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Table of Contents 2 LetterfromtheFounder 3 TestPrepCompanyDiscounts

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QuantitativeFlashcards49General74 DataSufficiency

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Back to Table of Contents

Letter from the Founder

DuringmyGMATpreparation,ImadehundredsofflashcardstohelpmestayfreshonthestrategiesandmaterialsIhadstudiedoverthecourseofseveralmonths.Thisdocumentcontainsthedigitizedversionofmyflashcards—pleaseusethemasastudyaid.

Theseflashcardsareafreeresourceforeveryone.Theyareupdatedfrequently,sobesuretovisitthefollowingpagetomakesureyouhavethelatestversion:

http://go.beatthegmat.com/flashcards

AlsonotethattheseflashcardshavebeenreviewedandeditedbytopGMATinstructorsforqualitycontrol.Todatethisdocumenthasbeendownloadedover100,000times!

AllthebestinyourGMATprep,EricBahnFounderofBeatTheGMAThttp://www.beatthegmat.com

http://www.beatthegmat.com/mba/free-gmat-prep-flashcards



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Other Links 2 LetterfromtheFounder 3 TestPrepCompanyDiscounts


QuantitativeFlashcards49General74DataSufficiency


V E R B A L S E N T E N C E C O R R E C T I O NF L A S H C A R D S

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V E R B A L S E N T E N C E C O R R E C T I O N




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“Agree”Agreewithanotherperson.

CORRECT: “IagreewithJoeyonthisissue.”Agreetooruponsomethinginanimate.

CORRECT: “Iagreetoyourproposal.” CORRECT: “Acourseofactionwasagreedupon.”

“Whether” vs. “If ”“Whether”iscorrectwhenasentencedescribesalternatives.

CORRECT: “Whethertovoteornot.”“If ”iscorrectwhenasentencedescribesahypotheticalsituation.

CORRECT: “Ifheweretoparticipate,hewould…”

Idiom“Incontrastto”

CORRECT: “Incontrasttomostparents,Jimmy’sparentslethimstayoutallnight.”

“Similarto” CORRECT: “Theresa’sparentingstyleissimilartoChristine’s.”

“Just as”“Justas”canreplace“inthesamewaythat”.

CORRECT: “JustasElvischangedthefaceofrockn’roll,Hawkingchangedthefaceofastrophysics.”





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Pronoun ErrorsAmbiguouspronounreference-eachpronounmustagreeinnumberwiththenounitreplaces

INCORRECT: “FredandVijaywenttothesoccermatch,buthesaidthathelikedcricketbetter.”

Singular/Pluralnounagreement-eachpronounmustreferdirectlyandunambiguouslytothenounitreplaces

INCORRECT: “Theaveragedentistexpectspatientstobeontime,andtheyareusuallymistaken.”

“not…but”Use“not…but”tojoinlinguisticallyequivalent(parallel)things.

CORRECT: “Blakeisnotagolferbutatennisplayer.”

“rather than”Use“ratherthan”toexpressapreference.

CORRECT: “Iwouldprefernonfatmilkratherthancreaminmycoffee.”

“Due to”Thebestmeaningfor“dueto”is“causedby.”

• “Dueto”shouldnotbeusedtomean“onaccountof”. INCORRECT: “Thegamewaspostponedduetorain.” CORRECT: “Thegamewaspostponedonaccountofrain.” CORRECT: “Thegame’spostponementwasduetorain.”





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Verb TenseAsentencethatbeginsinonetenseshouldgenerallystayinthattense.

•Oftenrelatedtoparallelconstructionquestions. EXCEPTION: Pastperfect(ex:“had/have+verb”).Anactionsetinthepastperfectmusthaveanotheractionthatcomesafteritsetinthesimplepast. CORRECT: “Bobwasfiredafterhehadworkedatthecompanyforonlytwoweeks.”

Parallel ConstructionAsignalthatyoumayhaveaparallelconstructionerrorisagroupofphrasessetoffbycommas.Spotthisproblemby:

•Findingaseriesofactions,lists,orsentencesdividedintoparts.

•Makesurethateachlistitemhassimilarstructure(i.e.,noonepartofthelistisdistinctfromtheothersintermsofgrammaticalconstructionorlength).

Ambiguous Gerundial Clauses, 2 of 2 INCORRECT: “Drivingtoaholidaydinner,Fred’swalletwaslost.”

Anotherwaytofixexampleabove:Changefirsthalfofsentenceintoadverbialclause,whichclarifiesthesubjectofthesentencethatisinthesecondphrase.

CORRECT: “Whiledrivingtoaholidaydinner,Fredlosthiswallet.”

Ambiguous Gerundial Clauses, 1 of 2 INCORRECT: “Drivingtoaholidaydinner,Fred’swalletwaslost.”

ThissentenceimpliesFred’swalletdrovetoaholidaydinner.Onewaytofixexampleabove:Rearrangesentenceorderandaltersecondhalfofsentencesothatinanimateobjectdoesnotrefertoactionverbinfirsthalfofsentence.

CORRECT: “Fredlosthiswalletashedrovetoaholidaydinner.”





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Correct Sentences20%ofSCsentencesarecorrectaspresentedinthefirstinstanceontheGMAT.

•Thisisapproximatelythreequestionspertest.

Quantity Words and Idioms CORRECT: “OntheflighttoChicago,Bettyhadtochoosebetweentwodrinkoptions.” CORRECT: “OntheflightbacktoNewYork,Bettyhadtochooseamongthreedinneroptions.”

CountableItems: Non-CountableItems: •Fewer •Less •Number •Amount,quantity •Many •Much

Avoid Apples to Oranges ComparisonsComparenounstolikenouns:

CORRECT: “TherosesatSarah’sweddingwereprettierthantheorchidsatJane’swedding.” INCORRECT: “IenjoyreadingthepoemsofKennethKochmorethanEmilyDickinson.”

Compareactionstolikeactions: CORRECT: “Beeswaxcandlesburnmorecleanlythansyntheticcandles.”

Common Word TrapPolitics–Singularword

CORRECT: “Politicsisnotforthefaintofheart.”People–Pluralword

CORRECT: “PeopleareoftenconfusedaboutgrammaticalissuesthatariseontheGMAT.”





