaryPurposequestionsinthesensethatthey both askwhy the author included certain information in the passage.However,SpecificPurposequestionsaskaboutsomethingveryspecific,whilePrimaryPurposequestionsaremoregeneral.Thesequestionscanbeidentifiedbyphrasessuchas inordertoandserveswhichofthefollowingfunctions.

VocabularyinContextquestionsreferenceawordorphrasefromthepassagethattheauthorincludedtoproveapoint.Thetaskofthesequestionsistodeterminethepointorthemeaningofthewordsofphrasesindicatedinthequestionstem.

3.ComplexQuestionsThe complex questions are Weaken and Strengthen questions. Weaken andStrengthen questions ask the test taker to weaken or strengthen some claim in thepassage.Often, the test takermustconsiderpossiblescenarios thatcouldaffect theoutcome of the claim. Be on the lookout for wrong answers that accomplish theopposite task. For example, answers that weaken are common on Strengthenquestions. These questions are identified by the presence of the wordsweaken orstrengthen.

FinalThoughtsAbove all, remember that the answers to Reading Comprehension questions arealways foundwithin the text.Whenyouencounterananswerchoice,alwaysverify itwiththeinformationinthepassage.

STEP3

CoverUptheAnswersforSentenceEquivalence

CoverUptheAnswersforSentenceEquivalenceDirections forSentenceEquivalencequestionsareas follows:Select the twoanswerchoicesthat,whenusedtocompletethesentence,fitthemeaningofthesentenceasawholeandproducecompletedsentencesthatarealikeinmeaning.

Inotherwords, figureout the storybeing toldandpick the twowords in theanswerchoices that complete the story in the same way. These are, in fact, SentenceCompletion questions, but you are picking two words rather than one for the sameblank.

The other part of Sentence Equivalence is the answer choices. They will always fitgrammaticallyintothesentence,andquiteafewofthemwillmakeadegreeofsense.They represent ETS’s suggestions for what to put in the blank. We don’t like theirsuggestions,wedon’ttrusttheirsuggestions,andwedon’twanttheirsuggestions.Theanswerchoiceshavebeencarefullyselectedandthentestedonthousandsofstudentsforthesolepurposeofmessingwithyourhead.ThefirststepinansweringSentenceEquivalence questions is to always cover up the answer choices. Literally. Put yourhandonthescreenanddon’tletthemshow.

Nowback to the sentence.Thinkof this asamini reading comprehensionpassage.Beforeyoudoanything, find themain idea.Who is thepassagetalkingabout?Whatareyoutoldaboutthispersonorthing?Onceyouhavethestoryfirmlyinmind,comeup with your own word for the blank, and eliminate the answer choices that don’tmatch.

Let’strythisquestion:

Wilsonworked__________onhis firstnovel, cloisteringhimself inhis studyfordaysonendwithoutfoodorsleep.

carelessly

assiduously

creatively

tirelessly

intermittently

voluntarily

Step1—Coveruptheanswerchoices.

Step2—Findthestory.Whoisthemaincharacter?Wilson.WhatareyoutoldaboutWilson?He’sworkingonhisfirstnovelandhaslockedhimself inhisstudyforalongtimewithoutfoodorsleep.Thedudeisworkinghard.Theblank,infact,describeshowWilsonisworking.

Step3—Comeupwithyourownwordfortheblank.Hard?Dedicated?Unceasing?

Step 4—Use Process of Elimination (POE). Use your word to eliminate answerchoices.Ofeachanswerchoice,askyourself,“Doesthiswordmeanthesamethingasorsimilarto__________(myword)?”Iftheanswerisno,getridofit.Iftheansweris“I’mnotsure,”giveitthe“maybe”andmoveon.Iftheanswerisyes,giveitthecheck.Allofthisworktakesplaceonyourscratchpaper.

(A) Doescarelesslymeanthesamethingasorisitsimilartohard,dedicated,orunceasing?No.Crossoff(A).

(B) Doesassiduouslymeanthesamethingasorisitsimilartohard,dedicated,orunceasing?Notsure?Giveitthequestionmarkandleaveitin.

(C) Doescreativelymeanthesamethingasorisitsimilartohard,dedicated,orunceasing?No.CouldWilson,thefirst-timenovelist,beworking“creatively”?Sure,butit’snotwhatyou’relookingfor.Crossoff(C).

(D) Doestirelesslymeanthesamethingasorisitsimilartohard,dedicated,orunceasing?Suredoes.Giveitacheck.

(E) Doesintermittentlymeanthesamethingasorisitsimilartohard,dedicated,orunceasing?Nope.Crossoff(E).

(F) Doesvoluntarilymeanthesamethingasorisitsimilartohard,dedicated,orunceasing?Nope.Crossoff(F).

Nowlookatyourscratchpaper.Youhavefourno’s,oneyes,andonequestionmark.You’re done.Whateverassiduouslymeans, itmust be similar tohard, dedicated, orunceasing.Thecorrectanswersaretirelesslyandassiduously.

FindingtheClueHowdid you know to puthard,dedicated, orunceasing in the blank?The sentencesays,“cloisteringhimselfinhisstudyfordaysonendwithoutfoodorsleep.”Whatelsecoulditbe?Thatpartofthesentenceiswhatwecallaclue.Everysentencewillhaveone.Everysentencemusthaveonebecauseit’sthepartofthesentencethatmakesoneanswercorrectandanotheroneincorrect.Theclueislikeanarrowthatpointsonly

torightanswers.Findingthecluewillhelpyoutocomeupwithyourownwordfortheblankandwillhelptoeliminatewronganswers.Nowtrythefollowingactivities.

Activity1Ineachofthefollowingsentences,findtheclueandunderlineit.Then,writedownyourownwordfortheblank.Itdoesn’tmatterifyourguessesareawkwardorwordy.Allyouneedtodoisexpressthecorrectidea.

1. Despitetheapparent____________ofthedemands,thenegotiationsdraggedonforoverayear.

2. MoststudentsfoundDr.Schwartz’slectureonartexcessivelydetailedandacademic;somethoughthisdisplayof____________exasperating.

Activity2Nowlookatthesamequestionsagain,thistimewiththeanswerchoicesprovided.Useyourwordsabovetoeliminateanswerchoices.

1. Despitetheapparent____________ofthedemands,thenegotiationsdraggedonforoverayear.

hastiness

intolerance

publicity

modesty

desirability

triviality

2. MoststudentsfoundDr.Schwartz’slectureonartexcessivelydetailedandacademic;somethoughthisdisplayof____________exasperating.

pedantry

fundamentals

logic

aesthetics

erudition

literalism

NowreviewtheanswerstoActivity2.

Question1:Theblankreferstothedemands.Theclueisthenegotiationsdraggedonforoverayear.ThewordDespiteindicatesacontrast,soagoodwordfortheblankissomethingthatindicatestheoppositeofwhatwouldbeexpectedtocausenegotiationstodragonforoverayear.Therefore,agoodwordfortheblankissomethingsuchas“smallness.”Check theanswerchoices forawordsimilar to “smallness.”Choice(A),hastiness,whichmeansastateofbeinghurried,doesnotmatch“smallness.”Eliminate(A).Choice(B), intolerance,meaningan inability toenduresomething,alsodoesnotmatch“smallness,”soeliminateit.Choice(C),publicity,whichmeanspublicattention,isnotagoodmatchfor“smallness,”soeliminateitaswell.Choice(D),modesty,isagoodmatchforsmallnessinthiscontext,sokeepit.Choice(E),desirability,meaningastate of being wanted, doesn’t match smallness. Eliminate (E). Choice (F), triviality,matches“smallness.”Keep(F).Thecorrectansweris(D)and(F).

Question 2: The blank refers to the display. The clue isMost students found Dr.Schwartz’s lectures on art excessively detailed and academic. The semicolon is asame direction transition and indicates that there isn’t a contrast in the sentence.Therefore,thecluecanberecycled,so“anexcessivelydetailedandacademiclecture”is a good choice for the blank. Choice (A), pedantry, is a good match for “anexcessively detailed and academic lecture,” so keep it. Choice (B), fundamentals,which means the basics, does not match “an excessively detailed and academiclecture.” Eliminate (B). Choice (C), logic, meaning reason, also does not match “anexcessively detailed and academic lecture,” so eliminate it. Choice (D), aesthetics,whichisthephilosophyofart,doesnotmatch“anexcessivelydetailedandacademiclecture.” Eliminate (D). Choice (E), erudition, is a good match for “an excessivelydetailed and academic lecture.” Keep (E). Choice (F), literalism, meaning an exactportrayal,doesnotmatch“anexcessivelydetailedandacademiclecture,”soeliminateit.Thecorrectansweris(A)and(E).

TransitionWordsImagine a conversation that begins, “That’s Frank. He won the lottery and now___________.” Something good is going to go into that blank. Frank could be amillionaire, livingonhisown island,oragreat collectorof rare jeweledbeltbuckles.Whateveritis,thisstoryisgoingtoendhappily.

Nowconsiderthisstory:“That’sFrank.Hewonthelotterybutnow___________.”Thisstoryisgoingtoendbadly.Frankcouldbetiedupincourtfortaxevasion,panhandlingonthecorner,orinamentalinstitution.

Theonly differencebetween these two stories is thewordsbut andand. These aretransitionwords.

They provide important structural indicators of themeaning of the sentence and areoftenthekeytofiguringoutwhatwordshavetomeantofillintheblanksinaSentenceCompletion. Some of themost important SentenceCompletion transitionwords andpunctuationarelistedbelow.

TransitionWords/Punctuationbut incontrastalthough(though,eventhough) unfortunatelyunless heretoforerather thusyet anddespite thereforewhile similarlyhowever ;or:

Paying attention to transition words is crucial to understanding the meaning of thesentence. Thewords frombut to heretofore are “change direction” transition words,indicating that the two parts of the sentence diverge inmeaning. The abovewords,fromthustothecolon(:)andsemicolon(;),are“samedirection”transitions,indicatingthat the two parts of the above sentence agree. For example, if your sentence said“Judywasa fairand___________ judge,” theplacementof the “and”would tellyouthat theword in theblankwouldhave tobesimilar to “fair.”Youcouldevenuse theword“fair”asyourfill-in-the-blankword.

Whatifyoursentencesaid,“Judywasafairbut___________judge”?Theplacementof the “but” would tell you that the word in the blank would have to be somewhatoppositeof“fair,”somethinglike“tough.”

Let’strythisquestion(we’vetakentheanswerchoicesawayagain,fornow):

Althoughoriginallycreatedfor____________use,thecolorful,stampedtinkitchenboxesoftheearlytwentiethcenturyarenowprizedprimarilyfortheirornamentalqualities.

What’s theclue in thesentencethat tellsyouwhytheboxeswereoriginallycreated?Well,youknowthatthey“arenowprizedprimarilyfortheirornamentalqualities.”Doesthismean that theywere originally created for “ornamental” use?No. The transitionword “Although” indicates that the word for the blank will mean the opposite of“ornamental.”Howabout“useful”?Itmaysoundstrangetosay“usefuluse,”butdon’tworryabouthowyourwordssound—it’swhattheymeanthat’simportant.

Now,herearetheanswerchoices:

utilitarian

traditional

practical

occasional

annual

commercial

(A) Doesutilitarianmean“useful”?Yes,giveitacheckonyourscratchpaper.(B) Doestraditionalmean“useful”?No.Crossitoffonyourscratchpaper.(C) Doespracticalmean“useful”?Yes,giveitacheckmark.(D) Doesoccasionalmean“useful”?Nope.Getridofit.(E) Doesannualmean“useful”?Nope,crossitoff.(F) Doescommercialmean“useful”?No.Crossitoff.

Theansweris(A)and(C).

Positive/NegativeIn somecases, youmay thinkof severalwords that couldgo in theblanks.Or, youmightnotbeabletothinkofany.Ratherthanspendingalotoftimetryingtofindthe“perfect”word,justaskyourselfwhetherthemissingwordwillbeapositivewordoranegativeword.Then,writea+ora–symbolonyourscratchpaperand take it fromthere.Here’sanexample(again,withoutanswerchoices,fornow):

Tremblingwithanger,thebelligerentcolonelorderedhismento____________thecivilians.

Use those clues. You know the colonel is “Trembling with anger,” and that he’s“belligerent” (which means war-like). Is the missing word a “good” word or a “bad”word? It’s a “bad” word. The colonel is clearly going to do something nasty to thecivilians. Now go to the answer choices and eliminate any choices that are positiveand,therefore,cannotbecorrect.

congratulate

promote

reward

attack

worship

torment

Choices (A), (B), (C), and (E) are all positive words; therefore, they can all beeliminated. The only negative words among the choices are (D) and (F), the bestanswers.Positive/negativewon’tworkforeveryquestion,butsometimesitcangetyououtofajam.

WhenitcomestoSentenceEquivalencequestions,rememberthesethreethings:

1. Investyourtimeinthesentence.Stickwiththesentenceuntilyoufindthestory.Youcannotgototheanswerchoicesuntilthatstoryiscrystalclear.

2. Useyourwordasyourfilter.Comeupwithyourownwordfortheblankanduseittoeliminateanswerchoices.Youshouldbeactivelyidentifyingandeliminatingwronganswers.Keepyourhandmovingonyourscratchpaper.Processingtheanswerchoicesshouldtakenomorethan20seconds.Note:Ifananswerchoicehasnosynonymamongtheotheranswerchoices,it’sunlikelytobecorrect.

3.Markandcomeback.Ifasentenceisn’tmakingsense,ornoneoftheanswerchoiceslookcorrect,moveon.Don’tkeepforcingthesentence.Youmayhavereadsomethingwrong.Godoafewotherquestionstodistractyourbrainandthentakeasecondlookatit.

STEP4

FillIntheBlanksforTextCompletion

FillIntheBlanksforTextCompletionQuestionsText Completions occupy a middle ground between Sentence Equivalence andReading Comprehension questions. You will be given a small passage—one to fivesentences—withone,two,orthreeblanks.Ifthepassagehasoneblank,youwillhavefive answer choices. If it has two or three blanks, you will be given three answerchoices per blank. You have to independently fill in each blank to get credit for thequestion.

Theoverallapproachisthesame.Ignoretheanswerchoices.Findthestorybeingtold(therewillalwaysbeastory),andcomeupwithyourownwordsfortheblanks.Here’swhatathree-blankTextCompletionwilllooklike:

SampleQuestionDirections:Foreachblank,selectoneentryfromthecorrespondingcolumnofchoices.Fillallblanksinthewaythatbestcompletesthetext.

Theimageofthearchitectasthelonelyartistdrawingthree-dimensionalformsis(i)____________thepublic’sunderstandingofthearchitect’srole.Asaresult,buildingsareviewedasthesingularcreationsofanartisticvisionwiththeartist(ii)____________thearchitect.Certainlyarchitectsshouldtakemuchofthecreditfortheformofauniquebuilding,butthefinalproductishardlya(iii)____________.Thearchitectreliesheavilyuponfaçadeconsultants,engineers,andskilledbuilders,whiletheformofthebuildingmaydepend,inaddition,uponzoningregulations,cost,andmarketdemands.

Step1—Findthestory.Inthiscase,thestoryisaboutthepublicperceptionoftheroleofthearchitectversustheactualroleofthearchitect.

Step2—Prepyourscratchpaper.Asopposed tocolumnsofA’s,B’s,C’s,D’s,E’s,andF’s,TextCompletionscratchpaperwilllooklikethis:

Step 3—Pick a blank. Some blankswill be easier to fill in than others. In general,blankshavetworoles.Theytesteithervocabularyorcomprehension.Ablanktestingvocabularymaybeeasy to fill inwith your ownwords, but then theanswer choicesmayconsistofdifficultvocabularywords.Ablanktestingcomprehensionmaydependuponwhatyouput inanotherblank,or itmaycontainmultiplewords, includingafewtransitionwordsandprepositions.Startwithwhicheverblankseemstheeasiest.Inthiscase,thelastblankmaybetheeasiest.

Step 4—Speak for yourself. The sentence contains the transition word “but.”Transition words are always significant. Sensitize yourself to transition words. Theyalwayscomeintoplay.Thepassagesaysthatthearchitectshouldgetlotsofcreditforabuilding,BUT…itisclearthatotherpeopleshouldgetsomecredittoo.Comeupwith

yourownwordsfortheblanks.Thefinalproductisclearlynot“thearchitectsalone.”

Step5—UsePOE.Thereare threechoices. “Virtuosoperformance”sounds like “thearchitectsalone.”Keepitin.“Collaborativeeffort”istheoppositeofwhatwe’relookingfor.Get rid of it. “Physical triumph” introduces a new concept to the sentence. Thatautomaticallyknocksitout.Acorrectanswerchoicewillalwaysbesupportedbyproofin the passage. An answer choice that adds something new to the sentence(physicality,inthiscase)isautomaticallywrong.Atthispoint,thestoryinthesentenceis quite clear, and your scratch paper should look like the example on the followingpage.

Step6—RinseandRepeat.Forthefirstblank,thewaybuildingsareviewedshouldbesimilartothewayarchitectsareviewed.Evenifyoucan’tcomeupwithawordforthefirstblank,youatleastknowthatyouneedsomethingthatkeepsthesentencegoinginthesamedirection.Ofthethreechoices,“atoddswith”clearlychangesthedirection,sogetridofit.“Irrelevantto”isneutralatbest,sogetridofit.“Centralto”istheonlyanswerchoiceinthesamedirection.Giveitacheck.

For thesecondblank, thinking in termsofdirectionwillworkwellagain. In thisstory,whatistherelationshipbetweenthe“artist”andthe“architect”?Thetwoseemtoservethesamefunction.Youneedananswerchoicethatindicatesequivalence.“Justifiablyembodiedby”istheclosestthingintheanswerchoicestoanequalssign.

Here’swhatyourscratchpapercouldlooklike:

Thatmayseemlikealongprocess,butit’sreallyjustawayofthinking.Findthestory.Playcloseattentiontotransitionwords.Comeupwithwordsfortheblankorestablishdirection.Keepthehandmovingandeliminate.

Tryonemore.

Despitehundredsof(i)____________attemptstoproduceaworkinglightbulb,Edisoneventuallytriumphed,his(ii)____________contributingtohisultimatesuccess.

Blank(i) Blank(ii)felicitous grandiloquencestymied indifferenceauspicious tenacity

Who’s the main character and what’s the story being told? The sentence is aboutEdisonandhisattemptstomakeaworkinglightbulb.Therearetwokeywordsinthissentence, “Despite” and “eventually.” “Despite” tells you that the sentence has tochange direction and “eventually” tells you that it took a long time. The end of thesentencedescribeshis“ultimatesuccess,”sothebeginningmustcontainsomefailure.Put“failed”inforthefirstblankandeliminate.Felicitous(thinkfelicity)andauspicious

arebothpositivewords,socross themoff.Stymiedstays in.Youalsoknow that theprocesstookalongtime,soEdisonmusthavebeenthekindofguywhodoesn’tgiveup.Put“stickwithit-ness”inforthesecondblank.Youdon’thavetoputaperfectETSwordintheblank.Anythingthatcapturesthemeaningorideawilldo.Grandiloquencehas todowith thewayyou talk,which isnotwhatyou’re looking for, socross it off.Indifference does not mean stubbornness, so get rid of it. You’re down to one, soyou’redone.

Hereareafewkeyconceptstokeepinmind.

1. ScratchPaper—Usingscratchpaperfavorsanefficient“maybeorgone,”two-passapproachthroughtheanswerchoices.WithTextCompletionquestionsthereareeffectivelysixtonineanswerchoicesratherthanfive.Scratchpaperiscrucial.

2. Clues—InaregularSentenceCompletionquestion,ifthewordintheblankisanoun,someotherpartofthesentencewilldescribethenoun.Ifitisaverb,therewillbesomeotherpartofthesentencedescribingthesubjectorobjectofthatverb.Ifitisanadjective,therewillinvariablybesomeotherpartofthesentencedescribingthenounthattheadjectiveismodifying.Thisistheessenceofwhatmakesaclueaclue.Thesameconceptholdstrueherebutonaslightlylargerscale.Whateverinformationismissinginonesentencemustbepresentinanotherone.Itistheonlywayfortheretobeanidentifiablycorrectanswer.Iftheconceptofthecluefeelstooabstract,thinkofitasthestorybeingtold.Everysentencewilltellastory.Whoisthemaincharacter,whatisthemaincharacterdoing,andwhatareyoutoldaboutthemaincharacter?Ifyoudon’thavethestoryfirmlyinfocus,you’reintrouble.TheanswerchoicesrepresentETS’ssuggestionsforwhattoputintheblank.Infact,theanswerchoiceshavebeenpainstakinglyselectedandtestedwiththesolepurposeofmessingwithyourhead.Unlessyoucanphysicallyputyourfingeronaclueorkeysentence,youareatthemercyofETSandtheanswerchoices.

3. DirectionalVersusVocabulary—Itisalwayspreferable,ormoreexact,tocomeupwithyourownwordsfortheblank.Whilesometimesnecessaryoreveneffective,simplydecidingwhetherablankcallsfora“good”wordor“bad”wordcanbeacrutchforthelazy.WithTextCompletionquestions,however,theanswerchoicesmaybeallaboutwhetherthetextwillkeepthesentencemovinginthesamedirectionortheoppositedirection.Inotherwords,itisoftenthetransitionwordsorphrasesthatyouarebeingaskedtosupply.Withonlythreeanswerchoices,simplyidentifyingeitherthenecessarydirectionorneedforapositiveornegativewordmaytakecareofalloftheeliminationyouneedtogetitdowntooneanswerchoice.

STEP5

KnowYourMathVocabulary

KnowYourMathVocabularyETSsays that theMathsectionof theGRE tests the “ability to reasonquantitativelyand to model and solve problems with quantitative methods.” Translation: It mostlytestshowmuchyourememberfromthemathcoursesyoutookinseventh,eighth,andninthgrades.Asyoumightknow,manypeoplestudylittleornomathincollege.IftheGRE tested “college-level”math, everyone butmathmajors would bomb. So, juniorhighmathitis.Bybrushinguponthemodestamountofmathyouneedtoknowforthetest,youcansignificantlyincreaseyourGREMathscore.