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Either...or / Neither...norVerbsagreewithwhateverfollows“or/nor”

CORRECT: “NeitherthemusiciansnortheconductorisfromDallas.” CORRECT: “NeithertheconductornorthemusiciansarefromDallas.”

Misplaced or Dangling ModifiersModifiersshouldbeascloseaspossibletothewordorclausetheymodify.

INCORRECT: “SarahJanerarelysparkedinterestinmen,thoughnotaplaingirl.” CORRECT: “SarahJane,thoughnotaplaingirl,rarelysparkedinterestinmen.”

Collective Nouns that are SingularBewarecollectivenounswhichareactuallysingular:“audience,committee,everyone”meritsingularverbs

3-Step Method1.Readoriginalsentencecarefully.2.Scananswerchoicesfordifferencesthathelpidentify

commonly-testederrors.3.Eliminateachoiceassoonasyoufindanerror. TIP:Ifyounarrowaquestiondowntotwopossible

“candidate”sentences,readeachoneslowlyanddeconstructeachpartofthesentenceuntilanerrorjumpsoutatyou.





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Like ThingsComparelikethingsonly(ex:nounstonouns,peopletopeople,actionstoactions,etc).Comparisonwords:“like,as,comparedto,lessthan,morethan,other,thatof,thoseof ”.

Gerunds (words that end with “ing”)WhentheGMATgivesyouachoicebetweenoneverbtensethatusesan“ing”formandanotherthatdoesnot,usuallythe“ing”formiswrong.

Verb Tense – 3 Tips1.Makesurethattheverbtenseyouchooseproperly

reflectsthesequenceofevents.2.UsePresentPerfect(verb+“ing”)toemphasize

continuingnatureofanactionorthattwoormoreactionsareoccurringsimultaneously. CORRECT: “IhavebeencorrectingRaul’sGMATgrammarconstantly.” “IwaswalkingandchewinggumwhenIcollidedwithalamppost.”

3.AvoidPassiveVoice.Usesimplepasttenseinsteadof“had”+pasttense.

“so…as to”Use“So[ADJECTIVE]asto[VERB]”asacomparator.

CORRECT: “Herdebtsaresoextremeastothreatenhercompany.”

Donotuseittosubstitutefor“inorderto” INCORRECT: “Heexerciseseverydaysoastobuildhisstamina.”





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“None, No one”“None”shouldbesingular,evenwhentoyourearitseemsasthoughitshouldbeplural.

CORRECT: “Noneoftheboysenjoyscampingashedoes.”“Noone”isalwayssingular.

CORRECT: “Nooneenjoyscampingasmuchashedoes.”

Idioms involving “as”Memorize:

•“regardedas”(don’tuse“tobe”)•“aslongas”•“suchquestionsas”•“playsas”

“like, such as”“like”=“similarto”

CORRECT: “Hergracefulcomportmentmadeherseemlikeadancer,althoughshehadneversetfootonastage.”

“suchas”=“forexample” CORRECT: “Ienjoyactivitiessuchasskydiving,heliskiingandscubadiving.”

GuessingWhenindoubt,choosethemostconcise(shortest)an-swer.





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Idiom: “to be” CORRECT: “Likelytobe”

Passive vs. Active Verb TenseAvoidpassiveverbtenses!Theseareusuallypresentorpastperfectformsofverbs.

• “Have/Had+VERB+-ing”israrelythecorrectchoice.• Activetenseispreferredinsentencecorrectionquestions.• “By”isoftenanindicationofthepassivevoice.

“Compare”“Compareto”comparesUNLIKEthings,whereas“comparewith”comparesLIKEthings.“Compareto”isusedtostressresemblance.

CORRECT: “Shecomparedtheeveninggowntothecocktaildress.“

“Comparewith”canbeusedtoshoweithersimilarityordifference(usuallydifference).

CORRECT: “WhencomparedwithLaura’sworkproduct,Jim’sshowedaworldofdifference.”

Idiom: “Concern”“Concernedfor”=“worried,anxious”

CORRECT: “Iamconcernedforhersafety.”“Concernedwith”=“relatedto”

CORRECT: “ThismatterisconcernedwiththeSmithcase.”





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Idiom: “rates for”When“rates”refertothepricecharged,itshouldbefollowedby“for”

CORRECT: “Ratesfortelephoneservicehaveincreasedinrecentyears.”

Coordination, Subordination Coordination(comma+coordinatingword/conjunction)

•Equalemphasiswithindependentclauses• “and,or,but,for,nor,yet,so”

Subordination(placedbeforeorafterindependentclausewithcomma)

•Emphasizeotherpartwithoneindependentclauseandonedependentclause

•“although,while,since”

“Greater than, More than”“Greaterthan”isappropriatewhendescribingnumbersalone.

CORRECT: “Greaterthan100…”“Morethan”shouldbeusedwhendescribingthenumbersofobjectsorwhenmakingcomparisons.

CORRECT: “Morethan100fish.”

Idiom: “same to…as to” CORRECT: “SametoXastoY”





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Passive VoiceThepassivevoiceisnotgrammaticallyincorrect,buttheGMATusuallyconsidersitstylisticallyinferiortotheactivevoice.

•Eliminatepassivelywordedchoicesifthereisagrammaticallycorrectalternativeintheactivevoice.

“Less”Lessisawordusedtodescribenon-countnouns,butalsousedforsumsofmoney,periodsoftimeanddistance,andcitationsofnumerical/statisticaldata.

CORRECT: “It’slessthan35milestoSanFrancisco.” CORRECT: “Wespentlessthan$100.” CORRECT: “Thetownspentlessthan95%ofitsbudget.”

ParticiplesParticiplesaresentencefragments.Theyareoftenadjectivesformedfromverbs.Theyareoftengrammaticallyambiguous,andcauseproblemsduetothisambiguity.

CORRECT: “Peter,distractedbyhiscatandwantingtodohiswork…”

PronounApronounmust:

•Agreewithitsantecedentinnumber(pluralvssin-gular)andgender

•RefertoaspecificantecedentwithoutambiguityRemember:“that”issingularand“those”isplural





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Idiom: “just as…so”Makesureelementsareparellel.

CORRECT: “Justasgillsaretofish,solungsaretohumans.”

Idiom: “Deciding that…” CORRECT: “Decidingthatthebestcoursewastocontinue,theDonnerPartyfatefullyelectedtoforgeahead.”