So, ETS is limited to the math that nearly everyone has studied: arithmetic, basicalgebra,basicgeometry,andbasicstatistics.There’snocalculus(orevenprecalculus),notrigonometry,andnoadvancedalgebraorgeometry.Becauseof these limitations,ETShastoresorttotricksandtrapsinordertocreatehardproblems.Eventhemostdifficult GRE Math problems are typically based on pretty simple principles; whatmakessomedifficultisthatthesimpleprinciplesaredisguisedwithtrickywording.Inaway,thisismoreofareadingtestthanamathtest.

KeyMathTermsVocabularyintheMathsection?Well,iftheMathsectionisjustareadingtest,theninordertounderstandwhatyouread,youhavetoknowthelanguage,right?

Quick—what’s an integer? Is 0 even or odd? How many even prime numbers arethere?Thesetermslookfamiliar,butit’sbeenawhile,right?(We’vesortedthetermsinalphabeticalorder,butfeelfreetoskiparound.)Reviewthevocabbelow.

• Consecutive—Integerslistedinorderofincreasingvaluewithoutanyoftheintegersinbetweenmissing.Forexample:−3,−2,−1,0,1,2,3.

• Decimals—Whenyou’readdingorsubtractingdecimals,justpretendyou’redealingwithmoney.Simplylineupthedecimalpointsandproceedasyouwouldifthedecimalpointsweren’tthere.

34.50087.000123.456+0.980245.936

Subtractionworksthesameway:17.66−3.214.46

Tomultiply,justproceedasifthedecimalpointsweren’tthere.Thenputinthedecimalpointafterward,countingthetotalnumberofdigitstotherightofthedecimalpointsinthenumbersyouaremultiplying.Then,placethedecimalpointinyoursolutionsothatyouhavethesamenumberofdigitstotherightofit:

3.451×8.930.7139

Thereareatotalof4digitstotherightofthetwonumbersbeingmultipliedabove,sotherearefourdecimalplacesinthesolution.Exceptforplacingthedecimalpoint,thisisexactlywhatyouwouldhavedoneifmultiplying3,451and89.Todivide,setuptheproblemasafraction,thenmovethedecimalpointinthedivisor(akathenumberyouaredividingby)allthewaytotheright.Thenmovethedecimalpointinthenumberbeingdividedthesamenumberofplacestotheright.Forexample:

RememberthattheGREhasanon-screencalculator.Youcanworkthroughmostproblemsinvolvingdecimalssimplybyusingthecalculator.

• Difference—Theresultofsubtraction.• Digit—Thenumbers0,1,2,3,4,5,6,7,8,and9.Justthinkofthemasthenumbersonyourphone.Thenumber189.75hasfivedigits:1,8,9,7,and5.Fiveisthehundredthsdigit,7isthetenthsdigit,9istheunitsdigit,8isthetensdigit,and1isthehundredsdigit.

• Distinct—Different.Forexample,theinteger123has3distinctdigits,whiletheinteger122has2distinctdigits.

• Divisible—Whenoneintegerisdivisiblebyanother,theresultisalsoaninteger.Forexample,6isdivisibleby3becausetheresultis2,aninteger.Anintegerisdivisibleby2ifitsunitsdigitisdivisibleby2.Anintegerisdivisibleby3ifthesumofitsdigitsisdivisibleby3.(Forexample,123isdivisibleby3because1+2+3=6and6isdivisibleby3.)Anintegerisdivisibleby5ifitsunitsdigitiseither0or5.Anintegerisdivisibleby10ifitsunitsdigitis0.

• Even/Odd—Anevennumberisanyintegerthatcanbedividedevenlyby2(like4,

8,and22);anyintegerisevenifitsunitsdigitiseven.Anoddnumberisanyintegerthatcan’tbedividedevenlyby2(like3,7,and31);anyintegerisoddifitsunitsdigitisodd.Putanotherway,evenintegershavearemainderof0whendividedby2whileoddintegershavearemainderof1whendividedby2.Herearesomerulesthatapplytoevenandoddintegers:Even+even=even;odd+odd=even;even+odd=odd;even×even=even;odd×odd=odd;even×odd=even.Whatifyouaren’tsureabouttherule?Justtrysomenumbers.Forexample,even+evenisevenbecause2+4=6,whichiseven.Don’tconfuseoddandevenwithpositiveandnegative.Thetermsevenandoddapplyonlytointegers,sofractionsareneitherevennorodd.

• Exponent—Exponentsareasortofmathematicalshorthand.Insteadofwriting(2)(2)(2)(2),write24.Thelittle4iscalledan“exponent”andthebig2iscalleda“base.”Thereareprimaryexponentrules.WecallthesetheMADSPMrules.MADSPMstandsforMultiply-Add,Divide-Subtract,andPower-Multiply.Here’showitworks.Tomultiplyexponentexpressionsthathavethesamebase,addtheexponents.Forexample,22×24=22+4=26and(x3)(x4)=x3+4=x7.

Todivideexponentexpressionsthathavethesamebase,subtracttheexponents.

Forexample,26÷24=26−4=22and =x7−4=x3.

Whenanexponentexpressionisraisedtoapower,multiplytheexponents.Forexample,(22)3=22×3=26and(x3)4=x3×4=x12.Ifyouareeverunsureofoneoftheserules,justremember:Whenindoubt,expanditout.Forexample,22×24=(2)(2)×(2)(2)(2)(2)=26.

HereAreSomeAdditionalExponentRules

Raisinganumbergreaterthan1toapowergreaterthan1resultsinabiggernumber.Forexample,22=4.

Raisingafractionbetween0and1toapowergreaterthan1resultsinasmallernumber.Forexample, 2=

Anegativenumberraisedtoanevenpowerresultsinapositivenumber.Forexample,(−2)2=4.

Anegativenumberraisedtoanoddpowerresultsinanegativenumber.Forexample,(−2)3=−8.

Whenyouseeanumberraisedtoannegativeexponent,justputa1overitandgetridofthenegativesign.Forexample,(2)−2= ,

which= .

• Factor—Integeraisafactorofintegerbiftheresultwhenbisdividedbyaisaninteger.Forexample,1,2,3,4,6,and12areallfactorsof12becausetheresultwhen12isdividedbyanyoftheseintegersisalsoaninteger.Allnumbers,evenprimenumbers,haveatleasttwofactors:oneandthenumberitself.Tofindfactors,it’sbesttolistthefactorsinpairs.Forexample,thefactorsof24are1and24,2and12,3and8,and4and6.Youknowyou’vefoundallthefactorswhentherearenointegersbetweenthelastpairoffactorsthatalsodivideevenlyintoyourstartingnumber.

• Fractions—Afractionisjustshorthandfordivision.OntheGRE,you’llprobablybeaskedtocompare,add,subtract,multiply,anddividefractions.Tomultiplyfractions,justmultiplythenumerators(thetopsofthefractions)anddenominators(thebottomsofthefractions)straightacross.

Todivide,youmultiplybythesecondfraction’sreciprocal;inotherwords,turnthesecondfractionupsidedown.Putitsdenominatoroveritsnumerator,thenmultiply:

Ifyouwereaskedtocompare and ,allyouhavetodoismultiplydiagonallyup

fromeachdenominator,asshown:

Now,justcompare42to49.Because49isgreater,thatmeans isthegreater

fraction.ThistechniqueiscalledtheBowtie.YoucanalsousetheBowtietoaddor

subtractfractionswithdifferentdenominators.Justmultiplythedenominatorsofthe

twofractions,andthenmultiplydiagonallyupfromeachdenominator,asshown:

Ifthedenominatorsarethesame,youdon’tneedtheBowtie.Youjustkeepthesamedenominatorandaddorsubtractthenumerators,asshownbelow.

• Integer—Integersarewholenumbers.Integerscanbepositiveornegative.Zeroisalsoaninteger.Allofthefollowingareintegers:−5,−4,−3,−2,−1,0,1,2,3,4,5,6.Notethatfractions,suchas ,arenotintegers.Neitheraredecimals.

• Multiple—Amultipleofanumberisthatnumbermultipliedbyanintegerotherthan0.10,20,30,40,50,and60areallmultiplesof10.

• Nonnegative—Allthepositivenumberspluszero.IfETSusesthistermratherthanpositive,itwillbeimportanttoremembertothinkaboutzero.

• Orderofoperations—AlsoknownasPEMDAS,orPleaseExcuseMyDearAuntSally.Parentheses>Exponents>Multiplication=Division>Addition=Subtraction.Thisistheorderinwhichtheoperationsaretobeperformed.Forexample:

10–(6−5)–(3+3)−3=Startwiththeoperationsinsidetheparentheses.Theoperationinsidethefirstpairofparentheses,6−5,equals1.Theoperationinsidethesecondpairequals6.Nowrewritetheproblem,asshownbelow.

10−1−6−3=9−6−3=3−3=

=0

Here’sanotherexample:Sayyouwereaskedtocompare(3×2)2and(3)(22).(3×2)2=62,or36,and(3)(22)=3×4,or12.Notethatwithmultiplicationanddivision,youjustgolefttoright(hencethe“=”signinthedescriptionofPEMDASabove).Samewithadditionandsubtraction.Inotherwords,iftheonlyoperationsyouhavetoperformaremultiplicationanddivision,youdon’thavetodoallmultiplicationfirst,becausemultiplicationanddivisionareequivalentoperations.Justgolefttoright.

• Positive/Negative—Positivenumbersincreaseastheymoveawayfromzero(6isgreaterthan5);negativenumbersdecreaseastheymoveawayfromzero(−6islessthan−5).Notethatzeroistheonlynumberthatisneitherpositivenornegative.Positive×positive=positive;negative×negative=positive;positive×negative=negative.Becarefulnottoconfusepositiveandnegativewithoddandeven.

• Prime—Aprimenumberisanumberthatisevenlydivisibleonlybyitselfandby1.Zeroand1arenotprimenumbers,and2istheonlyevenprimenumber.Otherprimenumbersinclude3,5,7,11,and13(buttherearemanymore).

• Primefactors—Primefactorsarefactorsofanumberthatarealsoprime.Forexample,theprimefactorsof12are3and2.Tofindprimefactors,useafactortree.

• Probability—Probabilityisequaltotheoutcomeyou’relookingfordividedbythetotaloutcomes.Ifitisimpossibleforsomethingtohappen,theprobabilityofithappeningisequalto0.Ifsomethingiscertaintohappen,theprobabilityisequalto1.Ifitispossibleforsomethingtohappen,butnotnecessary,theprobabilityisbetween0and1.Forexample,ifyouflipacoin,what’stheprobabilitythatitwilllandon“heads”?Oneoutoftwo,or .Whatistheprobabilitythatitwon’tlandon

“heads”?Oneoutoftwo,or .

• Product—Theresultofmultiplication.• Quotient—Theresultofdivision.• Reducingfractions—Toreduceafraction,“cancel”orcrossoutfactorsthatarecommontoboththenumeratorandthedenominator.Forexample,toreduce ,

justdivideboth18and24bythegreatestcommonfactor,6.Thatleavesyouwith .Ifyoucouldn’tthinkof6,both18and24areeven,sojuststartcuttingeachinhalf(orinthirds)untilyoucan’tgoanyfurther.Andremember—youcannotreducenumbersacrossanequalssign(=),aplussign(+),oraminussign(–).

• Remainder—Theremainderisthenumberleftoverwhenoneintegercannotbedividedevenlybyanother.Theremainderisalwaysaninteger.Remembergradeschoolmathclass?It’sthenumberthatcameafterthebig“R.”Forexample,the

remainderwhen7isdividedby4is3because4goesinto7onetimewith3leftover.ETSlikesremainderquestionsbecauseyoucan’tdothemonyourcalculator.

• Squareroot—Thesign indicatesthesquarerootofanumber.Forexample,meanstofindthenumberthatmultipliedbyitselfequals2.Youcan’taddorsubtractsquarerootsunlesstheyhavethesamenumberundertherootsign( + doesnotequal ,but + =2 ).Youcanmultiplyanddividethemjustlikeregularintegers:

Youwillhaveasquarerootsymbolonyourcalculator,butitisofteneasierifyouknowthevaluesofsomecommonlyusedroots.Hereareafewsquarerootstorememberthatmightcomeinhandy:

Note:Ifyou’retoldthatx2=16,thenx=±4.YoumustbeespeciallycarefultorememberthisonQuantitative

Comparisonquestions.Butifyou’reaskedforthevalue,youarebeingaskedforthepositiverootonly,sotheansweris4.Asquarerootisalwaysnonnegative.

• Standarddeviation—Thestandarddeviationofagroupofdatapointsisameasureofthegroup’svariationfromitsmean.You’llrarely,ifever,havetoactuallycalculatethestandarddeviation,sojustrememberthis:Thegreaterthestandarddeviation,

themorewidelydispersedthevaluesare.Thesmallerthestandarddeviation,themorecloselygroupedthevaluesarearoundthemean.Forexample,thestandarddeviationofthenumbers6,0,and6isgreaterthanthestandarddeviationofthenumbers4,4,and4,because6,0,and6aremorewidelydispersedthan4,4,and4.

• Sum—Theresultofaddition.• Zero—Anintegerthat’sneitherpositivenornegativebutiseven.Thesumof0andanyothernumberisthatothernumber;theproductof0andanyothernumberis0.

QuantitativeComparisonThere are four question formats on the Math section: five-choice Problem-Solvingquestions, four-choice Quantitative Comparisons (or quant comps), All that Applyconsistingof three toeightanswerchoices,andNumericEntry inwhichyouhave totypeyourownanswerintoabox.AQuantCompisamathquestionthatconsistsoftwoquantities,one inQuantityAandone inQuantityB.Youcompare the twoquantitiesandchoose:

(A) QuantityAisgreater.

(B) QuantityBisgreater.

(C) Thequantitiesareequal.

(D) Therelationshipcannotbedeterminedfromtheinformationgiven.

Quant Comps have only four answer choices. That’s great: A blind guess has onechanceinfourofbeingcorrect.So,theoddsofguessingcorrectlyonaQuantCompstart off better than the odds for guessing correctly on a Problem-Solving question.AlwayswriteA,B,C,D (but noE) on your scratch paper so that you can cross offwronganswerchoicesasyougo.ThecontentofQuantCompproblemsisdrawnfromthesamebasicarithmetic,algebra,andgeometryconceptsthatareusedonGREMathproblemsinotherformats.Ingeneral,then,you’llapplythesametechniquesthatyouuse on other types of math questions. Still, Quant Comps do require a few specialtechniquesoftheirown.

ThePeculiarBehaviorofChoice(D)There are only two optionswhen two numbers are compared.Either one number isgreater than the other or the two numbers are equal. So,when both quantities in aQuant Comp problem contain numbers, it’s always possible to determine the

relationship.Therefore,thefourthbubble,or(D),canbeeliminatedimmediatelyonallsuchproblems.Forexample:

QuantityA QuantityB

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

Youknowtheanswercanbedetermined,sotheanswercouldneverbe(D).Sorightoff thebat,assoonasyouseeaQuantComp that involvesonlynumbers, youcaneliminate(D)onyourscratchpaper.Theanswertothisoneis(B),bytheway.UsetheBowtiesoyouendupwith8versus9.

CompareBeforeYouCalculateYou don’t always have to figure out the exact values for both columns tomake thecomparison.Theprimedirectiveistocomparethetwocolumns.FindingETS’sanswerfrequently is merely a matter of simplifying, reducing, factoring, or expanding. Forexample:

QuantityA QuantityB

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

First,eliminate(D),becausethereareonlynumbersinbothcolumns.Then,noticethat

there are fractions common to both columns; both contain and . If the same

numbersare inbothcolumns, theycan’tmakeadifferenceto thetotalvalue.So just

crossthemoff(aftercopyingdowntheproblemonyourscratchpaper,ofcourse).Now,

what’sleft?QuantityAis ,andQuantityBis .Allyouhavetodonowiscompare to

.UsetheBowtietoget(B).

STEP6

TurningAlgebraintoArithmetic

TheProblemwithGREAlgebraImaginegoingtoacandystorytopurchase10piecesofcandyfor5centseach.Howmuchchangewouldyougetifyougavetheclerkaone-dollarbill?

Theanswerisobviously50cents.Evenifthenumberswerealittlemoredifficult,thearithmetictosolvetheproblemisprettysimple.Forinstance,ifyoupurchase8piecesofcandyfor30centseachandyougivetheclerkafive-dollarbill,howmuchchangewouldyoureceieve?Theprocesstofindtheanswerisexactlythesameasbefore.Youwouldstillmultiply8piecesofcandyby30centsandsubtract thatproduct from fivedollarstoget$2.60.Sinceweuseoperationslikethisonadailybasis,it’scommontothinkintermsofactualnumbersbecausearithmeticismorecomfortable.

However, GRE questions often do not use actual numbers. Instead, test takers areofferedvariablesandthesimplequestionsdescribedabovearewrittenmorelike:

IfSydneygoestoacandystoretopurchaseppiecesofcandyforccentseachandpaystheclerkddollars,thenwhatisherchange?

Acommonapproach to thisalgebraquestionwouldbe tomultiplypandc and thensubtractthatproductfromd,aswedidintheearlierproblems.Thiswouldgiveusd−pc,whichwouldbewrongbecause it doesnotaccount for converting thecents intodollars. Try it out using the numbers from the first example if you don’t believe us.Replacepwith10,cwith5,anddwith1.Theresultingexpressionis1–(10)(5),whichequals−49.

However, you can be sure that the GRE would have d − pc as a possible answerchoicethatmanytesttakerswouldchoose,neverrealizingitisnotthecorrectanswer.Because we rarely do algebra, we’re more prone to make mistakes that are easilyavoidablewhenusingarithmetic.

Consideringwe’rebetteratarithmeticthanweareatalgebra,itisinourbestinteresttoturnalgebraproblems intoarithmetic!Todo this,simplyPlug In realnumbers for thevariables in algebra problems. Performing addition, subtraction, multiplication, anddivisionoperations,aswedidintheversionsofthecandystoreproblemthatusedrealnumbers, was far simpler than thinking in terms of variables. Anytime you see analgebraquestionon theGRE,be ready touseactualnumbers rather thanvariables.Here’sanexample:

KylehasfourfewertoysthanScottbutsevenmoretoysthanJody.IfKylehask

toys,thenhowmanytoysdoScottandJodyhavetogether?

2k+11

2k+7

2k+3

2k−3

2k−11

Step1—Recognizetheopportunity.Whenvariablesappear in theanswerchoices,bereadytoPlugIn.

Step 2—Set up your scratchpaper.WriteA,B,C,D, andE in a column on yourscratchpaper.

Step3—PlugInaneasynumber.Sinceit’seasiertothinkoftentoysthanitistothinkofktoys,PlugInanumberforthevaluek.Besuretochooseanumberthatwillmakethemath easy, such as 2, 5, 10, or 100. Let’s say k = 10.Write this down on thescratchpaper.

Step 4—Work the problem. Nowwork the problem. Kyle has four fewer toys thanScotthas.IfKylehas10,thenScotthas14.Writedowns=14onthescratchpaper.Kylehas7moretoysthanJodihas.Therefore,Jodihasthreetoys.Writej=3onthescratchpaper.

Step5—Circlethetargetnumber.Thetargetnumberisthenumberthatthequestionultimatelyasksfor.Inthiscase,thequestionasks,“HowmanytoysdoScottandJodyhave together?”SinceScotthas14andJodihas3, the targetnumber is17.Write itdownandcircleit.

Step6—Checkalltheanswerchoices.Anywherethereisakintheanswerchoices,PlugIn10.Remembertolookforananswerchoicetoequal17,thetargetnumber.

(A) 2(10)+11=31.Nope.Crossitoff.(B) 2(10)+7=27.Nope.Crossitoff.(C) 2(10)+3=23.Nope.Crossitoff.(D) 2(10)−3=17.Thislooksgood,butalwayscheckallanswerchoices.(E) 2(10)−11=9.Nope.

Theansweris(D).Here’swhatyourscratchpapercouldlooklike:

HereareacoupleofthingstokeepinmindaboutPluggingIn:

• Doallworkonthescratchpaper.Whenyou’redone,youshouldseeallvariablesgivennumericvalues,atargetnumbercircled,andallanswerchoiceschecked.

• Keepthematheasy.IfyouPlugInanumberandthemathgetscomplicated,don’tpanic;justchangethenumberthatyouPluggedIn.

• Checktoseeifmorethanoneanswerchoiceworks.Ifso,PlugInanewnumber,findanewtargetnumber,andonlychecktheanswerchoicesthatremain.Continuethisprocessuntilthereisonlyoneanswerchoiceleft.

• KnowwhatnottoPlugIn.AvoidPluggingIn0,1,thesamenumberformultiplevariables,ornumbersthatyoufindinthequestion.Thesenumbersarenotnecessarilygoingtogiveyouthewronganswer,buttheyaremorelikelytoyieldtwoanswerchoicesthatmatchthetargetnumber.ThiswillthenforceyoutodomoreworkbyPluggingInagain.

PluggingInonQuantitativeComparisonsYou will also see Quantitative Comparison questions with unknown quantities. UsetheseopportunitiestoPlugIn,aswell.

y≠0

QuantityA QuantityB−10y –y

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

Step1—Recognizetheopportunity.ThefirstthingtonoticeisthatitisaQuantitativeComparisonproblem.Thesecondthingtonoticeisunknownquantities.ThisindicatesthatitisaQuantCompPlugInquestion.

Step2—Setupyourscratchpaper.WriteA,B,C,andDhorizontallyonthescratchpaper, with columns forQuantity A andQuantity B on either side, as shown on thescratchpaperonthefollowingpage.

Step 3—Plug In an easy number. Make y = 2. This would transform the value ofQuantityAfrom−10yinto−20andthevalueofQuantityBfrom−yinto−2.WritethesedownintheQuantityAandQuantityBcolumnsonthescratchpaper.

Step4—EliminatetwoofanswersA,B,andC.Determinethatthegreatervalueis−2,which isQuantityB.ClearlyQuantityA isnotalwaysgoingtobegreater,norwilltheanswersalwaysbeequal.Therefore,eliminate (A)and (C).Thisstepwillalwaysleadtotheeliminationoftwoanswerchoices.Nowdeterminewhether(B)isalwaysthegreatervalue.

Step5—RepeatusingFROZEN.AfterPluggingInaneasynumber,testoutwhether(B)willalwaysbecorrectbyusingtrickiernumbers.Toknowwhichtrickynumberstouse,thinkoftheacronymFROZEN.Itstandsforalltheweirdnumbersthatyoumightnormally shy away from, or not think of, when Plugging In the first time: Fractions,Repeats from theproblem,One,Zero,Extremenumbers, andNegatives.DeterminewhichofthesetypesofnumbersmightyieldavalueofQuantityBthatislessthanthatofQuantityA.Sincetheproblemasksaboutnegativenumbers,thatisagoodplacetostart.Makey=−2.QuantityAisnow20,whileQuantityBis2.QuantityAisgreater,soeliminate(B).Thecorrectansweris(D).

Hereiswhatyourscratchpapercouldlooklike:

Besure to keepPlugging Inuntil youhaveeliminated (A), (B), and (C)or youhavetried enough types of FROZEN numbers to reasonably conclude an answer. If aftergoingthroughanumberofFROZENnumbers,and(A),(B),or(C)remains,itislikelythecorrectanswer.

Tryonemore:0<x<100<y<1

QuantityA QuantityBx–y 9

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

Step1—Recognizetheopportunity.Thereareunknownquantities(xandy),sothisisanopportunitytoPlugIn.

Step2—Setupyourscratchpaper.WriteA,B,C,andDhorizontallyonthescratchpaper,withcolumnsforQuantityAandQuantityBoneitherside.

Step3—PlugInaneasynumber.Onthisproblem,therearerangesforxandy,soPlugInthegreatestxandtheleastytofindthemaximumrangeforx−y.Makex=9andy=0.1.QuantityAnowequals8.9andQuantityBequals9.

Step4—EliminatetwoofanswersA,B,andC.SinceQuantityBisthegreatervalue,eliminate(A)and(C).

Step 5—Repeat using FROZEN. Consult the FROZEN numbers to find a way toeliminate(B).Afractionandarepeatednumberfromtheproblem(inthiscase,9)havebeenused.Zeroandnegativenumbersarenoteligibleaccordingtotheconstraintsoftheproblem.Tryextremenumbers.Thevalueofx has tobe less than10, so9.9 isaboutasextremeasxcanbe.Makex=9.9andy=0.1,andx−ywillnowequal9.8,whichisgreaterthan9.Eliminate(B)andchoose(D).

MustBeThereareotherquestionsbesidesQuantitativeComparisons thatmayrequireyou toPlugInmorethanoncebeforeyoufindthecorrectanswer.Takealookatthisquestion.

Thepositivedifferencebetweenthesquaresofanytwoconsecutiveintegers,xandx+1,mustbe

thesquareofaninteger

amultipleof5

aneveninteger

anoddnumber

aprimenumber

Thephrase“mustbe”isacluetoletyouknowthatnotonlyareyougoingtohavetoPlugIn,butyouwillalsolikelyhavetodoitmorethanonce.Inthatrespect,youcantreatthesethesamewayyoudoQuantitativeComparisons.

Step1—Recognizetheopportunity.Thephrase“mustbe”inaquestionisatriggerthatindicatesaPlugInquestion.

Step2—Setupyourscratchpaper.Afterseeing“mustbe,”markdownA,B,C,D,andEinaverticalcolumn.Totherightofyourcolumn,leavespacesforthevariables.Itcouldlooklikethis:

Step3—PlugInaneasynumber.Tryx=2.Ifx=2,thenx+1=3.

Step 4—Eliminate incorrect answer choices. The squares are 4 and 9, and thepositivedifferenceis5.Choice(A)doesnotwork,soeliminateit.Choice(B)works,sokeepit.Eliminate(C)sinceitdoesnotwork.Choices(D)and(E)bothwork,sokeepthem.

Step5—RepeatusingFROZEN.Since“mustbe”isacluetoPlugInmorethanonce,PlugInagainusingFROZENnumberstotryandeliminatemoreanswerchoices.Tryanextremenumber,suchasx=10.WhenPlugging In10, thesquaresare100and121.Thedifferenceis21.Choice(B)nolongerworks,soeliminateit.Keep(D)sinceitstillworks.Andeliminate(E),whichdoesnotwork.Theonlyanswerchoiceremainingis(D),whichisthecorrectanswer.Yourscratchpapercouldlooklikethis:

PITAThere is one more kind of Plugging In strategy. It is called PITA, which stands forPluggingIntheAnswers.ItisoneofthemostpowerfultypesofPluggingInbecauseitcan take some of the hardest problems on the GRE and turn them into simplearithmetic.Thehardest thingabout this technique,however, is rememberingwhen touseit.Takealookatthisquestion:

Twopositiveintegers,xandy,haveadifferenceof15.Ifthesmallerinteger,y,

is ofx,thenwhatisthevalueofy?

40

25

20

15

10

Step1—Recognizetheopportunity.TherearewaystoknowifacertainproblemisagoodcandidatetoPlugIntheAnswers:

• thequestionasksforaspecificamountthattheanswerchoicesrepresent• thequestionsask“howmany”or“howmuch”• itseemsappropriatetowriteandsolveanalgebraicequation

Step 2—List the answer choices on your scratch paper.Write down the answerchoices(inthiscase40,25,20,15,and10)inaverticalcolumn.

Step3—Labeltheanswerchoices.Thequestionasks,“Whatisthevalueofy?”Theanswerchoices,therefore,representpotentialvaluesfory.Labelthefirstcolumn(theonewiththeanswerchoices)“y.”

Step4—PlugIn(C).Sincetheanswerchoicesarelistedinascendingordescendingorder,itwillbehelpfultostartwith(C).Assumeforamomentthatthemiddlevalueisthecorrectanswerchoice.Ify=20,thenwhatelsewouldbetrue?

Step5—Work theproblem inbite-sizedpieces,makinganewcolumn foreachnewstep.Theproblemsaysthatyis ofx.Soify=20,thenx=32.Makeacolumnlabeled“x”andwrite32inthecolumnnexttothe20.

Step6—POE.Whatwould have to happen for (C) to be the correct answer?Theremustbeadifferenceof15betweenxandy.With(C),thereisadifferenceof12.Crossoff (C).Becausethedifferenceneedstobegreater, thenumbersneedtobegreater.Therefore,alsoeliminate(D)and(E),asthosechoicesarelessthan(C).Thisiswhyitis useful to start PITA problems with (C). Because the answer choices are listed ineitherascendingordescendingnumericalorder,if it’spossibletodeterminethevalueof(C) iseithergreateror lessthanneeded, it’salsopossibletoeliminatetheanswerchoicesthataregreaterorlessthan(C).Atthispoint,onlytwoanswerchoicesremain.Treatthecolumnslikeaspreadsheetfortheremaininganswers.Fill intherestoftherowfor(B)wherey=25.Movingright, it isevident thatx=40.Thedifference is15,whichisexactlywhatthequestionislookingfor.WithPITAquestions,onlyoneanswerchoicecanwork,sothereisnoneedtocheckouteveryanswerchoice.Choice(B)iscorrect.Hereiswhatyourscratchpapercouldlooklike:

Tryonemore.

Vicken,Roger,andAdambuya$90radio.IfRogeragreestopaytwiceasmuchasAdamandVickenagreestopaythreetimesasmuchasRoger,howmuchmustRogerpay?

$10

$20

$30

$45

$65

Step 1—Recognize the opportunity. The question asks “How much must Roger

pay?”Recallthatwhenhowmuchandhowmanyshowupinaquestion,besuretosetupthescratchpaperforPITA.

Step2—List theanswerchoicesonyourscratchpaper.List$10,$20,$30,$45,and$65inaverticalcolumn.

Step3—Labeltheanswerchoices.Whatdothosenumbersrepresent?TheamountRogerpays.LabelthisfirstcolumnRoger(or“R”forshort).

Step4—PlugIn(C).AssumeRogerpays$30.

Step5—Work theproblem inbite-sizedpieces,makinganewcolumn foreachnewstep.IfRogerpays$30,thenAdampays$15.MakeacolumnforAdamwith$15writtenunderthatcolumninthesamerowas(C).Vickenpays$90,solikewisemakeacolumnforVickenwith$90writtenunderit.

Step6—POE.Addupallthethreemen’scontributionstofindatotalof$135,whichisgreaterthanwhattheproblemstatestheradioactuallycosts.Eliminate(C).Since(C)istoogreat,alsoeliminate(D)and(E),whichareevengreater.Fillinthecolumnsfor(B).IfRogerpays$20,thenAdampays$10andVickenpays$60.Allthreecombinetopay$90,whichiswhattheproblemstatestheyactuallypaid.Thecorrectansweris(B).

Yourscratchpapercouldlooklikethis:

Toreview,therearefourkindsofPluggingIn:

1. PluggingInforVariables.Whenyouseevariablesintheanswerchoices,PlugIn.Makesureyougivethevariablesnumericvalues,circlethetargetnumber,andcheckallanswerchoices.

2. QuantitativeComparisonPlugIn.WhenyouseeunknownvaluesonQuantitativeComparisonquestions,setupforPluggingIn.UseaneasiernumberfirstandthengothroughtheFROZENnumbersuntilyouareleftwithoneanswerchoice.

3.MustBe.“Mustbe”meansthatyoushouldbereadytoPlugInmorethanonce.PutanswerchoicesinaverticalcolumnandleavespaceabovetoPlugInforavarietyofvariables.RemembertostartwithaneasynumberandthengothroughtheFROZENnumbersuntilyouareleftwithoneanswerchoice.

4. PITA.Whenaquestionasks“howmuch,”“howmany,”orforaspecificvaluethattheanswerchoicesrepresent,youcanPlugInTheAnswers(PITA).Labelthefirstcolumn,startwith(C),andmakeanewcolumnforeverystep.Whenyoufindonethatworks,you’redone!

STEP7

FindtheMissingPiecesinGeometry

FindtheMissingPiecesinGeometryGeometryon theGRE is really likeaseriesofbrainteasers. It isyour job to find themissing piece of information. They will always give you four out of five pieces ofinformation,andyouwillalwaysbeabletofindthefifth.Thereareonlyaboutone-halfdozenconceptsthatshowup.Onceyoulearntorecognizethem,youshouldbeabletohandleanyproblemsyoumightsee.Thebasicproblemsaremadeupofparallellines,triangles,circles,andquadrilaterals.

First,afewbasics:

Line—Aline(whichcanbethoughtofasaperfectlyflatangle)isa180-degreeangle.

Perpendicular—When two lines are perpendicular to each other, their intersectionformsfour90-degreeangles.

Rightangle—90-degreeanglesarealsocalledrightangles.Arightangleisidentifiedbyalittleboxattheintersectionoftheangle’ssides:

Vertical angles—Vertical angles are the angles across from each other that areformed by the intersection of two lines. The degreemeasures of vertical angles areequal.

x=ya=b

a°+b°+x°+y°=360°

Parallel lines—First,neverassume two linesareparallelunless that isstated in theproblemor you canprove it from the information in theproblem.When you see thesymbol for parallel lines, however, there’s generally only one thing interesting aboutparallellines.Whenyouseeapairofparallellinesintersectedbyathirdline,twokindsof angles are formed: big ones and small ones. All big angles are equal to all biganglesandallsmallanglesareequaltoallsmallangles.Anybig+anysmall=180°.Whenyousee thesymbol forparallel lines,alwaysandautomatically identify thebigangles and the small angles. They are almost assuredly going to come into play.Otherwise,whymakethemparallel?

Forexample,takealookatthefollowingfigure.Theanglemarked40°isasmallangle.(Thesmallanglesaretheangleswithdegreemeasureslessthanorequalto90°.)Theanglemarkedaisalsoasmallangle,soitisalso40°.Theanglemarkedbisalargeangle.Sincebig+small=180°,bis140°.

b=140°

Triangles

There are several basic facts that ETS expects you to know about triangles. The

degreemeasuresofthethreeanglesaddupto180°.Thelongestsideisoppositethe

largestangle,justastheshortestsideisoppositethesmallestangle.Theformulafor

theareaofatriangleisA= (b)(h).Anequilateraltriangleisoneinwhichthelengthsof

allthreesidesareequal.Also,thethreeangleshaveequalmeasuresandareall60°.

An isosceles triangle is one inwhich twoof the sides are equal in length.Naturally,

sidesoppositeequalanglesareequalinlengthandviceversa.

A lesser-known triangle rule is theThirdSideRule. The lengthof the third sideof atriangle isalwayslessthanthesumofthelengthsoftheothertwosides,butgreaterthantheirdifference.

ThemostfrequentlytestedtrianglesontheGREarerighttriangles.Arighttrianglehasone90°angleandtwosmallerangles.Ifyouknowthelengthsoftwosidesofarighttriangle,youcanalways find the lengthof the thirdusing thePythagoreanTheorem.ThePythagoreanTheoremstates thata2 +b2 =c2wherec is the hypotenuse. Thehypotenuseofarighttriangleisthelongestsideofthetriangle.Thehypotenuseisalsothesideoppositetherightangle.

It’sgood tounderstandhowthePythagoreanTheoremworks,butyourarelyneedtouse it because there are three right triangles that come up all the time. Once yourecognize these three right triangles, you can save yourself some timebecause youwon’tneedtodothecalculations.SobeonthelookoutforrighttrianglesontheGRE!Ifyouseeatriangleanditisarighttriangle,beextremelysuspicious.Itislikelytobeoneof threecommonright triangles.Thecommonright trianglesarePythagorean triples,45-45-90triangles,and30-60-90triangles.

PythagoreanTriples

ThePythagoreanTheorem is true forany right triangle,butwhenall threesidesareintegers,it’scalledaPythagoreantriple.Notethesecondtripleinthediagramabove:6-8-10.Seehowit’samultipleofthe3-4-5triple?AnymultipleofaPythagoreantripleisalsoaPythagorean triple. If youseea right triangle,start looking forPythagoreantriples.Aslongastwoofthesidesmatchoneofthetrianglesabove,youdonotneedtocalculatethethirdside.

45-45-90

Whenasquare(allsidesareequal,allanglesare90°) iscut inhalfalongoneof itsdiagonals,theresultistwo45-45-90triangles.Ifeachsideofthesquareisa,thenthediagonalofthesquare(alsoknownasthehypotenuseoftherighttriangle)isa .Ifaproblemhasarighttriangleanda init,think45-45-90triangle.Onecommonuseforthe45-45-90triangleontheGREis to findthe lengthof thediagonalofasquareforwhichyouknoweitherthelengthofthesideorthearea.

30-60-90

When an equilateral triangle is cut in half, the result is two 30-60-90 triangles.Oneangleisstill60°.Theangleatthetopgotcutinhalfandisnow30°.Theangleatthebaseis90°.Ifthesmallsideofthenewtriangleisa,thenthebigside(oppositethe90°angle)is2a.Themiddleside,oppositethe60°angle,isa .Onecommonuseforthe30-60-90triangleontheGREistofindtheareaofanequilateraltriangle.Ifyouknowthelengthofthesideoftheequilateraltriangle,youcanusethe30-60-90relationshiptofindtheequilateraltriangle’sheight.Ifaproblemhasarighttriangleanda , lookfora30-60-90triangle.

Circles

CircleFacts

• Allcirclescontain360°.• Theradiusofacircleisthelinethatconnectsthecenterofthecircletoapointonthecircumferenceofthecircle.

• Thediameterisalinethatconnectstwopointsonthecircumferenceofthecircleandgoesthroughthecenterofthecircle.Thediameteristhelongestlinethatcanbedrawninacircle.Thelengthofthediameteristwicethatoftheradius.

• TheformulafortheareaofacircleisA=πr2.• Theformulaforthecircumference(perimeter)ofacircleisC=πd,orC=2πr.

Ifyouknowtheradius,youcanfindanythingelseyouneedtoknowaboutacircle.Youshould be comfortable going from circumference to radius to area and back.Rememberthatpiequalsapproximately3.14,butasageneralrule,leaveitaspi.

QuadrilateralsFour-sided figure—Any figure with four sides has 360°. That includes rectangles,squares,andparallelograms(four-sidedfiguresmadeoutoftwosetsofparallellines).

Parallelogram—A four-sided figure consisting of two sets of parallel lines. Theoppositeanglesareequal,andthebigangleandthesmallangleaddupto180°.

x=120°,y=60°,z=120°

Rectangle—A four-sided figurewhere opposite sides are parallel and all angles are90°.Theareaofarectangleislengthtimeswidth(A=lw).

perimeter=4+8+4+8=24area=8×4=32

Square—Asquare isarectanglewith fourequalsides.Thearea is the lengthofanysidetimesitself,whichistosay,thelengthofanysidesquared(A=s2).

AFewOtherOddsandEndsCoordinategeometry—Thisinvolvesagridwherethehorizontallineisthex-axisandthevertical line is they-axis. Inanorderedpair, thex-coordinatealwayscomes first,

andthey-coordinatealwayscomessecond.

TheorderedpairforpointAonthediagramaboveis(2,4)becausethex-coordinateis2overfromtheorigin(0,0)andthey-coordinateis4abovetheorigin.PointBisat(−7,1).PointCisat(−5,−5).

Inscribed—One figure is inscribed within another when points on the edge of theenclosedfiguretouchtheouterfigure.

Perimeter—Theperimeterofarectangle,square,parallelogram,triangle,oranysidedfigureisthesumofthelengthsofthesides:

perimeter=26

Slope—Theslopeof a line describes the steepnessof the line’s slant. The slope isfoundbypickingtwopointsonthelineanddividingthechangeintheiry-coordinatesbythe change in theirx-coordinates. This is often described as the “rise over the run.”Slopeisalsousedintheformulafortheequationofaline:y=mx+b.Inthisequation,mistheslopeandbisthey-intercept,thepointatwhichthelinecrossesthey-axis.

Surfacearea—Thesurfaceareaofarectangularboxisequaltothesumoftheareasofallof itssides.Inotherwords,forarectangularsolidwithdimensions2by3by4,therearetwosidesthatare2by3(areaof6),twosidesthatare3by4(areaof12),andtwosidesthatare2by4(areaof8).So,thesurfaceareais6+6+12+12+8+8,whichis52.

Volume—ThevolumeofarectangularsolidisV=l×w×h(lengthtimeswidthtimesheight).Thevolumeofarightcircularcylinderisπr2(theareaofthecirclethatformsthebase)timestheheight(inotherwords,πr2h).

TheBasicApproachStep1—Drawthefigure.Youwillneedtoworkwiththefiguresandfillinlotsofpiecesofinformation,soit isimportanttodrawthefigureonyourscratchpaper.Trytodrawthe figure to scale, but remember to base your drawing upon what you’re told, notnecessarily what you’re shown on screen. Drawing your own figure is particularlyimportantwhentheproblemdoesn’tprovideyouwithone.

Step 2—Fill in what you know. The problem will give you various pieces ofinformation. Itmightgiveyouanangleor two, the lengthofaside,ora relationshipbetweentwoelements,forexample.Parkallofthatinformationonyourdrawing.

Step3—Makedeductions. Ifaproblemgivesyou twoangles ina triangle,youcancalculate the third.Always fill inanythingelseyoucan findasamatterofgood test-taking habits. Sometimes deductions alone are enough to lead you to the correctanswer.

Step4—Writedownrelevantformulas.GeometryontheGREisallaboutfindingthemissing piece of information. Writing down the formulas you need will help you toorganizetheinformationyouhaveandwillalsohelpyoudeterminewhichpiecesyouare missing. For example, if you are working with triangles and you see the word“area,”automaticallywritedowntheformulafortheareaofatriangle.Youwillendupneeding this formula sooner or later. This is true for any problem that involves aformula.

Step5—Dropheights/drawlines.Whentakingthetest,youalwayswanttobedoing,notthinking.Whenyougetstuckonageometryproblem,firstwalkawayanddoafewotherproblemstodistractyourbrain.Whenyoucomeback,youneedtofindanotherwaytoviewtheproblem.ThisiswhereStep5comesin.Trydroppingtheheightofatriangle or parallelogram, drawing in a few extra radii in a circle, or subdividing astrangeshape tomake twoshapesyou recognize.Keep trying things!Staringat theproblemisn’tgoingtomakeiteasier.

Here’sanexample:

Inthetriangleabove,ifBC=4 ,thenAB=

6

4

8

4

10

Step1—Drawthefigure.

Step2—Fill inwhatyouknow.BC is4 .This is ahighly suspiciousnumber.Noone,notevenETS,randomlydecidestomakeonesideofatriangleincludeasquareroot.Theremustbeareason.Whatkindoftriangleusesa ?

Step3—Makedeductions. You know the third angle. It’s 45°.Now you have a 45-degreeangleanda inthesameproblem.Theremustbea45-45-90triangleinheresomewhere.

Step4—Writerelevantformulas.Thisproblemdoesn’tcallforanyformulas.

Step5—Dropheights/drawlines.Anytimeyoudrop theheightofa triangle,a rightangleisformedbytheintersectionoftheheightandthebaseofthetriangle.Lookatthat.There’sthe45-45-90triangle!Theangleatthetopis45°too.Ifthehypotenuseis4 ,theneachofthesmallersidesis4.Putthosenumbersonyourdrawing.Ontheother side there is another triangle. This onehas a 30° angle anda 90° angle.Youdon’tevenhavetocalculatethethirdangle;itmustbe60°.Thisisa30-60-90triangle,whichmeans that you know the ratio of the sides. The short side opposite the 30-degreeangleis4.Thelongsideoppositetherightangle,therefore,mustbe8.ThisissideAB, which is the side youwere asked to find. The correct answer is (C). Yourscratchpapercouldlooklikethis:

Geometryproblemsareoften likeasmallpieceofknitting.Onceyoufindandtugonthe loose thread, thewhole thingbegins tounravel.Thestepsaredesignedto teaseoutthatloosethread.