“One of the…”“Oneofthe[PLURALNOUN]that/who[PLURALVERB]”

CORRECT: “Heisoneofthepersonswhobakespectacularcakes.”

“Onlyoneofthe[PLURALNOUN]that/who[SINGULARVERB]”

CORRECT: “Heistheonlyoneoftheemployeeswhowaspromoted.”

“Consider”When“consider”means“regardas,”“as”shouldnotbepresentwith“consider”inthesentence.“Consider”isalsonotfollowedbyaninfinitivelike“tobe”.

INCORRECT: “Scientistsconsidercontrolfactorstobeanintegralelement…” CORRECT: “Scientistsconsidercontrolfactorsanintegralelement…”





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Idiom: “Forbid” vs. “Prohibit”“XforbidsYtodoZ.”

CORRECT: “Sarah’sfatherforbidshertodateJosh.”“XprohibitsYfrom[VERB+ing].”

CORRECT: “Sarah’sfatherprohibitedSarahfromgoingoutwithJosh.”

StrategySometestprepsourcesclaimthatwhentheentiresen-tenceisunderlinedinthequestion,theanswerhasahigherprobabilityofbeing‘D’or‘E’.

Verb Phrase EllipsisMostofthetimewhenweuseacomparisonusing“than”or“as”,weomitverbcomparators,astheyareimplied.

CORRECT: “Heisshorterthanshe.”(Notetheomissionof“is”attheend.) CORRECT: “Heisasdepressedasthey,buthesoldieredonwardanyway.”(Notetheomissionof“are”.)

Idiom: “not so much…as” CORRECT: “NotsomuchtoshowJaneupastomakeherappearfoolish,SarahpointedoutJane’serrortotheirsupervisor.”





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Comparison Words“Like”usedtoexpresssimilarity,normallybetweentwonouns

CORRECT: “Tangerinesarelikemandarins.”“As”normallyusedtocomparetwoclausesincludingverbs,NOTjusttwonouns

CORRECT: “Helooksasthoughheisdrunk.”“Suchas”normallyusedtogiveexamples.

CORRECT: “Investmentbankinghastaughtmeskillssuchasdiscountedcashflowmodeling.”

“Compare”Use“compareto”forunlikethings

CORRECT: “Hecomparedhertoanevilshrew.”Use“comparewith”forlikethings

CORRECT: “Theparalegalcomparedthecopiedsignaturewiththeoriginal.”

Singular or PluralThefollowingarealwayspluralpronounswhenusedasthesubjectofasentence:

•Some•More•Most•All

Idiom“For”=“despite”“Alongwith”=“inadditionto”





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Idiom: “so [adj.]…as to be [adj.]” CORRECT: “Hewassojovialastobepracticallysilly.”

“Number”A“number”requiresapluralverb.

CORRECT: “AnumberofpeoplearequeuingtoentertheTate.”

“Thenumber”requiresasingularverb. CORRECT: “Thenumberofpeopleinlineisdecreasing.”

“Each”“Each”isusuallysingular.Exception:when“each”followsapluralsubject,theverbandsubsequentpronounsremainintheplural.

CORRECT: “Threecatseachchasebirds.” CORRECT: “Threecats,eachofwhichchasesbirds….”

PronounWhenyouseeanypronoun,especially“it”or“they”,immediatelychecktheantecedent.





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Pattern to AvoidAvoidanysentenceconstructionwith:“[PREPOSITION][NOUN][PARTICIPLE]”

INCORRECT: “…withshowerfacilitiesincluded.”

Infinitives to Avoid“Toinclude”isusuallyincorrect,while“including”ismoreoftencorrect.“Toimplement”isusuallyincorrect,while“implementing”ismoreoftencorrect.

Idiom: “just as…, so too…” CORRECT: “Justasstealingisfrownedupon,sotooischeating.”

“Majority”“Majority”shouldbeusedwithcountnounsonly.

INCORRECT: “Themajorityofthetalk…” CORRECT: “Thegreaterpartofthetalk…” CORRECT: “Themajorityofthepeople…”





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Idiom: “between…and”“Between”alwaysgoeswith“and.”

CORRECT: “Shewasbetweenarockandahardplace.” CORRECT: “Hecouldn’tdecidebetweenoneandtheother.”

“they”Alwaysbesuspiciousofthepronoun“they”.

•Acommontrapisfor“they”torefertoasingularsubjectnoun.

Idiom – Paired Coordinates“NotX,butratherY”

CORRECT: “Itwasnotabird,butrather,aplane.”

“Target to” and “Target at”“Targetto”isnormallyfollowedbytheinfinitiveformofaverb.

CORRECT: “That’sagoodtargettochoose.”“Targetedat”isnormallyfollowedbyanoun.

CORRECT: “Thegunistargetedatyou.”





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Numbers Greater than 1Numbersgreaterthan1arepluralunlessyouarerefer-ringtothenumberitself.

CORRECT: “TwooutofeverythreedogownersintheU.S.alsoownacat.” CORRECT: “Twoismyfavoriteprimenumberbecauseitisalsoeven.”

Gerunds (verb + “ing”)The“ing”(presentparticiple)formintroducesanactionthatissimultaneouswiththeactionofthemainclause.

CORRECT: “Whilewatchingforpedestrians,Janemadealefthandturnthroughthecrosswalk.”

Comparison of ActionsWatchoutforcomparisonofactions/inanimateobjectsperformingcomparedactions:

INCORRECT: “FrenchwinestastebetterthanAustralianwines.”(Implieswinesaretasting.)

CORRECT: “FrenchwinestastebetterthanAustralianwinesdo.” “FrenchwinestastebetterthanAustralianwinestaste.” “FrenchwinestastebetterthandoAustralianwines.”

StrategyWheneveryounarrowcandidateanswerstotwooptionsthatarebothgrammaticallycorrect,butoneinvolvesachangeinmeaningfromtheoriginalsentence,choosetheanswerwhichpreservestheuncorrectedsentence’soriginalmeaning.





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“Hopefully”“Hopefully”isnearlyalwayswrongontheGMAT.

•Avoidsentencechoiceswiththisword.

QuantifiersWithfractions,percentages,andindefinitequantifiers,theverbshouldagreewithmainsubjectofthesentence,notthenouncontainedwithintheprepositionalphrase.