GeometryonQuantComp

QuantityA QuantityBTheareaofasquareregionwith

perimeter20Theareaofarectangularregion

withperimeter20

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

When solving a Quantitative Comparison with variables, always Plug In more thanonce. The equivalent of Plugging In more than once with a geometry question isdrawingthefiguremorethanonce.Askyourself,“Istheremorethanonewaytodrawthisfigure?”

You can set this problem up just like a Quant Comp Plug In. Quantity A does notchangebecause there isonlyoneway todrawasquare. If theperimeter is20, thenonesideis5,andtheareais25.NowdrawarectangleforQuantityBandmaketheareaassmallaspossible.Youcouldhavealongskinnyrectanglewithlongsidesof9andshortsidesof1.Theperimeteris20,buttheareais9.Crossoff(B)and(C).Nowredrawthefigure.Howbigcanyoumakethatarea?Thebiggestyoucouldmakeitistomakeasquarewithsidesof5(asquareisarectangle).Theperimeteris20,andtheareais25.Crossoff(A).Theansweris(D).

Yourscratchpapercouldlooksomethinglikethis:

STEP8

BallparktheEquations

BallparktheEquationsManyGREmathproblems involvewords, letters, or variables, suchasn,x, ory, inequations.It’stimetolearnhowtodealwiththose.

SolvingforOneVariableAnyequationwithonevariablecanbesolvedbymanipulating theequation.Yougetthevariablesononesideoftheequationandthenumbersontheotherside.Todothis,you can add, subtract, multiply, or divide both sides of the equation by the samenumber.Justrememberthatanythingyoudotoonesideofanequation,youhavetodototheotherside.Besuretowritedowneverystep.Lookatasimpleexample:

4x−3=9

Youcangetridofnegativesbyaddingsomethingtobothsidesoftheequation,justasyoucangetridofpositivesbysubtractingsomethingfrombothsidesoftheequation.

4x−3=9+3+34x=12

Youmayalreadysee thatx=3.Butdon’t forget towritedown that last step.Dividebothsidesoftheequationby4.

x=3

MoreMathVocabF.O.I.L.—F.O.I.L. stands for First, Outer, Inner, Last—the four steps of multiplicationwhenyouseetwosetsofparentheses.Here’sanexample:

Thisalsoworksintheoppositedirection.

Factoring—If you rewrite the expression xy + xz as x(y + z), you are said to befactoringtheoriginalexpression.Thatis,youtakethefactorcommontobothtermsoftheoriginalexpression(x)and“pullitout.”Thisgivesyouanew,“factored”versionoftheexpressionyoubeganwith. Ifyourewritetheexpressionx(y+z)asxy+xz,youareunfactoringtheoriginalexpression.

Functions—No,not realmathematical functions.On theGRE,a function isa funny-

lookingsymbolthatstandsforanoperation.Forexample,sayyou’retoldthatm@nis

equalto .What’sthevalueof4@6?Justfollowdirections: ,or ,or2.

Don’tworrythat“@”isn’tarealmathematicaloperation;itcouldhavebeena“#”oran

“&,”oranyothersymbol.Thepointistodowhatyouaretoldtodo.

Inequalities—Herearethesymbolsyouneedtoknow:≠meansnotequalto;>meansgreaterthan;<meanslessthan;≥meansgreaterthanorequalto;≤meanslessthanorequalto.Youcanmanipulateanyinequalityinthesamewayyoucananequation,withoneimportantdifference.Forexample,

10−5x>0

Youcansolve thisbysubtracting10 frombothsidesof theequation,andendingupwith−5x>−10.Nowyouhavetodividebothsidesby−5.

Withinequalities,anytimeyoumultiplyordividebyanegativenumber,youhavetoflipthesign.

x<2

Percent—Percentmeans “per100”or “outof100”or “dividedby100.” Ifyour friend

findsadollarandgivesyou50cents,yourfriendhasgivenyou50centsoutof100,or

ofadollar,or50%ofadollar.Whenyouhavetofindexactpercentages,it’smuch

easier if you knowhow to translatewordproblems,which lets youexpress themas

equations.Checkoutthe“translationdictionary”onthenextpage.

TranslationDictionaryWord Translatestopercent /100(example:40percenttranslatesto )

is =of ×what anyvariable(x,k,b)

whatpercent

Let’slookatthisquestion:

Whatis30%of200?

First,translateitusingthe“dictionary”above.

x= ×200

Nowreducethat100and200,andsolveforthevariable,likethis:

x=30×2

x=60

So,30%of200is60.

Percentchange—Tofindapercentage increaseordecrease, first find thedifferencebetween the original number and the new number. Then, divide that by the originalnumber,andthenmultiplytheresultby100.Inotherwords:

Forexample, ifyouhadtofindthepercentdecreasefrom4to3,firstfigureoutwhatthedifferenceis.Thedifference,ordecrease,from4to3is1.

Theoriginalnumberis4.So,

PercentChange= ×100

PercentChange=25

So,thepercentdecreasefrom4to3is25percent.

Quadraticequations—Three equations that sometimes showup on theGRE.Heretheyare,intheirfactoredandunfactoredforms.

Factoredform Unfactoredformx2−y2= (x+y)(x−y)(x+y)2= x2+2xy+y2

(x−y)2= x2−2xy+y2

Simultaneousequations—Twoalgebraicequations that include thesamevariables.Forexample,whatifyouweretoldthat5x+4y=6and4x+3y=5,andaskedwhatx+yequals?Tosolveasetofsimultaneousequations,youcanusuallyeitheraddthemtogether or subtract one from the other (just remember when you subtract thateverythingyou’resubtractingneedstobemadenegative).Here’swhatyougetwhenyouaddthem:

5x+4y=6+4x+3y=59x+7y=11

Adeadend.So,trysubtraction.

5x+4y=6−4x−3y=−5x+y=1

Eureka!Thevalueoftheexpression(x+y)isexactlywhatyou’relookingfor.

BallparkingSayyouwereasked to find30%of50.Beforeyoudoanymath, lookat theanswerchoicesbelow:

5

15

30

80

150

Whatever30%of50is, itmustbelessthan50,right?Soanyanswerchoicegreaterthan50cannotbecorrect.Thatmeansyoushouldeliminateboth80and150rightoffthebat,withoutdoinganymath.Youcanalsoeliminate30,ifyouthinkaboutit.Half,or50percent,of50 is25,so30percentmustbe less than25.Congratulations,you’vejusteliminatedthreeoutoffiveanswerchoiceswithoutdoinganymath.

What you’ve done here is known as Ballparking. Ballparking will help you eliminateanswerchoicesandincreaseyouroddsofzeroinginonETS’sanswer.Remembertoeliminateanyanswerchoicethat is“outof theballpark”bycrossingthemoffonyourscratchpaper(remember,you’llbewritingdownA,B,C,D,Eforeachquestion).

ChartsBallparkingwillalsohelpyouonthefewchartquestionsthateveryGREMathsectionwill have. You should Ballpark whenever you see the word “approximately” in aquestion,whenevertheanswerchoicesarefarapartinvalue,andwheneveryoustarttoansweraquestionandyoujustifiablysaytoyourself,“Thisisgoingtotakealotofcalculation!”

TohelpyouBallpark,hereareafewpercentsandtheirfractionalequivalents:

If,onachartquestion,youwereaskedtofind9.6percentof21.4,youcouldBallparkbyusing10%asa“friendlier”percentageand20asa“friendlier”number.10%of20is2.That’sallyouneedtodotoanswermostchartquestions.

Try Ballparking on a real chart. Keep in mind that while general charts display the

information theywantyou tosee tomake the informationeasier tounderstand,ETSconstructs charts tohide the information youneed to know tomake that informationdifficulttounderstand.Soreadalltitlesandsmallprint,tomakesureyouunderstandwhatthechartsareconveying.

NationwideSurveyofIceCreamPreferencesin1975andin1985,byFlavor

Looking over these charts, notice that they are for 1975 and 1985, and that all youknoware percentages. There are no total numbers for the survey, and because thepercentagesarepretty “ugly,”youcananticipatedoinga lotofBallparking toanswerthequestions.

Trythefollowingexample.

Tothenearestonepercent,whatpercentagedecreaseinpopularityoccurredforchocolatefrom1975to1985?

9%

10%

11%

89%

90%

First,youneed to find thedifferencebetween28.77(the1975 figure)and25.63(the1985 figure). The difference is 3.14. Second, notice that ETS has asked for an

approximate answer (“to the nearest one percent”) which is screaming “Ballpark!”Could3.14reallybe89or90percentof28.77?Noway;it’sclosertotheneighborhoodof10percent.Eliminate(D)and(E).Isitexactly10percent?No;thatmeans(B)isout.Isitmoreorlessthan10%?It’smore—exactly10%wouldbe2.877,and3.14ismorethan2.877.Thatmeanstheansweris(C).

Tryanotherone:

In1985,if20percentofthe“other”categoryislemonflavor,and4,212peoplesurveyedpreferredlemon,thenhowmanypeopleweresurveyed?

1,000

10,000

42,120

100,000

1,000,000

The first piece of information you have is a percentage of a percentage. Thepercentageofpeoplewhopreferred lemonin1985isequal to20%of21.06%.Makesure you see that before you go on. Now, notice that the numbers in the answerchoicesareverywidelyseparated—theyaren’tconsecutiveintegers.Ifyoucanjustgetintheballpark,theanswerwillbeobvious.

Ratherthantrytouse21.06%,we’llcallit20%.Andratherthanuse4,212,use4,000.The question is now: “20% of 20% of what is 4,000?” So, using translation, yourequationlookslikethis:

Doalittlereducing.

Thatmeanstheansweris(D).

STEP9

GetOrganizedWhenDoingArithmetic

GetOrganizedWhenDoingArithmeticQuestionsinvolvingratiosoraveragescanseemdauntingatfirst.Themathinvolvedintheseproblems,however,generallyinvolveslittlemorethanbasicarithmetic.Thetrickto these problems is understanding how to organize your information. Learning thetransitionwordsandsetups foreachof theseproblemscan takea four-minutebrainteaserandturnitintoa45-secondpieceofcake.

AveragesImagineyouareasked to find theaverage(arithmeticmean)of threenumbers,3,7,and 8. This is not a difficult problem.Simply add the three together to get the total.Dividebythree,thenumberofthings,togettheaverage.Allaverageproblemsinvolvethreebasicpieces:

• Total:18• Numberofthings:3• Average:6

ItisvirtuallyassuredthatETSwillnevergiveyoualistofnumbersandaskyoufortheaverage.Thatwouldbetooeasy.Theywill,however,alwaysgiveyoutwooutofthesethreepieces,anditisyourjobtofindthethird.That’swheretheAveragePiecomesin.Theminuteyouseetheword“average”onaproblem,drawyourpieonyourscratchpaper.

TransitionWord:“Average”

Response:DrawanAveragePieonyourscratchpaper.

Here’showyouwouldfillitin.

Aspreviouslystated,youwon’tbeaskedtofindtheaverageofalistofnumbers.Onthetest,theywillalwaysgiveyoutwooutofthethreepiecesofinformationyou’llneedtofindtheaverage.Justdrawyourpie,fill inwhatyouknow,anditbecomeseasytofindthemissingpiece.Here’showitworks.

Thelineinthemiddlemeansdivide.Ifyouhavethetotalandthenumberofthings,justdivideandyougettheaverage(18÷3=6).Ifyouhavethetotalandtheaverage,justdivideandyougetthenumberofthings(18÷6=3).Ifyouhavetheaverageandthenumberofthings,simplymultiplyandyougetthetotal(6×3=18).Asyouwillsee,thekeytomostaveragequestionsisfindingthetotal.

ThebenefitoftheAveragePieisthatyousimplyhavetoplugtheinformationfromthequestion into theAveragePieand thencomplete thepie.Doingsowillautomaticallygiveyoualltheinformationyouneedtoanswerthequestion.

Trythisquestion:

Theaverage(arithmeticmean)ofasetof6numbersis28.Ifacertainnumber,y,isremovedfromtheset,theaverageoftheremainingnumbersinthesetis24.

QuantityA QuantityBy 48

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

Theminuteyouseetheword“average,”makeyourpie.Ifyouseetheword“average”asecondtime,makeasecondpie.Startwiththefirstbite-sizedpiece,“Theaverageof

asetof6numbersis28.”Drawyourpieandfillitin.Withtheaverageandthenumberofthingsyoucancalculatethetotal,likethis:

Takeyournextpieceoftheproblem,“Ifacertainnumber,y, isremovedfromtheset,the average of the remaining numbers in the set is 24.” There’s theword “average”again, somakeanother pie.Again, youhave the number of things (5, becauseonenumberwasremovedfromourset)andtheaverage,24,soyoucancalculatethetotal,likethis:

The total for all six numbers is 168.When you take a number out, the total for theremainingfiveis120.Thenumberyouremoved,therefore,mustbe168−120=48.y=48.Theansweris(C).

RatiosWhenworkingwithfractions,decimals,andpercentages,youareworkingwithapartto

awholerelationship.Thefraction means3partsoutofatotalof5,and20%means

20partsoutofevery100.A ratio,on theotherhand, isapart toapart relationship.

Lemonsand limes inaratioof1 to4meansthatyouhaveone lemonforevery four

limes.IfyoumakeanAveragePieeverytimeyouseetheword“average,”youshould

makeaRatioBoxeverytimeyouseetheword“ratio.”

Here’sanactualGREproblem:

Inaclubwith35members,theratioofmentowomenis2to3amongthemembers.Howmanymenbelongtotheclub?

2

5

7

14

21

Theproblemsays,“theratioofmentowomen….”Assoonasyouseethat,makeyourbox.Itcouldlooklikethis:

Inthetoplineofthebox,listtheitemsthatmakeupyourratio,inthiscase,menandwomen.Thelastcolumnisalwaysforthetotal.Inthesecondrowofthebox,fillinyourratioof2to3underMenandWomen,respectively.Thetotal is5.Thisdoesn’tmeanthatthereareactually2menand3womenintheclub.Thisjustmeansthatforevery5

membersofthisclub,2ofthemwillbemenand3ofthemwillbewomen.Theactualnumberofmembers,you’retoldintheproblem,is35.ThisgoesinthebottomrightcellunderTotal.Withthissinglenumberinthebottomrowyoucanfigureouttherest.Togetfrom5to35,youneedtomultiplyby7.Themultiplierremainsconstantacrosstheratio,sofilla7inallthreecellsofthethirdrow,nexttotheword“multiplier.”Younowknow that the actual number ofmen in the club is 14, just as the actual number ofwomenis21.Theansweris(D).Here’swhatyourcompletedRatioBoxcouldlooklike:

Thefractionoftheclubthatismaleis .Ifyoureducethis,youget .Thepercentage

ofmemberswhoarefemaleis ,or60%.

Median/Mode/Range“Median”meansthenumber in themiddle, like themedianstriponahighway. In thesetofnumbers2,2,4,5,9,themedianis“4”becauseit’stheoneinthemiddle.Ifthesethadanevennumberofelements,let’ssay:2,3,4,6,themedianistheaverageofthe twonumbers in themiddleor, in thiscase,3.5.That’s it.There’snotmuch that’sinterestingabouttheword“median.”Thereareonlytwowaystheycantrickyouwithamedianquestion.One is togiveyouasetwithanevennumberofelements.You’vemasteredthatone.Theotheristogiveyouasetofnumberswhichareoutoforder.Ifyouseetheword“median,”therefore,findabunchofnumbersandputtheminorder.

“Mode”simplymeansthenumberthatshowsupthemost.Intheset2,2,4,5,9,themodeis2.That’sallthereistomode.Ifnonumbershowsupmorethananother,thenthesethasnomode.

“Range”iseveneasier.Itisthedifferencebetweenthebiggestnumberinasetandthesmallest. In other words, find the smallest number and subtract it from the biggestnumber.

Lookatthisproblem:

Ifinthesetofnumbers{20,14,19,12,17,20,24}vequalsthemean,wequalsthemedian,xequalsthemode,andyequalstherange,whichofthefollowingistrue?

v<w<x<y

v<x<w<y

y<v<w<x

y<v<x<w

w<y<v<x

Inthisquestionyou’reaskedtofindthemean,themedian,themode,andtherangeofasetofnumbers.Theminuteyouseetheword“median,”youknowwhattodo.Putthenumbersinorder:12,14,17,19,20,20,24.Dothisonyourscratchpaper,notinyourhead, and while you’re at it, list A, B, C, D, and E so that you have something toeliminate.Theminuteyouputthenumbersinorder,threeoutofthefourelementsyouareaskedtofindshouldbecomeclear.Therange,12,isequaltothesmallestnumberinthiscase,soyshouldbetheelementatthefarleftoftheseries.Crossoff(A),(B),and (E). The average will be somewhere in the middle. Without doing somecalculations, it’snotclear if it is largerthanthemedian(19)orsmaller,soskiptothemode.Themodeis20andlargerthanthemedianandcertainlylargerthanthemean.Variablexshouldbethelastelementintheseries.Crossoff(D).Thecorrectansweris(C).Alwaysrememberthattheanswerchoicesarepartofthequestion.Oftenitisfareasiertofindandeliminatewronganswersthanitistofindthecorrectones.

RatesandProportionsRates are really just proportions. Similar to ratios and averages, the basic math isstraightforward,but thedifficultpart isorganizing the information.Actually,organizingtheinformationisthewholetrick.Setupallrateslikeaproportionandmakesureyoulabelthetopandbottomofyourproportion.Lookatanactualproblembelow.

Standrivesatanaveragespeedof60milesperhourfromTownAtoTownB,adistanceof150miles.Olliedrivesatanaveragespeedof50milesperhourfromTownCtoTownB,adistanceof120miles.

QuantityA QuantityBAmountoftimeStanspendsdriving AmountoftimeOlliespendsdriving

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

Inthisproblemyouareaskedtocomparetwoseparaterates,eachconsistingofmiles(distance)andhours(time).StartwithStan.Stan’sspeed is60mph,which is tosaythathedrives60milesevery1hour.You’reaskedtofindhowmanyhoursitwilltakehimtotravel150miles.Justsetitupasaproportion,likethis:

Nowyoucancomparemilestomilesandhourstohours.Thereisanxinthesecondspaceforhoursbecauseyoudon’tyetknowhowmanyhours it’sgoingtotakeStan.Thenicethingaboutthissetupisthatyoucanalwayscross-multiplytofindthemissingpiece.If60x=150,thenx=2.5.Thismeansthat it tookStan2.5hourstodrive150miles(atarateof60milesperhour).

NowtryOllie.Thesetupisthesame.Olliedrives50milesforeveryonehour.Tofindouthowmanyhoursheneedstodrive120miles,justcross-multiply.If50x=120,thenx=2.4.ThismeansthatittookOllie2.4hourstodrive120miles(atarateof50milesperhour).QuantityAisStan,sothecorrectansweris(A).

ArithmeticSummaryHerearealistoftransitionwordsandwhatyoushoulddowhenyouseethemintheQuantitativesectionoftheexam.

TransitionWord ResponseAverage DrawanAveragePie.Ratio DrawaRatioBox.Median Findabunchofnumbersandputtheminorder.Mode Findthenumberthatappearsthemostoften.Range Subtractthesmallestfromthebiggest.Rate Setupaproportion;labeltopandbottom.

STEP10

PlanBeforeWritingYourEssays

PlanBeforeWritingYourEssays

TheIssueEssayYourissueessaywillbereadbytwograders,andeachwillassignascorefrom1to6,basedonhowwellyoudothefollowing:

• followtheinstructionsoftheprompt• considerthecomplexitiesoftheissueorargument• effectivelyorganizeanddevelopyourideas• supportyourpositionwithrelevantexamples• controltheelementsofwrittenEnglish

The graders will be judging your essays on three basic criteria: the quality of yourthinking,thequalityofyourorganizing,andthequalityofyourwriting.Thetwogradersscoreswillbeaveraged,andthetwoessayscoreswillbeaveraged.Quarterpointsareroundedupinthestudent’sfavor.

Anessaywithwell-chosenexamples,clearorganization,anddecentuseofstandardwrittenEnglishisautomatically inthetophalf,guaranteeingascoreofat leasta4.Ifanyoneofthosecategoriesisparticularlystrong,thenyourscoregoesfroma4toa5.Iftwoofthemareparticularlystrong,yourscoregoesuptoa6.Ontheotherhand,ifanyoneof thosethreeelements ismissing,nomatterwhat’sgoingonwiththeothertwo,youareautomatically in thebottomhalf.Since theywillbe judgingyouressaysbaseduponthesethreecriteria,youneedaprocessthatgiveseachitsdue.

Youwillbegivenatopicofgeneralinterest.Thetopicwillbegeneralenoughthatitisaccessible to any test taker anywhere. ETS could never ask a question about, say,Hamlet,becausethiswouldadvantageonegroupof test takersoveranother.Topics,therefore,tendtobeaboutloss,growth,education,theroleofgovernment,individualsandsociety,etc.Infact,alltopicsyoumightseearepostedrightnowonwww.ets.org/gre,onthe“PublishedTopicPoolsfortheAnalyticalWritingMeasure”page.

Yourjobistoformulateanopinionaboutthistopicandcraftaconvincinganargumentin support of your opinion. You will need to support your argument with specificexamples.Youcanchoosetoagree,disagree,orevenmodifytheissuetopic, justaslongasyoustayontopic.

Step1:ThinkOneofthemostcommonmistakesthatstudentsmakeistheywritetheiressaysbaseduponthefirst twoor threeexamplestheycomeupwith.Rarelyarethesethebestoreventhemostinterestingexamples.Rarelydotheyshowanydevelopment,andoftenthey are the same examples that everyone else comes up with. ETS graders arejudgingyouonthequalityofyourthinking,sotaketimetothink.

DefinetheTopicEssay topics typically fall into one of three general categories. There are extremestatements,wishy-washystatements,andopen-endedstatements.Your first job is tofigure out what itmeans to agree or disagreewith the statement. To agreewith anextremestatementistotakeanextremeposition.Thishasthebenefitofaveryclearthesisstatement,butmaybedifficult todefend. It isofteneasier todisagreewithanextremestatement.Toagreewithawishy-washystatementisusuallyprettyeasy.Justsay, “Sure, this isoften true.Herearesomeexamples….”Todisagreewithawishy-washystatement istotakeanextremeposition.Youmustshowthatthestatement isnevertrueoralwaystrue.Itisofteneasiertoagreewithawishy-washystatement.

BrainstormOnce you have defined the topic (this should take a minute or less), it’s time tobrainstorm.Yourjob,atthisstage,istopushyourthinkingasfarasitcango.Yourjob,whether you agree with the topic or not, is to come up with at least four “agree”examples,andfour“disagree”examples.Quantityandvarietyaremoreimportantthanqualityatthispoint.Onyourscratchpaper,drawa“T.”ontheleft,write,“Iagree,”andontherightwrite“Idisagree.”

Yourscratchpapercouldlooklikethis:

ArgueFromaPositionofStrengthTopics are always general enough so that they are accessible to all test takers, nomatterwho theyareorwhere they’re taking the test.Thismeans thatyoucanapplythemtojustaboutanyareaofexpertiseorexperience.Theplacetostartiswithyourownareasofexpertise.How is the topic true for you?Could it apply toyour fieldofstudy?Could itapply toyourschool? Is it true foryourcompany?Go into theexamprepared to talk about the things you know best. What was your major in school?Wheredoyouworknow?Whatbookshaveyourecentlyreadorpapershaveyouhaverecentlywritten?Essayswrittenfromanareaofstrengtharealwayseasiertowriteandfarmoreconvincing. It’salwayseasier to talkabout thingsyouknowwell,andwhenyoudo,youwillcomeacrossasanexpert,becauseyouare.

Whenyourbrainstormrunsdry,usethischecklist:

yourself,friends,family,school,city,country,company,species,old/young,history,science,literature

Thisshouldpushyourthinkinginnewdirections.Howisthetopictruefortheveryold

ortheveryyoung?Whataboutatthespecieslevel?Coulditoccurinanotherspecies?Canitbetrueforanindividualbutalsoacountryorcompany?

Thefirstthreeexamplesyoucomeupwitharelikelytobeverysimilar.Theymightbethreemajorfiguresinhistory,forexample.Oneofthoseexamplesmightbegood,butthesecondand thirddon’tadvanceyourargument.Write themdownaspartofyourbrainstorm,butmakesure topushyour thinking intootherareas.Eachexampleyouchooseshouldhaveaspecific job todo.Theyare the legsof theargumentyouarecreating.Anessay that showsdevelopment, or quality thinking,will lookat the topicfrommultipleangles.Eachexamplewillbringsomethingnewtotheargument.

Manystudentsareworriedabouttimeatthisstage.First,youarebeingjudgedonthequalityofyourthinking,soyoucannotignorethisstep.Next,agoodbrainstormandagoodoutlinewillhelpyoutobemoreefficientandmorefocusedwhenyouwrite.Andlastly,thinkingwhileyouwriteisdangerous.Essayswrittenontheflyoftenhavealackof focusandstructure.Whenyouare trying to thinkandworkat thesame time,youdistractyourbrainwhileyou’rewriting leading toembarrassingmistakes ingrammar,punctuation,anddiction.

The other thing to keep in mind is that the ETS website states, The GRE readersscoringyourresponsearenot lookingfora“right”answer—infact,asfarastheyareconcerned,thereisnocorrectpositiontotake.Instead,thereadersareevaluatingtheskill with which you address the specific instructions and articulate and develop anargument to support your evaluation of the issue. This means that you are free toapproachthetopicfromanyangleyouwant.Italsomeansthatyoucanfocusononeparticularareaorapplicationofthetopic.

Step2:OrganizeMoststudentscomeupwithapointofviewandthenracktheirbrainsfor theperfectexamplestosupportit.Theywilloftencomeupwiththatperfectexample,butusuallyitdoesn’t happen until hours after the exam. The best way to perfectly connect yourexamplesandyourthesisstatementistoselectyourexamplesfirst.

Someessay instructionswillberelativelystraightforward,suchas“Presentapointofview and support it with well-chosen examples.” Other instructions may be morespecific,suchas“Presentyourpositionontheissueanddescribeasituationinwhichtheimplementationofyourrecommendationwouldnotbeadvantageous.”Payingcloseattentiontotheinstructionsyouhavebeengiven,craftyourpointofviewbyselectingyourthreestrongestexamples.Besurethateachofyourexamplesperformsaspecificanddistinctjobinsupportofyourposition.

Onceyouhaveselectedyourbestexamples,writeathesisstatementtoaccommodate

yourexamples.Inthisway,youwillalwayshavetheperfectexamplesforyourthesisstatement because the examples came first! On your scratch paper, jot down yourthesis,andunderneathit,listyourthreeexamplesintheorderinwhichyouplantousethem.Nexttoeachexample,jotdownjustafewwordstoremindyourselfwhyyou’vechosenthatexample.Thesewordswillprovewhytheexampleisaperfectillustrationofyourthesis.

Younowhavethreeinterestingexamplesthatshowdifferentperspectivesontheissue:a thesis statement, which is perfectly supported by your examples; a clear, well-organizedoutlineforyouressay;andeventhemakingsofatopicsentenceforeachofyoursupportingparagraphs.Notonlyareyounowready towrite,butwhen itcomestime towrite, you can focus just on yourwriting.Youdon’t have to be distracted bythinkingaboutwhereyouressayisgoingnext.You’vegotagoodclearplan:Sticktoit.Youressayatthispointis60percentdone.Youhavethemajorityofyourintroductoryparagraph and the beginning of the topic sentences for each of your supportingparagraphs.Allyouneedtodoisexplaineachofyourexamplesingreaterdetail,comeupwithaconclusion,andyou’redone.It’stimetostartwriting.

Step3:WriteWhenitcomestowriting,therearetwothingsyouressaymusthaveandahandfulofthingsitmighthavetogetcreditforgoodwriting.

MustHave:

• Topicsentences—Atopicsentenceannouncesthesubjectandorpointofeachsupportingparagraph.Itcouldbequiteliteralsuchas“____________isanexampleofwhy[restateyourthesis],”orsomethingmorenuanced.Useyourtopicsentencetolinkeachexampletoyourthesisandtoindicatetothereaderthepointyouwouldlikeeachexampletomake.Makeiteasyforyourreadertogetyourpointandthedirectioninwhichyouaregoing.Theharderyourreaderhastoworktofindyourpoint,theloweryourscorewillgo.Itdoesnotpaytobeoverlysubtlewhenyourreaderwillspendonlyonetotwominutesonyouressay.

• Transitions—Transitionsgiveyouressayflow.Theyindicatechangesinscale,direction,orperspectiveandhelpthereadergetfromoneparagraphtothenext.Itmightbejustafewwordsattachedtoyourtopicsentenceorawholesentence.Ifyouarechangingdirection,forexample,simplysaying“ontheotherhand”or“incontrast”mightbesufficient.Ifyouarechangingscaleorperspective,youmightsay“Whenviewedfromtheperspectiveofa____________”or“Whatistrueforanindividualisequallytruefora____________.Forexample…”

MightHave:

• Specifics—Whenyouarguefromapositionofstrength,specificsshouldbeeasy.Usenames,dates,places,andanyotherrelevantdetails.Thedetailsbringanexampletolifeandmakeyousoundlikeanexpert.

• Quotes—Inmanyways,aquoteisliketheultimatespecific.Youcan’talwaysusequotes,butifyouhaveagoodoneandyoucandropitcomfortablyintoyouressay,it’squiteimpressive.

• Bigwords—Bigwordsusedcorrectlyalwaysscorepoints.Theyareawaytodistinguishyourselffromtheotherwriters.Theyarealsosomethingthatcanbepreparedinadvance.Generatealistofimpressivewordsthatyouknowwellandlookforplacestousethem.

• Analogies—Tosaythatcensorship,forexample,isadouble-edgedswordmaybeabitclichéd,butitisalsoaterrificwaytosetupanargumentthathastwosides.Usingagoodmetaphorisliketuckingasnazzysilkhandkerchiefinyourbreastpocket.It’snotnecessaryorevencommon,butifyoucanpullitoff,itraisesthewholeensembletoanotherlevel.

• Length—Lengthcounts.Statisticallyspeaking,longeressaysscorebetter.Thatmeansbeefingupyourtypingskills.Ifyouhavetime,dropinafourthexampleoraddafewmoredetailstoeachofyourfirstthreeexamples.

• Rhetoricalquestions—Doesanythingsoundmoreprofessorialinanessaythantheoccasionalrhetoricalquestion?Itisarhetoricalflourishthatisrarelyusedbutparticularlyeffectiveforthistypeofessay.Itallowsyoutospeakdirectlytoyourreaderandrepresentsasophisticatedwayofjumpingintoatopicthatmostwritersneverconsider.

• Commands—Usethem.Theywillgrabthereader’sattention.Itisaboldstyleofwritingthatfewpeopleuse.

TheArgumentEssayForthe issueessay,your job is tocraftyourownargument.Fortheargumentessay,your job is the opposite. Youwill be given someone else’s argument, and youmustbreak it downandassess it. In someways, this isnotdifficult.Theargument you’regivenwillbefilledwithsomeprettyobviousflaws.

Here’sanexampleofthetypeofpromptsyouwillseeforyourargumentessay:

Thefollowingappeared inamemorandumfromtheregionalmanagerof theTasteofItalyrestaurantchain.

“Afterthefirstmonthofservice,thenewrestaurant intheFlatplainsMall,whichusestheChiplessbrandofwineglasses,hasreportedafarlowerrateofbreakagethanourotherrestaurantsthatusetheElegancebrand.Sinceserversandabartendersatallofourrestaurantsfrequentlyreportthatbreakageisaresultofthetypeofwineglass,andthe customers at the Flatplains Mall restaurant seem to like the Chipless style ofglasses,weshouldswitchallofourrestaurantsovertotheChiplessbrand.”

InstructionsTheargumenttextwillbefollowedbyabriefseriesofinstructions.Youmaybeaskedfor ways to strengthen an argument, find alternative explanations for an argument(weaken), discuss questions to be asked about the argument (identify premise andassumptions), discuss evidence needed to evaluate the argument, and so on. Allinstructionswillaskyoutoworkwiththebasicpartsofanargumentinsomeway.Nomatterwhat,youmustbeprepared to identify thepartsofanargumentanddifferenttypesofargumentandexplainhowtheyallwork.

BreakingDowntheArgumentThere are three basic parts to any argument: the conclusion, the premises, and theassumptions.

TheConclusionTheconclusion is thepoint of theargument.Theauthor is trying to convince youofsomething.Thatsomething is theconclusion.Typically, theconclusionwillbestated,andit isoftenindicatedbywordssuchas“therefore”or“inconclusion.”It ispossible,however,foraconclusiontobeimplied.

ThePremisesOnceyou identify theconclusion,askyourself, “Why?”Theanswers to thatquestionthatarestatedintheargumentarethepremises.Theyarealwaysstated.Therewillbeafewofthem.Theyaretheevidencecitedtosupporttheconclusion.

TheAssumptionsAssumptionsareneverstated.Theylinktheconclusiontothepremises,andtherearehundreds of assumptions. When you brainstorm an argument, the assumptions arewhatyouarelookingfor.Theyareallofthethingsthathavetobetrueinorderfortheconclusiontobetrue.

Whenyoubegintobreakdownanargument,youwillwanttousetheformallanguageof arguments. First, identify the conclusion, then the premises, and finally, theassumptions.

TypesofArgumentsTherearesometypesofargumentsthatyouwillseefrequently.Onceyouidentifythetypeofargument,spottingtheassumptioniseasy.

Causal:ACausesBAcausalargumentassumesacause-and-effectrelationshipbetweentwoevents.Forexample,employeeturnover isupbecausesalariesaredown.Theconclusion is thatlowersalariescausedemployeeturnovertogoup.Toweakenacausalargument,youneed to point out other potential causes for a particular event. Perhaps employeeturnoverisupbecauseofachangeinmanagementorotherpolicies.Perhapsthereisanothercompanyofferingbetter jobs.Tostrengthenacausalargument,youneed toshowthatotherpotentialcausesareunlikely.

SamplingorStatistical:A=A,B,CIn these arguments the author assumes that a particular group represents an entirepopulation.Forexample,nineoutoftendoctorssurveyedpreferaparticularbrandofchewing gum. The conclusion is that 90 percent of all doctors prefer this brand ofchewinggum.Isthattrue?Toweakenthisargument,youneedtoshowthatthepeoplein the group surveyed don’t represent thewhole population. Perhaps they surveyeddoctors at the chewing gum’s annual shareholder meeting. Perhaps they surveyeddoctors in the city where the chewing gum has its headquarters. To strengthen thisargument,youneedtoshowthatthesamplepopulationis,infact,representativeofthewhole.

Analogy:A=BAnalogyargumentsclaimthatwhat is true foronegroup isalso true foranother.Forexample,footballplayerslikeaparticularbrandofcleats,sosoccerplayersshouldtoo.Theconclusion is thatsoccerplayersshould likethisbrandofcleats.Why?Becausefootball players like them. This is the premise. Themain assumption is that soccerplayersshouldlikethesamethingasfootballplayers.Isthistrue?Toweakenanalogyarguments you need to show that the two groups are not at all analogous.Perhapsfootballplayersprefercleatsthatofferfootprotection,whilesoccerplayerswantonesthat mold to the foot. To strengthen these arguments, you must show that the twogroupsarequitesimilarindeed(atleastintheirshoechoice).

CraftingYourArgumentEssayTheoverallprocessforcraftingyouressaywillbethesameasitisfortheissueessay.Invariably, youwill have to follow the approach dictated by your instructions.But nomatter what, you will need to identify and address weaknesses in the argument.Throughoutyouressayyoushouldusethelanguageofargument.Thismeansnamingconclusionsasconclusions,samplingargumentsassamplingarguments,premisesaspremises,andassumptionsasassumptions.

ThinkingBeginbyidentifyingyourconclusionandthenidentifythemajorpremisesuponwhichitrests.Foreachpremisenotethetypeofreasoningused(sampling,causal,andsoon),andtheflawsassociatedwiththattypeofreasoning.Thisisasmuchbrainstormingasyouwillneed.

OrganizingRankthepremisesby thesizeof their flaws.Startwith themostegregiousandworkyourwaydown.Theoutlineofyouressaywilllooksomethinglikethefollowing:

• Theauthor’sconclusionisz.Itisfaultyandmoreresearch/informationisneededbeforethesuggestedactionistaken.

• Thefirstandbiggestflawispremisey.It’spossiblethatitistrue,butitrestsuponthefollowingassumptions.Canwereallymaketheseassumptions?Whataboutthesealternativeassumptions?

• Evenifweassumeytobethecase,thereispremisex.Premisexdrawsananalogybetweenthesetwogroupsandassumesthattheyareinterchangeable.Canwereallymakethisassumption?Whataboutthesealternativeassumptions?

• Evenifweassumextobetrue,thereisalsow.wisasamplingargument,buttheauthornotonlyhasnotproventhesampletoberepresentative,buthe/shealsopointsoutthatthismaynotbethecase!Perhaps,asnoted,blah,blah,blah.

In conclusion, this argument is incomplete and rests upon too many questionableassumptions.Toimprovethisargument,theauthorneedstoshowa,b,andc,beforethebuilding is tobe torndown(or thecompany is tochange tactics, theschool is toreorganizeitscurriculum,andsoon).

WritingFeel free to have fun with this essay. Reading essays can get pretty boring, and asmart, funnycritiqueofa faultyargumentcanbeawelcomedbreak foryour reader.

Youmightsay,“IfIwerethepresidentofcompanyx,Iwouldfiremymarketingdirectorforwastingmytimewithsuchapoorlyresearchedplan.”It’sokaytohavepersonalityaslongasyougettheanalysisoftheargumentdoneatthesametime.

Foramorein-depthlookatthetechniquesfortheargumentessayandsomesampleessays,checkoutourlatestCrackingtheGREbook.AlsocheckouttheScoreItNow!™OnlineWritingPracticeserviceavailableforpurchaseontheETSwebsite.

PARTIII

Drills

VerbalDrill1ClickheretodownloadaPDFofVerbalDrills1and2.

1. Children,aftermorethanagenerationoftelevision,havebecome“hastyviewers”;asaresult,ifthecameralags,theattentionoftheseyoungviewers__________.

expands

starts

alternates

wanes

clarifies

2. Certainlythearchitect’s_________isnotduetohispromotionalskills,indeed,heisolatedhimselffromeverythingthatcoulddisturbhiswork.

proficiency

temperament

prominence

superiority

reticence

3. Theviolinist’s(i)___________performance,coupledwiththe(ii)______________cadencesoftherenownedcomposer’smusic,rousedtheaudiencetoastandingovation.

Blank(i) Blank(ii)prosaic soporific

hackneyed mellifluousvirtuosic insipid

4. Researchintoearlychildhoodeducation,whichadvocatesprovidingtoddlersasyoungastwoorthreewithaplenitudeofintellectuallystimulatingactivities,hasproduced(i)________results.Suchfindings,however,havefailedto(ii)_________manyparentsfromenrollingtheirchildreninsuchunprovenprograms.

Blank(i) Blank(ii)conclusive disabuse

ambiguous dissuadeauspicious distinguish

5. Classicaleconomicsviewshumansasrational,pragmaticcreatureswhononethelessseektomaximizetheirown(i)_____________.Veblen,incontrast,depictshumansas(ii)_____________beings,pursuingsocialstatuswith(iii)___________regardfortheirownhappiness.

6. While(i)___________hasalwaysbeenaproblemincollegeclassrooms,somefearedtheavailabilityofonlineresourceswouldcausetheproblemto(ii)___________.However,educatorshavebeenabletotakeadvantageofInternettoolstochecktheirstudents’workagainstanymaterialonlineandthus(iii)___________thattheirstudentsaretrulysubmittingtheirownworkandnotsimplycopyingfromawebsite.

7. Theskilllevelofmedievalstoneworkersclearlyexceedsthatoftheirmoderncounterparts.Atradejournalrecentlypublishedtheresultsofadecade-longsurveyofmasterstonemasonsinEurope.Accordingtothereport,aclearmajorityofrespondentsnotedthatmedievalcathedralsexhibitaconsistentlyhigherlevelofcraftsmanshipintheirstoneworkthandosimilaredificesbuiltinthelasthundredyears.Whichofthefollowing,iftrue,wouldmostseriouslyweakentheaboveargument?

Thestonemason’smaintoolsarevirtuallyunchangedsincetheMiddleAges.

Thestoneworkincathedralsistypicalofthatinsurvivingmedievalstructures.

Mostmedievalcathedralsaresignificantlylargerthanmodernstoneedifices.

ThepracticeofapprenticeshiphaddeclinedsignificantlysincetheMiddleAges.

Higherqualitystoneworkislesslikelytofallintodisrepairandbedestroyed.

Questions8–11refertothefollowingpassage.

8. Theprimarypurposeofthepassageisto

presentanoverviewoftheeconomicchangesthatledtotheEnglishwomen’s

movement

evaluateaviewoftheEnglishwomen’smovementaspresentedinaliterarywork

describethesocialandpoliticalcontextofthewomen’smovementinEngland

offeranovelanalysisofEngland’sreactiontothewomen’smovement

profileseveralofthewomenwhowereinstrumentalinthesuccessoftheEnglishwomen’smovement

9. TheauthorincludesStrachey’sclaimthat“thetruehistoryoftheWomen’sMovement…isthewholehistoryofthenineteenthcentury”(lines15–16)inordertoemphasize

Strachey’sbeliefthattheadvancementofwomen’srightswasthemostsignificantdevelopmentofitscentury

theimportanceStracheyattributestothewomen’smovementinbringingabouttheEnlightenment

Strachey’sawarenessoftheinterconnectionofthewomen’smovementandothersocietalchangesinthe1800s

Strachey’scontentionthatthewomen’smovement,unlikeothersocialandpoliticaldevelopmentsofthetime,actuallytransformedsociety

Strachey’sargumentthatthenineteenthcenturymustplayaroleinanycriticismofthelimitationsofwomen

10. WhiletheauthoracknowledgesStrachey’simportanceinthestudyofwomen’shistory,shefaultsStracheyfor

focusingherstudyonthelegalandpoliticalreformenactedbythewomen’smovement

oversimplifyingherconceptionofthesocialconditionofwomenpriortothereformsofthewomen’smovement

failingtoeliminatetheanachronisticideaof“women’sduty”fromherarticulationofnineteenth-centuryfeminism

omittingMaryWollstonecraftandHannahMorefromherdiscussionofimportantinfluencesinfeminism

recommendingastaticanddomesticsocialroleforwomenfollowingthewomen’smovement

11. Whichofthefollowing,iftrue,wouldmostweakentheauthor’sassertionaboutthesimilaritybetweentheEnglishandAmericanwomen’smovements?

TheEnglishandAmericanwomen’smovementstookplaceinverydifferent

sociohistoricalclimates.

TheEnglishwomen’smovementbeganalmostacenturybeforetheAmericanwomen’smovement.

TheEnglishwomen’smovementexcludedmen,whiletheAmericanwomen’smovementdidnot.

FewmembersoftheEnglishwomen’smovementwereawareoftheimpactitwouldhaveonsociety.

ManyparticipantsintheEnglishwomen’smovementcontinuedtoperformtraditionaldomesticroles.