CORRECT: “ThirteenpercentofCleveland’steensarepregnant.”

NOTE:“ofCleveland’steens”isNOTthesubject!Withsingularornon-countnounsorclauses,useasingularverb.

Dangling ParticipleDescriptiveparticiplephrasemustbeascloseaspossibletothenounitdescribes.

INCORRECT: “Sarah’scamerawaslostwhileskiingtothebase.”(Underlinedportionisadanglingparticiple—it’shanging.) CORRECT: “Asshewasskiingtothebase,Sarahlosthercamera.”(Underlinedportionisaclausewithasubjectandverb.)

Idiom: “During”“During”+“[definedTIMEPERIOD]”iswrong.

INCORRECT: “Duringtwohours,Ifeltsleepy.” CORRECT: “Duringthepasttwohours,Ifeltsleepy.”





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“Number”“Anumberof ”alwaystakespluralverbs.

CORRECT: “Anumberofbirdshavemigrated…”“Thenumberof ”alwaystakessingularverbs.

CORRECT: “Thenumberofwarblershasincreased…”

Helping Verbs: “Might/May”“Might”isthepasttenseof“may”.

CORRECT: “Shemayarrivethisevening.” CORRECT: “Shemighthavearrivedyesterdayevening.”

Idiom: “Credit”“CreditAwithB”:giveresponsibilityfor

CORRECT: “Belliscreditedwithinventingthetelephone.”“CreditXtoY”:givemoneyorcreditto

CORRECT: “Thebankcredited$4milliontohisaccount.”“Creditfor[NOUN]”:moneyreceivedfororinexchangeforsomething

CORRECT: “Thepowercustomerreceiveda$20creditforaninterruptionofservice.”

Thinking WordsThinkingwordssuchas“theory,belief ”or“believe”areoftenfollowedby“that”.

CORRECT: “Lucy’sbeliefthattheHolocaustdidnotoccurismisguided.” INCORRECT: “Lucy’sbeliefof…”





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“Having”“Having[PASTPARTICIPLE]”isusedtoexpressactionsthatarefinishedandtoconveyorderofoccurrence.

CORRECT: “HavingeatenahugeThanksgivingdinner,Elliotloosenedhisbeltonemorenotch.”

Plural/Singular“[QUANTIFIER]of[NOUN][VERB]”Thenoundetermineswhetherverbissingularorplural.

CORRECT: “Mostofthestudentsare…” CORRECT: “Mostoftheschoolis…”





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V E R B A L C R I T I C A L R E A S O N I N GF L A S H C A R D S


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V E R B A L C R I T I C A L R E A S O N I N GV E R B A L C R I T I C A L R E A S O N I N G

V E R B A L C R I T I C A L R E A S O N I N G V E R B A L C R I T I C A L R E A S O N I N G

Find the ConclusionTheconclusionisoftenfoundinthefirstorlastsentenceofthepassage.

• Lookforconclusionsignposts:“therefore,hence,thus”,etc.

Premiseclausesusuallyshowsupportorofferevidence.•Examplesofpremisesignposts:“because,since,in

viewof,giventhat”,etc.

ScopeStaywithinthescopeoftheargument.

• Ifyourrationaleseemsfarfetched,oryoubringinoutsideknowledgetosolveaquestion,mostlikelyyouareoverreaching.

•Theharderyouhavetoworktojustifyananswerchoice,thelesslikelyitisthatthechoiceiscorrect.

Causal AssumptionAskwhethertheremightbeanalternativecauseifanargumentdoesnotnecessarilyseemasstraightforwardasaquestionstemmakesitouttobe.“CouldYhavecausedZinsteadofX?”

Supply Your Own ConclusionIn“supplyyourownconclusion”questions,theconclusionmustbesupportedbyALLpremises—notjustone.Beonthelookoutforhelpfulkeywordsinthesecondandlastsentence.





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Numbers, PercentagesWatchforthedistinctionbetweenNUMBERSandPERCENTAGES.

Strengthen the ArgumentFindthelogicalgapandfixitwithadditionalinformation.ThisistheONLYtypeofGMATquestionwhereadditionalinformation(outsideofthequestion)can/shouldbeused.

• Correctanswerstothisquestiontypewill:• Connectevidencewithconclusionbetter.• Makeconclusionstronger.• Strengthentheevidencewithnewinformation(perhaps

anassumptionisneededtomaketheargumentwork).

Assumptions - 2Askyourself,“Whatmustbetruetomaketheconclusionvalid?”(usingthepremise+assumption=equationformula).

• Remember,sincetheassumptionisanUNSTATEDpremise,anyanswerchoicethatcomesfromthepassagetosupportyourassumptionisnecessarilyincorrect.Theanswerwillbeimplied,notexplicitlystated.

Assumptions -1Anassumptionismerelyanunstated(implied)premise.Inlogicallycorrectargumentswhichcontainanassumption,thepremise+assumption=conclusion.Ifthequestionstemasksyou“whatisassumed…”thenyoushouldidentifyunstatedpremiseofpassage.Lookforagapinlogic.





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StrategyAlwaysreadthequestionfirst,thenreadthestimulusappropriatelyforthattypeofquestion.

Mimic the ReasoningFollowsamelineofreasoningfromthepassageintheanswer.Eliminatethequestionstemdetailtocreateashorthandversionoftheargumentstructure.

• QuestionStem:Ifitrains,thenIwillstayathometoday.”• Shorthand:IfA,thenB.”• Answer:“IfA,thenB.”

Resolve the ParadoxTosolvethistypeofquestion,lookforalogicallycontradictorydiscrepancy.

•Oftenthecorrectanswerwilltakeasimilarformat(intermsofanswerlengthorargumentstructure).

InferenceInferencequestionsareusuallyverybasic,aboutoneormorepremises.PICKTHEOBVIOUSANSWER(evenifitseemstooobvious).





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Number of Critical Reasoning (CR) Questions

Mostpeoplesee11CRquestionsontheGMAT.

Statistical AssumptionsArethestatisticsrepresentative?Isthequestionstemdoingabaitandswitchintermsofnumbers?Isthequestionstemusingnumberstoassumesomethingisso,whenthenumbersaren’tactuallyhelpingexplainthephenomenongiven?