12. Thoughnotcompletely___________,thenewesteditionofthebookiscertainlyverydifferentfromanypreviouslypublishedversion.

familiar

unrecognizable

answerable

legitimate

reworked

gentrified

13. Merzon’s___________behaviorconvincedhiscolleaguesthathehadulteriormotives.

inconspicuous

furtive

overt

unorthodox

predictable

surreptitious

14. Withitsrefinedinteriorsandamplystockedreadingroom,thehotelcateredtothemost__________oftravelers.

philistine

urbane

cosmopolitan

uncouth

grandiloquent

pretentious

15. Byfarnotthemost___________ofmen,Wilbertnonethelessenjoyedrenownthatwasunimpededbyhisinherentirascibility.

loquacious

pedantic

amiable

garrulous

affable

stentorian

16. Selectthesentenceinthepassagethatbestsupportstheauthor’smainidea.

It is hard from ourmodern perspective to imagine that theater has the power to influencepolitics,yettheplaysofpre-republicanIrelanddidjustthat.CrippledbythecensoriousEnglishrule and muted by population migration, Irish culture had fallen into an almost irrevocabledecline by the second half of the 19thCentury.A group ofDublin intellectuals andwriters,callingthemselvestheGaelicLeague,formedasocietydedicatedtotherevivalofIrishculture.Among its illustriousmembers, the League boastedWilliamButler Yeats, J.M. Synge, SeanO’Casey, andLadyGregory.The foundingof theAbbeyTheatre and the production of Irishplays were directly responsible for the resurgence of interest in Irish language and culture,culminatingintheEuropeanUnion’sdecisionin2005tomakeIrishanofficiallanguageofthatbody.

Questions17–20refertothefollowingpassage.

17. WhichofthefollowingbestdescribesthereasonthatscientistswereinitiallyperplexedatthediscoverythatmalariawasspreadbyAnophelesmosquitoes?

ScientistshadevidencethatmalariawascarriedbytheprotozoanbloodparasitePlasmodium.

ScientistsfeltthatbecausesomanyspeciesofAnophelesexisted,theycouldnotbecarriers.

ScientistswereunabletofindadirectcorrelationbetweenAnophelesdensityandfrequencyofmalariaoccurrence.

ScientistsknewthatmanyspeciesofAnophelesmosquitodidnotfeedonhumanblood.

ScientistsbelievedthattheAnophelesmosquitocouldnotbehosttotheparasitePlasmodium.

18. Inthecontextinwhichitappears,“host”(line12)mostnearlymeans

scarcity

sacrament

multitude

organismreceivingatransplant

organismsupportingaparasite

19. Itcanbeinferredfromthepassagethatamosquitobecomesacarrierofmalariawhen

itingeststhebloodofahumanbeinginfectedwithmalaria

itlivesinregionswheremalariaiswidespread

itconsumesbloodfromaprotozoanmalarialagent

ithasextendedcontactwithotherinsectvectors

itisspawnedinPlasmodium-infestedlocalities

20. Theboldedtextplayswhichofthefollowingrolesinthepassage?

Itprovidesevidencetoweakentheauthor’smainpoint.

Itprovidesevidencetostrengthentheauthor’smainpoint.

Itclarifiestheimportanceofsolvingaparadoxexpressedinthepassage.

Itgivestheresolutiontoaparadoxexpressedinthepassage.

Itexplainswhyaparadoxexpressedinthepassageresistedeasyresolution.

VerbalDrill21. Manyscholarsfeelthathistoricaleventscanbeseenas__________;whatonegroupseesaspeacekeeping,anothergroupmightseeassubjugation.

academic

portentous

paradoxical

trifling

bellicose

2. TheAmericanpublicveneratesmedicalresearchersbecausetheresearchersmakefrequentdiscoveriesoftremendoushumanitarianconsequence;however,thedailyroutinesofscientistsarelargelymadeupofresultverificationandstatisticalanalysis,makingtheiroccupationseem__________.

fascinating

quotidian

recalcitrant

experimental

amorphous

3. The(i)__________clothingstorefaceditsfirstrealcrisisjustsixmonthsafteropeningwhennewownerstookoverthebuilding,raisedtherent(ii)_____________,andaskedforafive-yearextensiononthelease.

Blank(i) Blank(ii)fledgling beneficentlyurbane precipitously

ostentatious minutely

4. RonaldReaganbecameknownas“TheGreatCommunicator”particularlybecauseofhisabilitytomake(i)__________topicsindomesticandforeignaffairsmore(ii)____________topersonsofwidelyvaryingeducationallevels.

Blank(i) Blank(ii)abstruse palatable

obtuse lucidmundane munificent

5. Thecensustaker’s(i)__________jobismadeevenmoredifficultbythe(ii)___________natureofmoderncivilization.Increasingnumbersofpeopleseldomresideinanyoneplaceforverylong.Evenamongthosewhodoremain(iii)___________,however,therearefrequentchangesoflivelihood,income,andevensocioeconomicstatus.

6. Bynightfallthecitycouncildebatehadlongsincedegeneratedinto(i)____________.Whathadbeguninthelateafternoonasanearnestbutpolitediscussionturnedpersonalasbothsideshurled(ii)_________andpersonalattacksateachother.Disinterestedobservers,however,blamedthe(iii)__________chairmanofthecouncilforallowingsuchdisarray,arguingthatamoderatorwithmoreexperiencecouldhavemanagedthemeetingmoreconstructively.

Questions7–9refertothefollowingpassage.

Onepopularbutcontroversialwayofregainingrevenueshortfallsinprofessionalsportsistosellstadiumnamingrights.Buildinganewsportsorentertainmentfacilityisamajorfinancialundertaking;asbrandingandsponsorshipbecomeincreasinglyubiquitous,itisperhapsinevitablethatbigbusinesswillshouldermoreoftheburdeninexchangeforpublicity.

Theoretically,thesellingofnamingrightsseemslikeawin-winproposition,butpractically,thesituationismorecomplicated.Fansareoftenopposedtochangingthenameofastadium,orwanttomakesuretheircontributiontoitsconstructionisrecognized.Neighborhoodresidentsmayalsoobjecttoaperceivedredecorationoftheircommunityincorporatecolors,logos,andadvertisements.Forcompanies,namingrightsaloneoftendonotjustifythehighpricescharged.Additionally,itisunclearwhethertheteamorthefacilitybenefitsfromthesale:ifthecorporationisa“sponsor,”theteamshouldreceivethemoney,butfacilityownersgleanrevenuefrom“advertisers.”Thus,thedifficultyofreachingamutuallyacceptablewordingofcomplicatedagreementscreatesaquagmireoflitigation.

Severalmeansofcompromisehavebeennegotiated,suchassellingthenameofthefieldwhilekeepingtheoriginalnameofthesportsarena,sellingsectionsofthefacility,allowingacompanyto“present”it,allowingthesponsortoprovideretailorconcessionservicesinsidethestadium,andofferingbusinessopportunitiessuchasdirect-to-consumercoupons,productsamples,andinformation.Thoughthepracticewasnearlyunheardofthirty-fiveyearsago,therearecurrently72sponsorshipdealsinplace.Andsportsisnottheonlyareato“gocorporate”—conventioncenters,concertvenues,publicworks,andeveneducationalinstitutionshavesoldnamingrightsinexchangeformuch-neededfundsandservices.

7. Thepassagementionsthedifferencebetween“sponsors”and“advertisers”primarilyinorderto

illustratetheconfusingnatureoflegalproceedingsthatsurroundnamingrights’deals

provideanexampleofthekindsofissuesthatsurroundanamingrightsagreement

provethatitisalwaysimportanttoconsiderterminologycarefully

revealtheperniciousnatureofoneandthebenevolentnatureoftheother

explainwhycommunitiesoftendonotbenefitfromneighborhoodstadiums

8. Inwhichsentenceofthepassagedoestheauthorattempttoanticipateandprecludeapossiblereactiononthepartofthereader?

Buildinganewsportsorentertainmentfacilityisamajorfinancialundertaking;as

brandingandsponsorshipbecomeincreasinglyubiquitous,itisperhapsinevitablethatbigbusinesswillshouldermoreoftheburdeninexchangeforpublicity.

Theoretically,thesellingofnamingrightsseemslikeawin-winproposition,butpractically,thesituationismorecomplicated.

Forcompanies,namingrightsaloneoftendonotjustifythehighpricescharged.

Thus,thedifficultyofreachingamutuallyacceptablewordingofcomplicatedagreementscreatesaquagmireoflitigation.

Thoughthepracticewasnearlyunheardofthirty-fiveyearsago,therearecurrently72sponsorshipdealsinplace.

9. Inthecontextinwhichitappearsinthelastparagraph,theword“practice”mostnearlymeans

observance

rite

rehearsal

action

office

Questions10–11refertothefollowingpassage.

OftenlostintheuproariouslyribaldnatureofAristophanes’greatwartimecomedyLysistrata(411BCE)istheauthor’sseriousmessage.Contemporaryaudiences,likemodernones,weretakenbythestoryofLysistrataorganizingtheGreekwomentowithholdsexualfavorsuntilpeaceisdeclaredbetweenAthensandSparta.ToitsAthenianaudience,though,embroiledinseeminglyendlessPeloponnesianWar,theworkhadaclearsymbolicmeaning:endthewar,butthroughcelebrationofGreekunity,notcelibacy.Thepartmeanttoresonatewithviewerswasnotthewithholdingofsex,butthepoweroftheconcordthewomenshowedinsodoing.Theplay’swomen,infact,representtheGreekpoleis,orcity-states.Theprotagonists,LysistrataandLampito,representAthensandSparta,respectively;theconspiracycan’tbeginuntilLampitoarrives,andpeacecanbeachievedonlywhentheymakecommoncausewiththeotherwomen.Thewomen’scohesioncarriesthemthroughtheirconfrontationwiththemagistrateandhishenchmen,andisemphasizedintheoracle:theillsoflifewillendwhen“theswallows…shallhaveallflockedtogether.”Andthemenonlyfinallyagreetogivethewomenahearingwhentheyrealizethatthey’refacing“ageneralconspiracyembracingallGreece.”Themen,fortheirpart,representanti-Greek,polis-basedattitudes,andareonlyovercomewhenledbyLysistratatofocusonGreekcommonalities,instancesofpastmutualaid,andthesharedexternalthreatofthePersians.

10. Withwhichofthefollowingstatementswouldtheauthormostlikelyagree?

AristophaneswasuniquelyinfluentialamongAthenianplaywrights.

Wartimecomedieswithoutaseriousmessageareinappropriatesubjectsofstudy.

Someknowledgeofhistorycanbeusefulininterpretingliteraturefromothereras.

11. Theauthormentionstheoracleprimarilyinorderto

emphasizetheimportanceofLampitoamongtheconspirators

provideadditionalevidenceinsupportofthemainideaofthepassage

clarifytheoriginsoftheconspiracyintheplay

suggestthatearlierinterpretationsofLysistratawerebasedonfalseassumptions

concedeapointinoppositiontothemainideaofthepassage

Question12referstothefollowingpassage.

StatisticsreleasedbytheNationalInstituteofHealthshowthatcancerpatients,onaverage,are living almost six months longer after the initial diagnosis of their condition than werepatients just twoyears ago.Moreover, these findings conform to a trend that goes backwelloveradecade.Clearly,themedicalcommunityismakingsignificantprogressinextendingthelivesofcancerpatients.

12. Theaboveargumentdependsonwhichofthefollowingasanassumption?

Cancerisnotbeingdiagnosedinprogressivelyearlierstages.

Thetrendismorepronouncedinsomekindsofcancerthaninothers.

Fewerpeoplearediagnosedwithcancereachyear.

Thenumberofpatientswhosecancergoesintofullremissionisalsorising.

Cancerisnolongertheleadingcauseofdeathamongpeopleover60yearsofage.

13. Ferventschismsamongthedelegateswerelargelyoverplayed;theareaof__________wassizableenoughtokeeptheconventionfrombeingdisbanded.

congruence

asperity

contradiction

concurrence

impassivity

truculence

14. WhatAndrewJohnsonlackedineducationhemadeupforwithhis____________;thoughheneverattendedschool,hetaughthimselftoreadandwrite,enteredpolitics,andultimatelysucceededAbrahamLincolnaspresidentoftheUnitedStates.

mettle

timidity

tenacity

tenuousness

candor

alacrity

15. The__________salesclerk,desperatetounloadherburgeoninginventory,unwittinglydrovemanyapotentialcustomerawaywithherpushy,overeagermanner.

loquacious

irreverent

officious

innocuous

meddlesome

vigilant

16. _________isnoguaranteeofworkerloyalty;eventhemostcompliantofemployeesmaybemotivatedbyahiddenagenda.

Effrontery

Deference

Prevarication

Complaisance

Truculence

Chicanery

Questions17–18refertothefollowingpassage.

Researchconductedon theneurological consequencesof illicit substances traditionallyhascenteredontheblockageofthereuptakeneurons(DAT)that,undernormalconditions,recycledopamine (DA) topreventoverstimulation.As seen in thebrainof ahealthy,non substance-abusing individual, DA is released through an electric pulse, it lingers momentarily arounddopamine receptors (D2) to pique the body, and then travels back up DAT for later use.Recently,positronemission tomographyhasenabled researchers toadiscoveranunexpected,completely different process: drug usemay actually decrease the quantity ofD2 available toreceiveDA, resulting in a perceiveddeficit of the latter and an irrepressible compulsion, thehallmarkofaddiction,toincreaseitsproductionthroughstimulants.

17. Inthecontextinwhichisappears,“pique”mostnearlymeans

impair

heal

excite

relax

irritate

18. Thepassageexplainstheconventionalfocusofsubstanceabuseresearchinorderto

arguethatsuchanapproachisbasedonafalseunderstandingofthewaythatmostillegaldrugsactonthebrain

suggestthatthepositronemissiontechnologyisnotaccurateinitsdepictionofD2reduction

provideevidenceinfavorofcontinuingresearchintoDATblockage

makeclearwhythediscoveryofanalternateconsequenceofsubstanceabusemightbeunexpected

offerareasonableexplanationfortheinabilityofmanypeopletoovercomedrugaddiction

Questions19–20refertothefollowingpassage.

Oneofthemostsignificantreasonsforthedramaticriseinbothagriculturalproductionandpopulation inwesternEurope around 1000CEwas the increase in the use of horses as draftanimals. Themilitary preeminence ofmounted cavalry since the Carolingian erameant thathorseswereselectivelybredforsizeandstrengthearlierthanwereotherfarmanimals,andtheninth-centurydevelopmentofnailedhorseshoes improvedboth tractionandresistanceagainstinfection.Most importantly, perhaps, harnesses designed for oxenwere adapted for horses: aneckstrapthatrestrictedbothairandbloodfromreachingthehorse’sbrainwasreconfiguredtoput theweighton thehorse’s shoulders, andhorsesquickly shed their ancient stigmaas lazybeasts.

Thechangefromoxtohorseastheprimarydraftanimalwasslowanderratic.Horseswereexpensive,untraditional,andrequiredanexpensivefood,oats.Wherethechangeoccurred,though,itgavetheEuropeancountrysideanewlookbygreatlyincreasingtheamountoflandthatcouldbeexploitedfromacentralhomestead.Whereoncefarmerswerelimitedtofieldstowhich theycoulddrive theiroxen,plow,andreturnhome inaday, theycouldnowride theirhorsesmuchgreaterdistances,doaday’swork,andstillreturntosafetybeforedark.Isolatedhamletsgrewtowardseachothertoformvastvillages,which,inturn,expandedintotowns,andthegreatprimevalforestsofEuroperecededintomemory.

19. Thepassageprovidesinformationtoanswerwhichofthefollowingquestions?

Howfarfromacentralhomesteadcouldoxenbedrivenforaday’swork?

Whatdevelopmentshelpedleadtothemilitaryprimacyofhorses?

Whatmadeancientharnessesunsuitableforhorses?

20. Inthepassage,thetextinboldfaceplayswhichofthefollowingroles?

Itcitesfactorsfacilitatingthedevelopmentunderdiscussion.

Itcitesfactorsinhibitingthedevelopmentunderdiscussion.

Iteliminatesanalternatecauseforthedevelopmentunderdiscussion.

Itresolvesaparadoxpresentedinthepassage.

Itsuggestsfurtherramificationsofaparadoxpresentedinthepassage.

MathDrill1ClickheretodownloadaPDFofMathDrills1and2.

RSTUisaparallelogram.

1. QuantityA QuantityB x 45

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

2. Mr.Jonespurchasedanewbedroomsetbyusinganextendedpaymentplan.Theregularpriceofthesetwas$900,butonthepaymentplanhepaid$300upfrontand9monthlypaymentsof$69each.

QuantityA QuantityB

$23 TheamountMr.Jonespaidinadditiontotheregularpriceofthebedroomset.

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

3. QuantityA QuantityB TheperimeterofΔBCD 42

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

4. Thecircumferenceofacirclewitharadiusof meterisCmeters.

QuantityA QuantityB C 4

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

5. QuantityA QuantityB x+1 1–x

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

6. Theaverage(arithmeticmean)oftwopositiveintegersisequalto17.Eachoftheintegersisgreaterthan12.

QuantityA QuantityB Twicethelargerofthetwointegers 44

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

7. QuantityA QuantityB xy x

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

8. QuantityA QuantityB

30 Thenumberofintegersfrom15to−15,inclusive

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

9. Mikeboughtausedcarandhaditrepainted.Ifthecostofthepaintjobwasone-fifthofthepurchasepriceofthecar,andifthecostofthecarandthepaintjobcombinedwas$4,800,thenwhatwasthepurchasepriceofthecar?

$800

$960

$3,840

$4,000

$4,250

10. Whatistheperimeterofthefigureabove?

51

64

68

77

91

11. Ifxandyareintegersandxyisaneveninteger,whichofthefollowingmustbeanoddinteger?

xy+5

x+y

4x

7xy

12. If3x=−2,then(3x−3)2=

13. Inthefigureabove,whatdoesbequalifa=3b?

40

30

25

20

10

Questions14−16refertothefollowingchart.

14. IfthetotalnumberofregisteredvotersinTownshipXincreased10%from2000to2010,thenhowmanyregisteredvoterswereinTownshipXin2000?

15. Whatisthesumofthetotalnumberoffemalevotersplusthetotalnumberofremainingvoterslessthan48yearsoldinTownshipXin2010?

5,701

5,715

6,745

6,815

8,106

16. InTownshipXin2010,theratioofthenumberofvotersregisteredasDemocratstothenumberofmaleregisteredvotersage48to62wasmostnearly

1to1

2to1

3to1

3to2

5to2

17. Whatistheleastnumberrforwhich(3r+2)(r−3)=0?

−3

−2

–

3

18. Whatistheperimeter,incentimeters,ofarectangularnewspaperad14centimeterswidethathasthesameareaasarectangularnewspaperad52centimeterslongand28centimeterswide?

19. Inacertainelection,60percentofthevoterswerewomen.If30percentofthewomenand20percentofthemenvotedforcandidateX,whatpercentofmenandwomenvotersintheelectionvotedforcandidateX?

18%

25%

26%

30%

50%

20. IfK=21×54×22,thenwhichofthefollowingisaninteger?Indicateallsuchintegers.

MathDrill21. QuantityA QuantityB 4(26) 6(42)

QuantityAisgreater.QuantityBisgreater.Thetwoquantitiesareequal.Therelationshipcannotbedeterminedfromtheinformationgiven.

2. QuantityA QuantityB Thepercentincreasefrom4to5 Thepercentdecreasefrom5to4

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

3. QuantityA QuantityB

Thecircumferenceofacircularregionwithradiusr Theperimeterofasquarewithsider

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

4. QuantityA QuantityB

Theaverage(arithmeticmean)of7,3,4,and2 Theaverageof2a+5,4a,and7−6a

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

5. Inthexy-plane,oneoftheverticesofsquareQisthepoint(−3,−4).ThediagonalsofQintersectatthepoint(2,1).

QuantityA QuantityB TheareaofQ 100

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

6. QuantityA QuantityB 317+318 (4)317

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

7. QuantityA QuantityB b+c 180–a

QuantityAisgreater.

QuantityBisgreater.

Thetwoquantitiesareequal.

Therelationshipcannotbedeterminedfromtheinformationgiven.

8. Ifthecostofaone-hourtelephonecallis$7.20,whatwouldbethecostofaten-minute

telephonecallatthesamerate?

$7.10

$3.60

$1.80

$1.20

$0.72

9. Whatisthevalueofninthefigureabove?

9

15

16

12

20

10. Ifx+y=zandx=y,thenwhichofthefollowingmustbetrue?Indicateallsuchequations.

2x+2y=2z

x–y=0

x–z=y–z

x=

x–y=2z

11. Amovietheateris3blocksduenorthofasupermarketandabeautyparloris4blocksdueeastofthemovietheater.Howmanyblockslongisthestreetthatrunsdirectlyfromthesupermarkettothebeautyparlor?

2.5

3

4

5

7

12. Theunitsdigitofa2-digitnumberis3timesthetensdigit.Ifthedigitsarereversed,theresultingnumberis36morethantheoriginalnumber.Whatistheoriginalnumber?

13

26

36

62

93

13. Arestaurantownersold2dishestoeachofhiscustomersat$4perdish.Attheendoftheday,hehadtakenin$180,whichincluded$20intips.Howmanycustomersdidheserve?

Questions14–16refertothefollowinggraph.

14. Iftherewere38childsafetyorganizationsandthefundscontributedtotheseorganizationsinSeptember1989wereevenlydistributed,howmuchdideachcharityreceive?

$12,000,000

$9,400,000

$2,500,000

$250,000

$38,000

15. FromSeptember1985toDecember1989,whatwastheapproximateratioofprivatedonationsinmillionsforhomelessaidtoprivatedonationsinmillionsforanimalrights?

20:9

3:2

4:3

9:7

6:5

16. WhichofthefollowingcharitablecausesreceivedtheleastpercentincreaseinprivatedonationsfromSeptember1989toOctober1989?

AnimalRights

DisasterRelief

HomelessAid

EnvironmentalProtection

ChildSafety

17. AlexgaveJonathanadollars.ShegaveGinatwodollarsmorethanshegaveJonathanandshegaveLouannethreedollarslessthanshegaveGina.Intermsofa,howmanydollarsdidAlexgiveGina,Jonathan,andLouannealtogether?

a−1

3a

3a−1

3a+1

18. Ifm+n=p,thenm2+2mn+n2=

4p

np–m

p2

p2+4(m+p)

p2+np+m2

19. Forallrealnumbersxandy,ifx*y=x(x–y),thenx*(x*y)=

x2–xy

x2−2xy

x3–x2–xy

x3–(xy)2

x2–x3+x2y

20. Ifxisanintegersuchthat1<x<10,thenwhichofthefollowingcouldbetheremainderwhen117isdividedbyx?Indicateallsuchnumbers.

1

2

3

4

5

6

7

PARTIV

DrillAnswersandExplanations

VerbalDrill11.D Theclueinthesentenceis“Children…havebecome‘hastyviewers.’ ”The

transitionpunctuationisa“same-direction”semicolon.Soagoodwordfortheblankwouldbewanders.Inanycase,ithastobeanegativeword.Thewordsin(A),(B),and(E)arepositive,and(C)isn’treallynegative.Thatleaves(D).

2.C Findthestory.Thisarchitectdoesn’tpromotehimself;therefore,hisfamecan’tbearesultofself-promotion.Tryawordlikefamefortheblank.Neitherproficiencynortemperamentmean“fame,”socrossoff(A)and(B).Prominencecouldwork,sogive(C)a“maybe”andmoveon.Thereisnothinginthesentencetoindicatethatthearchitectissuperior,soeliminate(D).Whilethearchitectmayhavebeenreticent,youarelookingforfame.Crossoff(E).Thebestansweris(C).

3.virtuosic,mellifluousTheclue“rousedtheaudiencetoastandingovation”indicatesthatbothblanksneedapositiveword.Thetoughestpartaboutfillingeitherblankisthedifficultvocabinthetwocolumns.Usepositive/negativetoeliminateunlikelychoices.Hackneyedsoundsnegative,whilevirtuosiclooksalotlikevirtue,apositiveword.Inthesecondcolumn,mellifluouslooksabitlikemellow,whichisusuallyagoodthing,butinsipidhastheprefixin,whichmeans“against.”Thatmaygiveitanegativeconnotation.Alltold,virtuosicandmellifluousbothhavepositivemeaningsandsuitthesentencebest.

4.ambiguous,dissuadeTheclueforthefirstblank,“suchunprovenprograms,”comesattheendofthesentence.Youneedawordmeaning“inconclusive”todescribetheresults.Conclusiveisclearlytheoppositeofwhatyouwant,butambiguouslooksgood,especiallygivenitsprefixambi,whichmeans“goinginbothdirections.”Auspicious,incontrast,maysoundlikesuspicious,butifyou’vebeenstudyingyourvocabulary,you’llknowthatithasapositivemeaning.Hangontoambiguousandworkthesecondblank.Youalreadyknowthattheprogram’sresultshavenotbeenproven,butthereverse-directiontransition“however”indicatesthatthosefindingsarehavinganunexpectedorcontradictoryeffectonparents’desiretoenrolltheirchildren.Sincethephrase“havefailedto”comesrightbeforetheblank,youneedawordmeaning“discourage.”Keepdisabuseanddissuadeifyou’renotsureoftheirmeanings,butgetridofdistinguish.Meanwhile,noticethatdissuadesharesthesamewordrootaspersuade,buthastheprefixdis,whichmeans“not.”Thatmakesitalikely

choice,leavingambiguousanddissuadeasthetwobestanswers.

5.bliss,irrational,scantThereverse-directiontransition“nonetheless”tellsyouthatthefirstblankneedsawordmeaningtheoppositeofeither“rational”or“pragmatic.”Sincethere’snosynonymforirrationalinthefirstcolumn,try“notpractical”andusePOE.Whileanimpracticalpersonmightmakehisownsufferingapriority—viamelancholyordiscord—blissmakesmoresense,especiallygiventhat“regardfortheirownhappiness”ismentionedlaterinthesentence.Anotherreverse-directiontransition,“incontrast,”isalsousedtoreverseeither“rational”or“pragmatic”forthesecondblank.Chooseirrationalfromthesecondcolumnandworkonthethirdblank.Thefirstpartofthesentencetellsyouthatclassicaleconomicsseeshumansastryingtomaximizetheirownhappiness,andthenthereverse-directiontransition“incontrast”givesyouVeblen’sview.Assuch,thethirdblankneedsawordthatmeanstheoppositeof“maximizinghappiness.”Scantistheclosestmatchfromthethirdcolumn,makingit,bliss,andirrationalthebestanswers.

6.plagiarism,proliferate,ensureTheclueattheendofthesentence,“copyingfromawebsite,”givesyouplagiarismforthefirstblank.Usethesecondpartofthesentenceandthereversetransition“However”forthesecondblank;sincetheirfearswerenotrealized,youknowyouneedawordlikeincrease.Ifyoudon’tknowthewordproliferate,studyingyourGreekrootscanmakeitagreatbet.Forthelastblank,youknowthattheeducatorsarecheckingtheirstudents’work,soagoodwordforthelastblankwouldbeprove.Rebutistemptingbutdoesn’tquitefit,andneglectisn’tevenclose,soyou’releftwithensure,thecorrectanswer.

7.E Theconclusionoftheargumentisthefirstsentence—medievalstoneworkersaremoreskilledthanmodernones—andtheresultsofthesurveyprovidethepremiseonwhichthisconclusionisbased.Theargumentassumes,though,thatcathedralsaretypicalofmedievalstonework;ifnot,themedievalmasonsarebeingevaluatedonanatypicalsampleoftheirwork.Thus,(E)mostweakenstheargument:Iflowerqualitystoneworkismorelikelytobedestroyed,thenmedievalmasonsarebeingjudgedontheirbestwork—theirworstworklikelyhavingbeendestroyedlongago.Choices(A)and(B)wouldbothstrengthentheargument:(A),byremovingapossibledistinctionbetweenmedievalandmodernmasonsthatmightotherwiseaccountforthedifferenceinquality;(B),bydirectlysupportingtheaboveassumption.Withoutfurtherinformationrelatingbuildingsizeorapprenticeshiplengthtoskillinstonework,finally,both(C)and(D)arebeyondthescopeoftheargument.

8.C Thisisamainideaquestionaboutthepassageasawhole.Your“treasurehunt”shouldhaverevealedthatthepassageisbasicallydiscussingthewayinwhich

StracheyinterpretstheEnglishwomen’smovement.Eliminate(B)rightawaybecauseit’snotabouta“literary”work.Eliminate(D)becauseit’snota“novelanalysis.”Eliminate(A)and(E)becausetheyaretoospecific.Thatleaves(C).

9.C Forlinereferencequestions,gobacktothelinescited,andreadaboutfivelinesbeforeandafterthoselines.Youcanfindtheanswerineitherplaceforthisquestion.ThefirstsentenceoftheparagraphtellsyouStracheyiswritingabout“thehistoricalconnectionsbetweenthewomen’smovementandothersocialandpoliticaldevelopments.”Choice(C)isjustaparaphraseofthis.

10.B Lookbackinthepassagefortheplacewheretheauthor“faults”Strachey.It’sinthelastparagraph.Theauthorstates,“WhereStracheypicturedarelativelyfixedimageofdomesticwomenthroughoutthefirsthalfofthe19thcentury,recenthistoricalandliteraryworkssuggestthatthisimagewasbothcomplexandunstable.”Soundslike(B).

11.D First,gobacktothepassagetofindoutwhattheauthorsaidabout“thesimilaritybetweentheEnglishandAmericanwomen’smovements.”It’sattheendofthefirstparagraph.Theauthorsaysthat“likeitsAmericancounterpart,theEnglishwomen’smovementhadapowerfulsenseofitsownhistoricimportanceandofitsrelationshiptowidersocialandpoliticalchange.”Soyou’relookingforananswerchoicethatwouldindicatethatwasnottrue.Choice(D)directlycontradictstheauthor’sassertion.

12.unrecognizable,reworkedThebestwordfortheblankhereissomethinglike“new”sinceyouknowthatitisverydifferentandyouhavethechange-directiontransition“Though.”Thebesttwoanswers,therefore,areunrecognizableandreworked.Noneoftheotherchoicesreallymatcheachotherorthemeaningoftheblank.

13.furtive,surreptitiousThecluefortheblankis“hehadulteriormotives.”Think“sneaky”or“secretive”andusePOE.Inconspicuousisout,sinceit’stheoppositeoftheclue,buthangontofurtive(evenifyoudon’tknowitsmeaning).Overtisalsotheoppositeofsneaky;getridofit.Unorthodoxandpredictable,meanwhile,don’tmatchtheclue,butsurreptitiousdoes.Thatleavesfurtiveandsurreptitious,thetwobestanswers.

14.urbane,cosmopolitanSincethehotelhadboth“refinedinteriors”andan“amplystockedreadingroom,”itwouldappealtoguestswhowerewell-readandlikedrefinement.Think“sophisticated”or“worldly”andusePOE.Philistineistheoppositeofrefinedorworldly,butbothurbaneandcosmopolitanaresolidmatches.Incontrast,uncouth’smeaningisverysimilartothatofphilistine,socrossoutthatchoice.Grandiloquentandpretentious,meanwhile,don’tmatchtheclue,leavingyou

withurbaneandcosmopolitan.15.amiable,affable

“Hisinherentirascibility”isreversedbythechange-directiontransition“not,”whichcomesbeforetheblankdescribingWilbert.Youneedawordthatmeanstheoppositeofirascibility.Think“friendly”or“good-tempered”andusePOE.Neitherloquaciousnorpedanticmeansfriendly,butamiablematches.Garrulous,meanwhile,hasthesamemeaningasloquacious,socrossitout.Finally,affableisagoodmatch,butstentoriandoesn’twork.Amiableandaffablesuitthesentencebest.

16. Itishardfromourmodernperspectivetoimaginethattheaterhasthepowertoinfluencepolitics,yettheplaysofpre-republicanIrelanddidjustthat.Thepassagestartsoutwithitsconclusionthat,inthecaseofIreland,theaterinfluencedpolitics.Therestoftheparagraphtellshowthisoccurred.

17.C Gobacktothefirstparagraph.Inlines6–7thepassagestates,“Insomelocalitiesthemosquitowasabundantbutmalariarareorabsent.”

18.C Tryputtingyourownwordinthepassagetoreplace“host.”Thetransition“but”indicatesthatthereferencetodistinctbiologicaltraitsshouldcontrastwiththestatementthatthemosquitoesseemalmostidentical,soyouneedawordthatmeanssomethinglike“largenumber.”Ofthechoices,multitudeisthebestmatch.Bewareof(A),which,thoughtempting,refersspecificallytopeople.Likewise,becarefulwith(E):Whilethemosquitoesinquestiondo,infact,supportparasites,thatusagewouldn’tmakesenseinthiscontext.

19.A Rereadthesecondsentenceofthesecondparagraph.Itsaysthatthemosquitobecomesacarrierwhenitfeedsonhumanblood.

20.E Choice(E)isbestsupportedinthepassage.Thefirstparagraphdiscussesaseeminglyinconsistentrelationshipbetweenthepresenceofthemosquitoesandtheprevalenceofmalaria,aparadoxresolvedbythediscoveryofmultiplespeciesamongtheinsects;theboldfacetextsuggestswhythismultiplicityofspecieswasn’timmediatelyapparent.Choices(C)and(D),whileappropriatelyreferringtotheparadox,incorrectlydescribethevalueoftheboldedtext:Itneitherresolvesnorclarifiestheimportanceofthatparadox.Choices(A)and(B),finally,arenotsupportedbecausetheboldfacetextdoesn’tdirectlyweakenorstrengthentheauthor’smainpoint,whichisthediscussionofoneimportantstepintheefforttoeradicatemalaria.

VerbalDrill21.C Thatsemicolonistransitionpunctuation.Ittellsyouthatthefirstpartofthe

sentenceagreeswiththesecondpart.Thesecondpartcontainstheclue“whatonegroupseesaspeacekeeping,anothergroupmightseeassubjugation.”Howcanyoudescribethat—itsoundslikeacontradiction.Howabout“contradictory”fortheblank?Timetogototheanswers.Youcaneliminate(A),academic,becauseitdoesn’tmean“contradictory.”Choice(B),portentous,means“predictingthefuture,”whichmightbetrueofhistoricaleventsbuthasnothingtodowiththissentence.Choice(C),paradoxical,means“seeminglycontradictory,”sokeepit.(Ifyouweren’tsure,you’dkeepitinanyway.)Choice(D),trifling,means“frivolous”or“oflittlevalue,”soeliminateit.Choice(E),bellicose,whichmightbetrueofsomehistoricaleventsbuthasnothingtodowiththissentence.Thebestansweris(C).

2.B Thecluefortheblankafterthetransitionword“however”is“dailyroutines,”sothewordintheblankcanbe“routine.”Thatdefinitelyeliminates(A),(D),and(E).Ifyouknowwhatquotidianorrecalcitrantmeans,youknowtheansweris(B).Ifyoudon’t,(C)isagoodguess(althoughit’swrong).

3.fledgling,precipitouslyTheonlythingthatwereallyknowaboutthestoreisthatitisprettynew,so“new”wouldbeagoodwordforthefirstblank.Whileurbaneandostentatiouscouldbothapplytoaclothingstore,theydonotmatchthemeaningoftheclue.Sinceyouknowthatthesituationisacrisis,agoodwordforthesecondblankwouldbesomethinglike“alot.”Thebestanswer,then,isprecipitously,sincenoneoftheotherchoicesmatchthedirectionoftheclue.

4.abstruse,lucidWhatwouldearnReaganthedistinctionof“TheGreatCommunicator,”otherthananabilitytomakedifficultorcomplicatedtopicseasytounderstand?Hangontoabstruse,butdon’tfallforthetrapofobtuse.Youcanalsocrossoutmundane,asitmeans“common”or“ordinary”—not“complicated.”Movingtothesecondblank,think“clear”or“understandable,”giventhefirstpartofthesentence.Palatableisclose,butlucidisamuchmoreprecisematch.Munificent,meanwhile,doesn’tmean“understandable,”makingabstruseandlucidthebestchoices.

5.arduous,transient,static“Ismadeevenmoredifficult”istheclueforthefirstblank.Recycle“difficult”and

usePOE.Onlyarduousmatches.Regardingthesecondblank,theclue“peopleseldomresideinanyoneplaceforverylong”suggestsawordmeaning“movingaround”or“mobile.”Inertistheoppositeoftheclue,andaestheticdoesn’tmatch,sochoosetransientandworkthethirdblank.Thechange-directiontransition“however,”whichcomesrightaftertheblank,callsforawordmeaningtheoppositeofmobile.Staticisastrongmatch,makingit,arduous,andtransientthebestchoices.

6.bedlam,epithets,neophyteThesecondandthirdblanksmightbealittleeasieronthisone.Agoodwordforthethirdblankwouldbesomethinglike“inexperienced,”sinceyouaretoldthatapersonwith“moreexperience”wouldhavehandledthingsbetter.Thebestchoice,then,isneophyte.Forthesecondblank,agoodwordwouldbesomethinglike“insults,”sinceyouaretoldthatthingsweregettingpersonal.Thebestanswerhereisepithets.Forthefirstblankagoodwordwouldbesomethinglike“chaos,”sincethemeetingstartedoutwellbutresultedindisarray.Thebestanswerhereisbedlam.

7.B Thepointabouthowdifferentterminologycandeterminewhobenefitsisanexampleofanissuethatmakessellingnamingrightslegallycomplicated,whichis(B).Namingrightsmaybecomplicated,buttheyarenotdescribedas“confusing”(A).Choice(C)drawstoolargeaconclusionfromaspecificexample.Choice(D)istooextremeforthesituationdescribed.Thedifferencesinbenefitsarebetweenfacilityownersandteams;theterminologydoesnotaffectthecommunity’sbenefits(E).Therefore,thebestansweris(B).

8.B Inthecreditedresponse,theauthorsuggeststhatthenamingrightsmayseemlikeawin-winproposition.However,therestofthesentence—andtherestoftheparagraph—isdevotedtoenumeratingsomeofthedifficultiesandconcernsthatsuchdealsoftenraise.

9.D Tryputtingyourownwordinthepassagetoreplace“practice.”Thetransition“Though”indicatesthatthefirstpartofthesentencewillcontrastwiththecurrentproliferationofsponsorships,soawordthatmeans“activity”or“deed”mightmakesense—anythingthatconveysthemeaningthatitwasonceunheardofforsomethingtohappen.Ofthechoices,actionisthebestfit.

10.C Choice(A)isnotsupported,asthepassagemakesnomentionofotherplaywrightstowhomacomparisoncanbemade.Choice(B)isalsonotsupported:Thefocushereisonawartimecomedywithaseriousmessage,buttheauthordoesn’tcommentontheproprietyofstudyingthisoranyotherplay.Choice(C)issupportedbythemainideaofthepassage—thatLysistratahasanoft-overlookedmeaningthatdependsonthepoliticalsituationinGreeceatthetimeofitscomposition.

11.B Choice(B)isbestsupportedbythepassage:Theoracleisbroughtupinalist

ofexamplessupportingtheimportanceoftheideaofGreekunityintheplay.Choices(A)and(C)canbeeliminatedbecausethepassagedoesn’tdirectlyrelatetheoracletoLampitoortheoriginoftheconspiracy.Choice(D)isalsonotsupported:AlthoughasuperficialinterpretationofLysistrataisbeingquestioned,thepassagedoesn’tprovideenoughinformationtocharacterizeeitherinterpretationasearlier.Choice(E),finally,isbackwards,astheoraclesupportstheauthor’semphasisoncohesionintheplay.

12.A Theconclusionoftheargumentisattheend:“Significantprogressisbeingmadetowardtheextendingthelivesofcancerpatients.”Thepremiseonwhichtheargumentisbasedisthatpatientsarelivinglongeraftertheirinitialdiagnosis.Forthisargumenttobevalid,though,youneedtoassumethatlengthoflifeisthesamethingastimeafterinitialdiagnosis.Hence,(A)isthebestresponse:Ifcancerisbeingdiagnosedprogressivelyearlier,thenpeoplecouldbeawareoftheirconditionlongerwithoutlivinganylonger.Keepacloseeyeonthescopeoftheargumenttohelpyoueliminatetheincorrectchoices.Theargumentisn’taboutacomparisonamongtypesofcancer,orbetweencancerandotherdiseases,soeliminate(B)and(E).Likewise,theargumentisn’taboutthenumberofeithercancerdiagnosesorpeoplewhomakefullrecoveries,soeliminate(C)and(D).

13.congruence,concurrence“Ferventschisms…werelargelyoverplayed”istheclueindicatingthattheblankneedsawordmeaningtheoppositeofdisagreement.Think“agreement”andusePOE.Congruencematches,butasperityandcontradictiongointheoppositedirectionofagreement.Concurrence,likecongruence,matchestheclue,butimpassivityandtruculence,likethesecondandthirdchoices,gointheoppositedirectionoftheclue.Thatleavescongruenceandconcurrenceasthetwobestanswers.

14.mettle,tenacityTheblankneedsawordmeaning“perseverance”or“determination,”giventhesemicolon,whichactsasasame-directiontransition,followedbytherestofthesentence,whichdiscussesallthatJohnsonachieved“thoughheneverattendedschool.”Mettleworks,buttimiditydoesnot.Tenacity,likemettle,isagoodmatchforperseverance,buttenuousnessgoesintheoppositedirection.Applyyourcluewordtothetworemainingchoices.Doescandormeanperseverance?Whataboutalacrity?Neitheronematches,leavingyouwithmettleandtenacity,thetwobestanswers.

15.officious,meddlesomeWhatdoesthesentencetellyouaboutthesalesclerk?Fromtheclue“drovemanyapotentialcustomerawaywithherpushy,overeagermanner,”youcanrecycle“pushy”or“overeager”fortheblankandusePOE.Eliminateloquacious

andirreverentifyouknowwhattheymean(here’swhereknowingyourvocabcomesinhandy).Officious,ontheotherhand,couldwork,butinnocuousdoesn’tmeananythingclosetopushy,socrossitout.Meddlesome,likeofficious,matchestheclue,butvigilantdoesn’tmeanpushyorovereager.Thatleavesyouwithofficiousandmeddlesome,whicharethetwobestchoices.

16.complaisance,deferenceThecluefortheblankis“eventhemostcompliantofemployees.”Recyclepartofthecluewordandapply“compliancy”totheanswerchoices.EffronteryandTruculencegointheoppositedirectionof“compliancy,”sotossthosetwo.Deferencemakessense(thinkdefer),butcrossoutbothPrevaricationandChicanery,sincetheyhavetodowithdishonesty(don’tletthephrase“motivatedbyahiddenagenda”shiftyourfocusawayfromthecluefortheblank,whichdescribescompliantemployees).Complaisance,incontrast,agreeswiththeclue,makingitandDeferencethetwobestchoices.

17.C Thefirstsentenceofthepassagesaysthatdopamineisrecycledtopreventoverstimulation.Thiscluetellsyouthatreleaseddopaminemusthaveastimulatingeffect,sopiquemeans“stimulate.”Neither(A)nor(D)hasthismeaning.Choice(E)specifiesanegativestimulation,whichisnotsupportedbythetext.Choice(B)isalsonotsupportedbycontext.Exciteisagoodsynonymfor“stimulate”andisthecorrectchoice.

18.D Choice(A)isnotsupportedbythetextbecausethediscoveryofadifferentprocessdoesnotnecessarilymaketheoldoneincorrect.Thesamelogicapplieswhenconsidering(B);thatonemethodistraditionaldoesnotmakeadifferentoneincorrect.Thepassagenevergivesanyindicationofpreferencesorpersonalbeliefs,so(C)isalsoincorrect.Choice(E)goestoofarinsayingthatmanypeoplecannotovercomeaddiction;thepassagedoesnotofferstatisticsonrecovery.Choice(D)iscorrectbecausethefirstsentenceindicatesalong-standingbeliefinDATblockageastheprimaryproblem.

19.C Choice(A)isnotsupported:Thepassagesuggeststhatthemanageabledistanceforoxenwaslessthanthatforhorses,butnospecificsareprovidedforeitheranimal.Choice(B)isalsonotsupported,asthepassagefocusesonagriculturaldevelopments;themilitarypreeminenceofmountedcavalryisonlymentionedasinspiringearlyselectivebreeding.Choice(C),finally,issupportedbythepassage:Thefirstparagraphindicatesthattheneckstrapoftheolderharnessesinhibitedtheflowofbothairandbloodtothehorse’sbrain.