Strengthen/WeakenStrengthen/WeakenquestionsarethemostcommonCriticalReasoning(CR)questiontypeontheGMAT.

•Breakdownpieceofevidence.•Attackvalidityofanassumption.•Don’ttrytoproveordisproveconclusion.•Tipthescales.

Analogy AssumptionsArethetwosituationsanalogous?Oristheanalogysilly?





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Paraphrasing and PrephrasingParaphrasing

•Activelytranslatepassagesintoyourownwords.•Pretendyouareexplainingtheinformationina

passagetoa10-year-oldkid.Prephrasing

•Thinkaboutwhatformthecorrectanswerwilltake.•Asyoudomorequestions,youwillbeginto“guess”

correctly,asyoustarttothinkasthetestmakersdo.

AssumptionAnassumptionbridgesthegapbetweenargument’sstatedpremisesandconclusion.

• Usedenialtest.• Comparepremisewordsagainstconclusion.

7 Principles of CR, 2 of 24.Judgeargument’spersuasivenesswhilereadingactively.5.Answerquestionbeingasked.6.Prephraseanswer.7.KeepSCOPEinmind.Moderateratherthanstrong

words/qualifiersusuallycorrect.

7 Principles of CR, 1 of 21.Understandstructureofargument.Identifypremise(P),

conclusion(C)andanyunstatedassumptions.LookforstructuralsignpostwordswhichmarkPandC.

2.Previewquestionbeforereadingpassage.3.Paraphrasepassage’spointormainideausingoneverb

“i.e.,explain,criticize,compare,contrast”.





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4-Step Method1.Previewquestionstem.2.Readstimulusandparaphraseiftricky.3.Prephraseanswer.4.Chooseananswerwhichanswersquestionstem.

InferenceConsidertheevidence,drawaconclusion.Aninferenceisanextensionofanargument,notanecessarypartofit.Avalidinferenceisaconclusion,butnotnecessarilytheconclusion,ofasetofstatements.

StrategyIdentifytheconclusionandfindtheanswerthataddressestheconclusion.Mostquestionsfollowthisguideline.

Strengthen/WeakenDon’tbecareless!Wronganswerchoicesoftenhaveexactlyoppositeofdesiredeffect.

•Double-checkthatyouranswersatisfiestheques-tionstem,nottheoppositeofthequestionstem.





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Indicate FlawUsetheinformationthatispresentinthepassagetoanswer“IndicatetheFlaw”CRquestions.Notaboutnewinformationlike“Weaken”CRquestions.

AssumptionForassumptionquestions,findtheconclusionanddeterminewhichanswerchoiceneedstobetrueforaconclusiontobevalid.

InferenceForinferencequestions,determinewhichanswerchoicemustabsolutely,positivelybetruebasedonwhatyou’veread.

•Picktheobviousanswerchoice.•Avoidextremeanswers(toostrongortooweak)

Weaken/StrengthenWhenyoucomparetwoitems,youmustbesurethatthetwoitemsareindeedcomparable.





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Questions Involving SurveysConsider:Doesthesurveyaccuratelyrepresenttheviewsofthewholegroupsurveyed?Isthereastatisticsbaitandswitch?

StatisticsWhenanargumentisbasedonstatistics,itisusuallyassumedthatthepeoplepolledarerepresentativeofthewhole.

NegateForassumptionquestions,negateCRanswerchoicetoseeiftheconclusioncansurvive.

IrrelevantWatchforirrelevantoroverlystronganswerchoicesinCR.StaywithinSCOPEandTONEofpassage.





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Scope ShiftsBewaryofscopeshifts.Lookfortestmakers’tricks:

•Sometimesapassagewillbeginwithonegroupanddrawaconclusionaboutanothergroup.Similarly,apassagemighthaveweakpremisesandthendrawanoverbroadconclusion.

•Othertimesthetoneofthepassagemovessofarthatthetesttakerisleftwondering,“Howdidthatconclusioncomeabout?”

Inference vs. AssumptionAninferenceisaconclusionthatcanbedrawnbasedononeormoreofthestatementsinthestimulus.Aninferencemustbetruebasedonsomethingthatyouread.Anassumptionisamissingbutnecessarypieceofevidence.Anassumptionissomethingthatmustbetrueinorderfortheargumenttobecomplete.

ExplanationWithexplanationquestions,reconcilethefactspresented.

•Staywithinscope.

PrephrasePrephraseananswerbeforelookingattheactualanswerchoices.





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Weaken2mostcommonwaystoweakenanargument:

• Breakdowncentralassumption.• Assertalternativepossibilitiesrelevanttotheargument.

Evaluate the ArgumentTestrelevance.Determinewhichachoicehelpstodeterminewhetheraconclusionisvalid.

For additional notesFor additional notes





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For additional notes








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V E R B A L R E A D I N G C O M P R E H E N S I O NF L A S H C A R D S


39






V E R B A L R E A D I N G C O M P R E H E N S I O N V E R B A L R E A D I N G C O M P R E H E N S I O N

V E R B A L R E A D I N G C O M P R E H E N S I O NV E R B A L R E A D I N G C O M P R E H E N S I O N

Yin-Yang ShiftAverycommonRCstructureisforoneexpertorviewtobeintroduced,andthen,shortlythereafter,acontradictoryexpertorviewispresented.Lookforthisyin-yangshift.

•Yinwords:“Generally,theoldview,thewidespreadbelief,mostXbelieve”,etc.

•Yingwords:“However,but,ontheotherhand”,etc.

Two Types of QuestionsGlobal(pertainstoentirepassage):

•Mainidea,structureLocal(pertainstoasmallsegmentofpassage):

•Specific

SignpostsWatchfortransitiontriggers.Transitiontriggerschangethetoneordirectionofapassage.Theyoftenrepresentashiftinviewbetweentwoexpertscitedinapassage.Examplesoftransitiontriggersinclude“however,but,although”,etc.

Analyzing Reading Comprehension (RC) Passage

WHYistheauthorwriting?WHATisbeingsaid?WHOisspeaking?Istheauthorshowinghisownpointofvieworcritiquinganexpert’spointofview?HOWdoestheauthoraccomplishhisgoal?





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Indisputable WordsNicevaguewords:

•“usually,sometimes,may,can,some,most”Toounequivocal—BAD!

•“always,most,everybody,all,complete,never”

Indisputable AnswersTheanswerchoicethatishighlyspecificandunequivocalisusuallywrong.

•VAGUE,BROADorGENERALanswersareoftenbest.

• Lookforsignpostwordslike“perhaps”and“may”inanswerchoices.

RespectGMACisalwaysrespectfulofprofessionalsandAmerica.Avoiddisparaginganswers.Respectfulanswersaboutminoritiesalways.Noprejudicedanswers.

InferenceGMATinferencesgoonlyatinybitfurtherthanwhatissaidinthepassage.Whenchoosinganswers,eliminateexaggerationsoroffensiveorextremewords.





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Main IdeaThesis:personalinterpretationbolsteredbyevidence.

StrategyMakementalroadmapofpassage.Getasenseoftheparagraphandargumentstructure.Onyourscratchpaper,jotdownnotessuchas:

•Para1:Oldview•Para2:Newtheory•Para3:WhycomboofOldviewandNewtheoryis

likelybest.

StrategyBemindfulof:

•Topic• Scope—narrowingoftopic•Author’spurpose•Structure•Author’svoice—factfromopinion

Strong emotionsAvoidstrongemotions.

•Avoidwordslike:“scornful,envious,overlyenthusiastic,resolve”,etc.





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Logic and Active ReadingAsyouread,thinkaboutwhytheauthor/testmakersdosomethinginthemannerthattheyhave:

•Citeasource•Bringupdetail• Introduceadefinedtermorvocabularyword•Structuresthepassagesinacertainway

InferenceTwotypesofinferences:

•Regularinference.EXPLAIN?HELP?•Agreement:“Author/Character/Groupwould

agreewith…”

ScopeScopeinvolvestheoverallreachandfeeloftheentirepassage.Nounsandverbscontainedinthecorrectanswermustbeconsistentwithtone/scope.Iftheyaretooweak/strong,theyareprobablywrongandshouldbeeliminated.

Global QuestionsStaywithintopicandscope.Recognizeauthor’soverallintentions,idea,passagestructure,purpose.





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FocusFocusonyourreadingonthebroadideaofthepassage,noteveryspecificfact.Thatsaid,notewhereoverly-specificfactsarefirstintroduced,soyoucanzeroinonthemifthereisadetailquestionlater.

ScopeScopeistheaspectofthetopic(subjectmatter)thattheauthordiscussesinthepassage.

Strategy1.Readactivelyanddon’tskim.2.Createamentalroadmap:labelparagraphs,lookfor

signpostwords.3.Notemainidea,structure,tone4.Attackquestions.

Explicit DetailForexplicitdetailquestions,theanswercanbepinpointedinthetext.

• Savetimebynotingwheredefinedterms,vocabularywordsordatesarefirstintroduced.Detailquestionswilllikelyfocusonsuchthings.





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Signpost Words: Supporting, Continuing PointsAdditionalpointsignposts:

• “furthermore,inaddition,also,too”Additionalexamplesignposts:

• “similarly,likewise,forexample”Structuralsignposts:

• “first,second,third”Conclusionsignposts:

• “thus,therefore,inconclusion”

QualifyToqualifyaclaimistoweakenorsoftenit.

AnticipateAnticipatewhat’snextbylookingforsignpostwords.

• Istheauthorabouttochangecourse?Agreewithanexpert?Disagreewiththeviewexpoundedinthepreviouspassages?Cementanideajustpresented?

InferenceInferencesaresuggestedbypassage.Remindyourselfwhethertheinferencesgivenasanswerchoicesarepositive,negativeorneutral.Incorrectinferences:

• Distort•Aresuperfluous,contradictory,outsideofscope





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General QuestionsDecoyanswersforglobalRCquestionsare:

•Toospecific•Toobroad•Tooextreme•Notrelevant

Main IdeaAlwaysbesearchingforthemainideaofapassageasyouread.

StrategyAstrategyforRC:

•Readforauthor’spurposeandmainidea.•Notewherespecificexamplespopup,butdon’t

spendtoomuchtimefullyunderstandingspecifics.•Paraphrasethestructure,toneofthepassage.•Don’tover-investtime.• Spendmaxof4min.onreading,1min.perquestion.

Direction Change SignpostsExamples:

•“although,though,eventhough”•“but• “despite,inspiteof ”•“except”•“however,nevertheless”•“unless”•“while”





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Good Words for RC Answer ChoicesExamples:

•“some,many”•“often,sometimes,rarely,usually”•“can,could,may,might”•“somepeople,fewpeople”•“more,less”•“likely,possibly”•“doubtful,unlikely”

Strengthen/WeakenDecoyanswersforstrengthen/weakenquestions:

•Outofscope•Weakeninsteadofstrengthen,viceversa•Logicalanswerbutnotmentionedorsupportedin

passage(bringinoutsideinfowhenthere’sacorrectansweramongthechoicesalready)

How to Spot a Good AnswerAcorrectanswerchoice:

• Paraphrasestextintermsoflanguagestyleormeaning• Isnice(notoverly-controversial)• Isnotextreme(stayswithinscope,authorintent).

Doesnotoverlypinpoint.

Specific QuestionsDecoyanswersforlocalRCquestions:

•Refertowrongpartofpassage•Makesensebutarenotmentionedinpassage•Arerefuteddirectlyinthepassage•Strayawayfrompassage’sscope•Misinterpretthemainpointoftheauthor

inthatsection





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Purpose, Main IdeaBemindfulofauthor’sPURPOSEandMAINIDEA. NOTEthattheoverallpurposeandmainideacan

differfromtheviewsofaspecificexpertinapassage.

Specific DetailsNotethelocationandpurposeofintricatedetails,theoriesorvocabularywords,butdonotattempttomemorizeorevenfullyunderstandthosedetailsunlessaquestionspecificallyasksaboutthem.

Topic and ScopeAlwaysbemindfulofTOPICandSCOPE:Topicandscopecanoftenbedeterminedinthefirstparagraphofapassage.Assoonasyoufindthem,listthemonyourscratchpaper.

Theconclusionparagraphwillalsorevealthescopeifitisnotimmediatelyobviousinthefirstparagraph.