20.B Choice(B)isbestsupported:Thepassagediscussesthemovetohorsesasprimarydraftanimals,andtheboldfacetextgivesfactorsthathinderedthattransition.Choices(A)and(C),then,bothcontradictthepassageandcanbeeliminated.Choices(D)and(E)arealsonotsupportedbythepassage.Althoughthefactorsinboldfacemightbeconsideredpartofaparadox—how

horsesovertookoxendespitesignificantdisadvantages—theinformationpresentedneithersolvesnorfurtherexplorestheramificationsofanysuchparadox.

MathDrill11.A Inaparallelogram,oppositeanglesareequal,andthebigangleplusthesmall

angleaddsupto180°.Sox+120=180.ThatmakesthevalueofQuantityA60,whichisgreaterthanthe45inQuantityB.Thecorrectansweris(A).

2.A TofindtheamountMr.Jonespaidinadditiontotheregularpriceofthebedroomset,multiply$69by9monthstoget$621.Thenaddthe$300payment.621+300=921.SoMr.Jonespaidanadditional$21.The$23inQuantityAisgreaterthanthe$21inQuantityB.Thecorrectansweris(A).

3.B TofindtheperimeteroftriangleBCD,findthelengthofBD.First,recognizethecommonPythagoreantriple5-12-13.Therefore,BD=12.NowfindthethirdsideoftriangleBCD.RecognizethattriangleBCDisa9-12-15multipleofthePythagoreantriple3-4-5.SoDCis9.Next,addupthesidesoftriangleBCD,tofindtheperimeter:9+12+15=36.QuantityAis36.BecauseQuantityBis42,thecorrectansweris(B).

4.B TheformulaforcircumferenceisC=2πr.Becauser= , ,or

π.QuantityAis π.Rememberthatπisabout3,soQuantityAisabout ,

whichisalittlemorethan2.QuantityBis4,whichisgreater.Thecorrect

answeris(B).

5.D ThisisaPluggingInproblem,soPlugInaneasynumber.Tryx=2.Ifx=2,thenQuantityAis3andQuantityBis−1,soeliminate(B)and(C).NowPlugInagainusingoneoftheFROZENnumbers.Tryx=0.QuantityAis1andQuantityBis1.Becausethetwoquantitiesareequal,eliminate(A).Thecorrectansweris(D).

6.B Becausethequestioninvolvesaverages,drawanAveragePie.Theaverageis17,andthenumberofthingsis2.Multiplytheaveragebythenumberofthingstofindthetotal,whichis34.Thetwonumbershavetoaddupto34,butneitherofthemcanbe12orless.BecauseQuantityAistwicethegreaterofthetwointegers,findthegreaterintegerbyusingtheleastintegerallowedbytheproblem,whichis13.Ifthetotalis34,andonenumberis13,thatmeanstheothernumberis21because21+13=34.QuantityAis42,whichistwice21.QuantityBis44,sothecorrectansweris(B).

7.D First,PlugIneasynumbers.Tryx=3andy=4;4isagoodnumbertoPlugIn

fory,because√4isaninteger.Therefore,QuantityAis12andQuantityBis6.QuantityAisgreater,soeliminate(B)and(C).NowPlugInagainusingFROZENnumbers.Tryx=0andy=0.NowQuantityAandQuantityBarebothzero,makingthemequal,soeliminate(A).Thecorrectansweris(D).

8.B First,therearenovariablesinthisproblem,soeliminate(D).Theword“inclusive”inQuantityBmeansboth−15and15areincludedinthelistofintegers.Writeoutthelist:−15,−14,−13,−12,−11,−10,−9,−8,−7,−6,−5,−4,−3,−2,−1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15.Thereare31integers.BecauseQuantity(A)is30,QuantityBisgreater.Thecorrectansweris(B).

9.D Theanswerchoicesinthisquestionrepresentinformationdirectlyaskedinthe

question,andthequestioncanbesolvedbywritingandsolvinganequation,so

usePlugIntheAnswers(PITA).Beginwith(C).Ifthepurchasepriceofthecar

is$3,840andthecostofthepaintjobwasone-fifthofthepurchasepriceofthe

car,thenthecostofthepaintjobis $3,840=$768.Therefore,thecostof

thecarandthepaintjobcombinedis$3,840+$768=$4,608.Thisislessthan

thecombinedcostidentifiedbythequestion,soeliminate(C).Eliminate(A)and

(B)aswell,astheywillresultinatotalcostthatisevenlessthan(C).Now,try

(D).Ifthepurchasepriceofthecaris$4,000andthecostofthepaintjobwas

one-fifthofthepurchasepriceofthecar,thenthecostofthepaintjobis

$4,000=$800.Therefore,thecostofthecarandthepaintjobcombinedis

$4,000+$800=$4,800.Thismatchesthetotalidentifiedbythequestion.The

correctansweris(D).

10.B Tofindtheperimeterofthefigure,themissingsideoftherectangleneedstobeidentified.Themissingsideisthesamelengthasthehypotenuseofthetriangle.Solveforthehypotenuse.EitherusethePythagoreanTheoremorrecognizethatthetriangleisa5-12-13Pythagoreantriple.Becausethehypotenuseofthetriangleis13,themissingsideisoftherectangleis13.Nowaddupallthesidesofthefiguretogettheperimeter:5+12+17+13+17=64.Thecorrectansweris(B).

11.A RemembertoPlugInmorethanonceon“mustbe”problems.First,tryx=2

andy=3.Choice(A)is(2)(3)+5=11,whichisoddsokeep(A).Choice(B)is

2+3=5,whichisalsooddsokeep(B).Choice(C)is ,whichisnotaninteger

soeliminate(C).Choice(D)is(4)(2)=8,whichisevensoeliminate(D).Choice

(E)is(7)(2)(3)=42,whichisalsoevensoeliminate(E).NowPlugInagain

usingFROZENnumberssuchasx=2andy=10.Choice(A)is(2)(10)+5=

25,whichisoddsokeep(A).Choice(B)is2+10=12,whichisevenso

eliminate(B).Thecorrectansweris(A).

12.25 Substitute−2for3xintheproblemtoyield(−2−3)2,or(−5)2,whichequals25.Thecorrectansweris25.

13.A Alinehas180°,soa+20+b=180,thereforea+b=160.Theproblemalsostatesthata=3b.NowusePITAandPlugIntheAnswersforb,lookingfortheanswerchoicethatproducesvaluesofaandbthatsumto160.Beginwith(C).Ifb=25,thena=75.So25+75=100,whichislessthan160.Therefore,eliminate(C).Eliminate(D)and(E)aswellbecausetheywillproducelesservalues.Try(A).Ifb=40,thena=120.So,40+120=160,whichmatchesthetargetanswer.Therefore,thecorrectansweris(A).

14.8,230

TheproblemstatesthatthenumberofregisteredvotersinTownshipX

increased10%from2000to2010.In2010,therewere4,382malevotersand

4,671femalevotersforatotalof9,053voters.The9,053votersin2010is

110%ofthenumberofvotersin2000,sotranslatethatintotheequation9,053

= x.Solveforthevalueofxtofindthatthenumberofvotersin2000was

8,230.Thecorrectansweris8,230.

15.D Thetotalnumberoffemalesis4,671.Thequestionalsoasksforthetotalnumberofvoterslessthan48yearsold.However,thefemalesvoterswhoarelessthan48yearsoldhavealreadybeencounted.Therefore,onlyaddthenumberofmalevoterslessthan48yearsold,whichis1,030+1,114=2,144.Therefore,thesumofthenumberoffemalevotersandthenumberofremainingvoterslessthan48yearsoldis4,671+2,144=6,815.Thecorrectansweris(D).

16.C FindtheratioofthepercentagesofDemocratstothepercentageofmalevoters

age48to62.ThechartalreadyprovidesthepercentageofDemocrats,so

calculatethepercentageofmalevotersage48to62.Tofindoutthe

percentageofmalevotersage48to62,translate“1,291iswhatpercentof

9,053?”into1,291= (9,053)=14.2%.Theratioof43%to14%isclosestto

3to1.Thecorrectansweris(C).

17.C Theanswerchoicesinthisquestionrepresenttheinformationdirectlyaskedfor

bythequestion,andthequestioncouldbesolvedbywritingandsolvingan

equation,soPlugIntheAnswers.Becausethequestionisaskingfortheleast

number,startbyPluggingIn(A).Choice(A)is{3(−3)+2}{−3−3}=(−7)(−6)=

42,whichisn’t0.Eliminate(A).Choice(B)is{3(−2)+2}{−2−3}=(−4)(−5)=

20,whichisn’t0.Eliminate(B).Choice(C)is

.Thecorrectansweris(C).

18.236Thenewspaperadwithawidthof14hasthesameareaasanotherad52longand28wide,socalculatetheareaofthesecondadusingtheformulaA=l×w:52×28=1,456.Nowusetheareaformulaagaintofindthelengthofthefirstad:1456=l×14,sol=104.Inordertofindtheperimeterofthefirstad,usetheformulaP=2l+2w:P=2(104)+2(14)=236.Theansweris236.

19.C Becausethisquestioninvolvestakingpercentagesofanunknownamount,this

isaHiddenPlugInquestion.PlugInforthetotalnumberofvoters.Makethe

totalnumberofvoters100.60%ofthevotersarewomen,sothat’s60women,

andtheremainingvotersaremen,sothat’s40men.30%ofthewomenvoted

forcandidateX,so30%of60,whichis (60),or18women,votedfor

candidateX.20%ofthemenvotedforcandidateX,so20%of40,whichis

(40),or8men,votedforcandidateX.Therefore,thetotalnumberofmenand

womenvotingforcandidateXis18+8,or26.26votersoutof100totalvoters

is26%.Thecorrectansweris(C).

20.B,C,andEFactor21,54,and22intotheirprimefactors:21=7×3,54=3×3×3×2,and22=2×11,makingacombinedprimefactorizationof2×2×3×3×3×3×7×11.Inorderfor21×54×22tobedivisiblebyanumber,allthefactorsofthatnumbermustalsobefactorsof21×54×22.Findtheprimefactorizationofallthedenominatorsoftheanswerchoices.Thedenominatorsin(A)and(F)eachhave5asafactor,which21×54×22doesnot,soeliminatetheseanswerchoices.Choice(D)hastoomany2’s,soeliminateitaswell.Allthefactorsofthedenominatorsin(B),(C),and(E)arealsofactorsof21×54×22,andsothesefractionswillyieldintegers.Theansweris(B),(C),and(E).

MathDrill21.A BecausetherearenovariablesineitherQuantityAorQuantityB,eliminate(D).

Now,findtheprimefactorizationofQuantityAandQuantityBtocomparetheirvalues.TheprimefactorizationofQuantityAis4(26)=28.TheprimefactorizationofQuantityBis6(42)=2×3×(22)2=2×3×24=25×3.Bothquantitiescontainatleast25,socomparethevaluesbyeliminating25frombothquantities.QuantityAisnow23andQuantityBisnow3.Because23isgreaterthan3,thecorrectansweris(A).

2.A ThisisaQuantCompquestionwithonlyrealnumbers,soeliminate(D)asa

valuescanbedeterminedforbothquantities.Usetheformulaforpercent

change,whichisthedifferencedividedbytheoriginal,multipliedby100,to

evaluatebothquantities.InQuantityA,thedifferenceis1,andtheoriginal

numberis4,sothat’s (100)=25%.ThepercentchangeinQuantityAis25%.

InQuantityB,thedifferenceis1,andtheoriginalnumberis5,sothat’s (100)=

20%.ThepercentchangeinQuantityBis20%.Therefore,QuantityAisgreater

thanQuantityB.Thecorrectansweris(A).

3.A ThisisaQuantCompquestionwithvariables,soPlugInmorethanonce.

Beginwithaneasynumber,suchasr=2.Ifr=2,thenQuantityAis2πr=4π

andQuantityBis4(2)=8.Becauseπisapproximately3,QuantityAis

approximately12.Therefore,QuantityAisgreaterthanQuantityB.Eliminate

(B)and(C).NowPlugInagainusingFROZENnumbers.PlugInr= .Then

QuantityAisπandQuantityBis2.QuantityAisgreateragain.PluggingIn

zerooranegativenumberisnotallowedherebecauseristheradiusofthe

circleandthesideofthesquare.NomatterwhatnumberisPluggedInforr,

QuantityAisgreater.Thecorrectansweris(A).

4.C Bothquantitiesinvolveaverages,sodrawanAveragePieforboth.InQuantityA,thetotalis7+3+4+2=16,andthenumberofthingsis4,sotheaverage,andQuantityA,is4.QuantityBistheaverageof2a+5,4a,and7−6a,soPlugInanumberfora.Trya=2.Ifa=2,thenthetotalinQuantityBis9+8−5=12,andthenumberofthingsis3,sotheaverageofQuantityBis4.Thetwoquantitiesareequal,soeliminate(A)and(B).NowPlugInagainforQuantityBusingFROZENnumbers.Trya=0.Ifa=0,thenthetotalinQuantityBis5+0+7.Thenumberofthingsis3,sotheaverageisstill4.5+0+7=12,which,whendividedbythenumberofthings,3,givesanaverageof4.Infact,nomatterwhatnumberisusedfora,thetwoquantitiesarealwaysequal.Thecorrectansweris(C).

5.C TherearenovariablesinthisQuantCompquestion,soeliminate(D).IfoneoftheverticesofsquareQisat(−3,−4)andthepoint(2,1)isthemidpointofthesquare,thenthevertexis5horizontalunitsand5verticalunitsawayfromthemidpoint.Thismeansthatthedistancebetweenthemidpointandthevertexonthesamediagonalas(−3,−4)isalso5rightand5upfromthemidpoint.Therefore,thediagonalfollowstothepoint(7,6),whichisalsoavertexofthesquare.Becauseitisasquare,allthesidesareequallength,sodeterminethedistancebetweenxoryvaluesofpoints(−3,−4)and(7,6).Thedistancebetweenthexvaluesis10,whichmeansallthesidesofsquareQare10.QuantityAasksfortheareaofsquareQwhichis102=100.ThisisthesamevalueasQuantityB,sothequantitiesareequal.Thecorrectansweris(C).

6.C BecausetherearenovariablesineitherQuantityAorQuantityB,eliminate(D).FactortheexpressionsinbothQuantityAandQuantityB.InQuantityA,factoringout317resultsin317(1+31),or317(4).ThisisthesamevalueasQuantityB.Thecorrectansweris(C).

7.C PlugInongeometryproblemswithvariables.PlugIna=50,andmakethetwoanglesinsidethetriangleoppositeofanglesbandc60and70°,respectively.Anynumberswillworkaslongastheyaddupto180°,thenumberofdegreesinatriangle.Becausebandcareverticalanglestothe60-and70-degreeanglesinthetriangle,anglebis60°andanglecis70°.Now,evaluatethequantities.QuantityAis,b+c=60+70=130.QuantityBis180−50=130.Thetwoquantitiesareequal.Thecorrectansweris(C).

8.D Thequestionstatesthataone-hourtelephonecallis$7.20.Usethis

informationtofigureoutthepricefora10-minutetelephonecallbysettingupa

proportion.Theproportionis .Cross-multiplytofindthat$72.00=

60(x).Divideby60tofindthatx=$1.20.Thecorrectansweris(D).

9.C Manipulatethetrianglestofindthevalueofn.Beginwiththetrianglethathastwoknownsides.Noticethatthisisa15-20-25multipleofthe3-4-5Pythagoreantriple.Sothethirdsideofthistriangleis20.Usethisinformationtosolveforn.Noticethatthistriangleisa12-16-20multipleofthe3-4-5Pythagoreantriple.Son=16.Thecorrectansweris(C).

10.A,B,C,andD

Thisisa“mustbe”problem,soPlugInmorethanonce.Startwithaneasy

numbersuchasx=2.Ifx=2,theny=2andzequals4.Nowtesttheanswer

choices.For(A),4+4=8whichistrue,sokeep(A).For(B),2−2=0,whichis

alsotrue,sokeep(B).For(C),2−4=2−4,whichisalsotrue,sokeep(C).

For(D),2= ,whichisalsotrue,sokeep(D).For(E),2−2=8,whichisnot

true,soeliminate(E).NowPlugInagainusingtheFROZENnumberssuchasx

=10.Ifx=10,theny=10,andz=20.Testalloftheremaininganswerchoices

again.Alltheremainingchoicesarestilltrue.Infact,nomatterwhatnumbers

areusedforthevariables,(A),(B),(C),and(D)arealltrue.Thecorrectanswer

is(A),(B),(C),and(D).

11.D Beginthisproblembydrawingtheinformationgiveninthepicture.Theinformationinthequestionshouldforma3:4:5righttriangle,sothestreetfromthesupermarkettothebeautyparloris5blockslong.Theansweris(D).

12.B PlugIntheAnswers(PITA).Thecorrectanswerwillmeetthefollowingcriteria.Thefirstconditionisthatthenumber’sseconddigitmustbe3timesthefirstdigit.Choices(C),(D),and(E)allfailthefirstconditionbecausetheunitsdigitsarenotthreetimesthetensdigits.Eliminatethem.Nowapplythesecondcondition,thatthereversedformofthenumbermustbe36morethantheoriginalnumber,tothetworemaininganswerchoices.For(A),31isnot36morethan13,soeliminate(A).For(B),62is36morethan26.Thecorrectansweris(B).

13.20 Solvethisprobleminbite-sizedpieces.Startbysubtractingthetipstogetthetotalcostofthecustomers’dishes:$180–$20=$160.Nowdividethatbythetotalamounteachcustomerspenttofindthenumberofcustomers.Ifeachcustomerboughttwo$4dishes,theneachcustomerspent$8total,and$160÷$8=20.Thecorrectansweris20.

14.D Dividethe$9.4millioninprivatedonationsreceivedbychildsafety

organizationsinSeptember1989bythe38organizationsoperatingatthetime.Theamountisapproximately$250,000.Thecorrectansweris(D).

15.C Fromthelinegraph,youseethathomelessaidgroupstookinabout$300millioninprivatedonations,andanimalrightsgroupsabout$225million.Theratioof$300millionto$225millionis4to3.Thecorrectansweris(C).

16.E IdentifythemarkersforSeptember1989andOctober1989onthechart.Thequestionisaskingabouttheleastpercentincreasebetweenthesetwodatapoints.So,beginbyevaluatingthedatapoints.Allofthedifferencesbetweenthedatapointsforthesetwomonthsareverysimilar;theyallseemtohaveadifferenceofapproximately0.5.Because0.5isalesserpercentofagreaternumber,theleastpercentincreasecorrespondstothedatapointwiththegreatestnumbers.Therefore,thecorrectansweris(E),childsafety.Alternatively,findthepercentincreaseforeachoftheanswerchoicesbydividingthedifferencebetweenthetwopointsbytheoriginal,whichinthiscaseisthenumberforSeptember1989.Theleastpercentincreaseisstill(E),childsafety,whichisthecorrectanswer.

17.E Therearevariablesinthequestionandanswerchoices,sothisisaPluggingIn

problem.PlugInandworkthisprobleminbite-sizedpieces.PlugInanumber

forasuchasa=10.IfAlexgaveJonathon10dollars,andshegaveGinatwo

dollarsmorethanshegaveJonathan,thenshegaveGina12dollars.Shegave

LouannethreedollarslessthanshegaveGina,soshegaveLouanne9dollars.

Soaltogether,AlexgaveGina,Jonathan,andLouanne10+12+9=31dollars,

whichisthetargetnumber.PlugInfortheanswerchoicestofindwhichone

matchesthetargetnumber.Choice(A)is ,whichdoesnotequal31,so

eliminate(A).Choice(B)is10−1,whichdoesnotequal31,soeliminate(B).

Choice(C)is3(10),whichdoesnotequal31,soeliminate(C).Choice(D)is

3(10)−1,whichdoesnotequal31,soeliminate(D).Choice(E)is3(10)+1=

31.Thismatchesthetargetnumber.Thecorrectansweris(E).

18.C Theequationm2+2mn+n2isjustthecommonquadraticx2+2xy+y2,whichcanberewrittenas(x+y)2,sorewritem2+2mn+n2as(m+n)2.Becausem+n=p,replacethem+ninthe(m+n)2withtheptogetp2.Thecorrectansweris(C).

19.E Thisisafunctionproblem,soPlugInforthevariablesandfollowthedirections.PlugInx=2andy=3.Theproblemstatesthatx*y=x(x–y)andasksforthevalueofx*(x*y).Beginwiththeportioninsidetheparentheses.x*y=2*3=2(2−3)=−2.Nowthequestionreadsx*−2,whichisthesameas2*−2=2(2–(−2)=2(2+2)=8,whichisthetargetnumber.PlugInthevaluesforxandyintotheanswerchoicesandlookforonethatmatchesthetargetanswer.Choice(A)is22−2(3)=−2,whichdoesnotmatchthetargetnumber,soeliminate(A).Choice(B)is22−2(2)(3)=−8,whichdoesnotmatchthetargetnumbersoeliminate(B).Choice(C)is23−22−2(3)=8−4−6=−2,whichdoesnotmatchthetargetnumber,soeliminate(C).Choice(D)is23–(2×3)2=8−36=−28,whichdoesnotmatchthetargetnumber,soeliminate(D).Choice(E)is22−23+22(3)=4−8+4(3)=8,whichmatchesthetargetnumber.Thecorrectansweris(E).

20.A,B,C,andEJuststartdividingtofindtheremainders.117÷2=58witharemainderof1,soselect(A).117isdivisibleby3,so3doesn’tprovidearemainder.117÷4=29witharemainderof1,whichisstill(A).117÷5=23witharemainderof2,soselect(B).117÷6=19witharemainderof3,soselect(C).117÷7=16witharemainderof5,soselect(E).117÷8=14witharemainderof5,but(E)hasalreadybeenselected.117isdivisibleby9,so9doesn’tgivearemainder.Thecorrectansweris(A),(B),(C),and(E).

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