Words to Avoid in RC Answer ChoicesExamples:

• “all”• “always”• “never”• “will”• “everyone,everybody”

• “noone,nobody”• “most,least”• “absolutely”• “impossible”

Topic:Generalsubject Examples:

•“blackholes” •“factorysafety”

Scope:Narrowingoftopic Examples: •“logisticsofviewing

formationofblackholes” •“analysisofindustrialrules

acrossdifferenthistoricaleras”





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Q U A N T I TAT I V E G E N E R A LF L A S H C A R D S


http://go.beatthegmat.com/flashcards

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Q U A N T I T A T I V E G E N E R A LQ U A N T I T A T I V E G E N E R A L


MultipleMultiplesof3:3,6,9…

Steps to SolveIngeneral…

•Mediumquestionsrequire2stepstosolve.•Difficultquestionsrequireatleast3steps.•TheGMATbeginswithamediumquestion.

AssumingAllnumbersontheGMATbelongtothesetofrealnumbers.

•Unlessyou’reexplicitlytoldthataspecifictypeofnumberisinvolved,donotmakeanyfurtherassumptions.

•Forexample,doNOTassumethatvariablesrepresentpositiveintegers.

Backsolving StrategyStartwithChoice‘E’andworkbackto‘A’whenbacksolvingfromtheanswerchoices.





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How to Check Whether Number is Multiple of 9

Sumofdigitsismultipleof9.


Numberismultipleof3and2.


Lasttwodigitsaremultipleof4.Thenumbercanbedividedby2twice.


Sumofdigitsismultipleof3.





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Gross ProfitGrossprofit=SellingPrice–Cost

Simple Probability

Common FactorBreakdownbothnumberstotheirprimefactorstoseewhatfactorstheyhaveincommon.Multiplysharedprimefactorstofindallcommonfactors.

CORRECT: Whatfactorsgreaterthan1do135and225haveincommon?

135=3x3x3x5 225=3x3x5x5 Bothshare3x3x5incommon—findallcombinationsofthesenumbers: 3x3=9; 3x5=15; 3x3x5=45


Sumofdigitsismultipleof3,lasttwodigitsmultipleof4.

(#offavorableoutcomes)(#ofpossibleoutcomes)





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Multiplication PrincipleThenumberofwaysindependenteventscanoccurtogethercanbedeterminedbymultiplyingtogetherthenumberofpossibleoutcomesforeachevent.

Combined EventsForeventsEandF:

•notE=P(notE)=1–P(E)•EorF=P(EorF)=P(E)+P(F)–P(EandF)•EandF=P(EandF)=P(E)P(F)

Multiplication PrincipleIfafirstobjectmaybechoseninmwaysandasecondobjectmaybechoseninnways,thentherearemnwaysofchoosingbothobjects.

Dependent EventsTwoeventsaresaidtobedependenteventsiftheoutcomeofoneeventaffectstheoutcomeoftheotherevent.





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3rd Rule of ProbabilityConditionalProbability:TheprobabilityofeventAANDeventBoccurringistheprobabilityofeventAtimestheprobabilityofeventB,giventhatAhasalreadyoccurred.P(AandB)=P(A)×P(B|A)

2nd Rule of ProbabilityComplementaryEvents:Theprobabilityofaneventoccurringplustheprobabilityoftheeventnotoccurring=1.P(E)=1–P(notE)

1st Rule of ProbabilityBasicrule:TheprobabilityofeventAoccurringisthenumberofoutcomesthatresultinAdividedbythetotalnumberofpossibleoutcomes.

4th Rule of ProbabilityTheprobabilityofeventAOReventBoccurringistheprobabilityofeventAoccurringplustheprobabilityofeventBoccurringminustheprobabilityofbotheventsoccurring.P(AorB)=P(A)+P(B)–P(AandB)





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Indistinguishable EventsTofindthenumberofdistinctpermutationsofasetofitemswithindistinguishable(“repeat”)items,dividethefactorialoftheitemsinthesetbytheproductofthefac-torialsofthenumberofindistinguishableelements.Example:HowmanywayscanthelettersinTRUSTbearranged?

CORRECT:

Probability of Multiple EventsRules:

•AandB<AorB•AorB>IndividualprobabilitiesofA,B•P(AandB)=P(A)xP(B)←“feweroptions”•P(AorB)=P(A)+P(B)←“moreoptions”

5!2!

= 60

Permutations: Order mattersNumberofpermutationsofrobjectsfromasetofnobjects:

Combinations: Order doesn’t matter

n!r!(n–r)! n!

(n–r)!n=numberofitemsr=numberofitemschosen

nCr=

nPr=





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Q U A N T I T A T I V E G E N E R A LQ U A N T I T A T I V E G E N E R A LQ U A N T I T A T I V E G E N E R A L

Trial ProblemsLookattheprobabilityofNOTOCCURRING.P(EventNotOccurring)=1–P(EventOccurring)

Multiple Event ProbabilityTodeterminemultiple-eventprobabilitywhereeachindividualeventmustoccurinacertainway:

• Figureouttheprobabilityforeachindividualevent.• Multiplytheindividualprobabilitiestogether.

Probability and GeometryIfapointischosenatrandomwithinaspacewithanarea,volume,orlengthofYandaspacewitharespectivearea,volume,orlengthofXlieswithinY,theprobabilityofchoosingarandompointwithinYisthearea,volume,orlengthofXdividedbythearea,volume,orlengthofY.

Circular PermutationsThenumberofwaystoarrangendistinctobjectsalongafixedcircleis:(n–1)!





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Odd FactorsOddnumbershaveonlyoddfactors.

Number Added or DeletedUsemeantofindnumberthatwasaddedordeleted.

•Total=meanx(numberofterms)•Numberdeleted=(originaltotal)–(newtotal)•Numberadded=(newtotal)–(originaltotal)

Slopey=mx+bm=slope=(differenceinycoordinates) (differenceinxcoordinates)

Triangles30-60-90

x(sq.rt3)

2xx

45-45-90

x(sq.rt2) x

x

3-4-5

34

5

5-12-13

13 12

5

9-12-15

15 12

9





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Prime Factorization: Greatest Common Factor (GCF)

1.Startbywritingeachnumberasproductofitsprimefactors.2.Writesothateachnewprimefactorbeginsinsameplace.3.GreatestCommonFactor(GCF)isfoundbymultiplying

allfactorsappearingonBOTHlists. 60= 2x2 x3 x5 72= 2x2x2x3x3 HCF=2x2 x3 =12

Exponentsxryr=(xy)r

3343=123=1728

Quadratic FormulaTofindrootsofquadraticequation:

Purchase Price vs. Market ValueRemember:purchasepriceisnotthesameasmarketvalue.

Purchase Price = price purchased for by wholesalerMarket Value = price sold for by retailer (after markup)

ax2+bx+c=0

x=[−b±√b2−4ac]

2a





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Factoring Exponents ExampleRate × Time = Distance (rt = d)Forafixeddistance,theaveragespeedisinverselyrelatedtotheamountoftimerequiredtomakethetrip.

CORRECT: SinceMieko’saveragespeedwas3/4ofChan’s,hertimewas4/3aslong.

rt=d CORRECT:

Check for Prime1.Pickanumbern.2. Startwiththeleastprimenumber,2.Seeif2isafactor

ofyournumber.Ifitis,yournumberisnotprime.3. If2isnotafactor,checktoseeifthenextprime,3,isafactor.Ifit

is,yournumberisnotprime.4.Keeptryingthenextprimenumberuntilyoureachonethatisa

factor(inwhichcasenisnotprime),oryoureachaprimenumberthatisequaltoorgreaterthanthesquarerootofn.

5. Ifyouhavenotfoundanumberlessthanorequaltothesquarerootofn,youcanbesurethatyournumberisprime.

Prime Factorization: Lowest Common Multiple (LCM)

1.Startbywritingeachnumberasproductofitsprimefactors.2.Writesothateachnewprimefactorbeginsinsameplace.3.Lowestcommonmultiplefoundbymultiplyingall

factorsinEITHERlist. 60= 2x2 x3 x5 72= 2x2x2x3x3 LCM= 2x2x2x3x3x5=360

(3)r(4)t=d 4 3

5k−15k

000 5

5k−5k−1

(1−1)5k

5

(4)5k

5





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Q U A N T I T A T I V E G E N E R A LQ U A N T I T A T I V E G E N E R A LQ U A N T I T A T I V E G E N E R A L

Area of a Trapezoid(sumofbases)(height)

2

Inscribed Angle, Minor Arc

ApproximationsSquarerootof2=1.4Squarerootof3=1.7

Squaring FractionsWhenpositivefractionsbetween0and1aresquared,theygetsmaller.

(1)2=(1) 4 16

Minorarc=70degrees

Minorarc=2x(inscribedangle)

Radius

Inscribedangle=35degrees

b1

b2

h





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Set ProblemEachof25peopleisenrolledinhistory,math,orboth.If20areenrolledinhistoryand18areenrolledinmath,howmanyareenrolledinboth?

Mixture ProblemExample:Howmanylitersofasolutionthatis15%saltmustbeaddedto5litersofasolutionthatis8%saltsothattheresultingmixtureis10%salt?

CORRECT: 0.15n+0.08(5)=0.1(n+5) 15n+40=10n+50 5n=10=>n=2liters

Evenly Divisible ProblemTodeterminethenumberofintegerslessthan5000thatareevenlydivisibleby15:

CORRECT: Divide4999by15=>333integers

Interest ProblemExample:If$10,000isinvestedat10%annualinterest,compoundedsemi-annually,whatisthebalanceafter1year?

CORRECT: 10,000+(10,000)(0.05)=10,500OR 10,500+(10,500)(0.05)=$11,025

CORRECT: 10,000(1+0.10)2=$11,025 2

ForCompoundInterest:Divideinterestby#oftimescom-poundedin1yeartofindinterestforthecompoundperiod. CORRECT: (20–n)+n+(18–n)=25=>n=13

20–n 18–nn

History Math





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Intersecting Sets|AunionB|=|A|+|B|–|AintersectB|

Always Try to Factor!

Prime NumberAprimenumberisapositiveintegerthathasexactlytwodifferentpositivedivisors:1anditself.

•1isnotprime.•2isboththesmallestprimeandtheonly

evenprime.

Rules of Exponentsxr=(x1)r=s√xr

s

s

x3−2x2+x=−5(x−1)2

x(x2−2x+1)=−5(x−1)2

x(x−1)2+5(x−1)2=0 (x+5)(x−1)2=0 x=−5,1

A B





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Use FOIL Method with Quadratics with Roots

n−4√n+4=>(√n−2)(√n−2)

x2−4x+4

Consecutive IntegersEven:2n,2n+2,2n+4Odd:2n+1,2n+3,2n+5

Standard Deviation of n NumbersStandarddeviationmeasuresthe“spread”ofthedatapointsvsthemean.HigherSD=HigherVariation1.Findarithmeticmean.2.Finddifferencesbetweenmeanandeachofthennumbers.3.Squareeachofthedifferences.4.Findaverageofsquareddifferences.5.Takenon-negativesquarerootofthisaverage.

Properties of 0Zeroisaneveninteger.Zeroisneitherpositivenornegative.Zeroisamultipleofeverynumber.Zeroisafactorofnonumber.





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Gross vs. NetGrossisthetotalamountbeforeanydeductionsaremade.Netistheamountafterdeductionsaremade.

Geometry: TrianglesExteriorangledisequaltothesumofthetworemoteinterioranglesaandb.

Geometry: Similar Triangle AreasTheratiooftheareasoftwosimilartrianglesisthesquareoftheratioofcorrespondinglengths.EachsideoftriangleDEFis2timesthelengthofcorrespondingtriangleABCTriangleDEFmusthave22,or4,timestheareaoftriangleABC.

Percent Increase vs. Percent ofBecarefulaboutpercentincreasevs.percentof.

%increase=(amountofchange)/(originalamount)%of=portion/whole

D

E F

84

A

B2 4

C

a

b c d

d=a+b





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Odd and EvenOdd+Odd=Even Odd×Odd=OddEven+Even=Even Even×Even=EvenOdd+Even=Odd Odd×Even=Even Anymultiplicationinvolving

anevennumbercreatesanevenproduct.

Simplify BaseAlwaystrytosimplifythebase.

• If27n=94

• then(33)n=(32)4=>n=8

3

AveragesThinkofaveragesasbalancing.Example:Theaverageof3,4,5,andxis5.Whatisx? 3is2lessthan5 4is1lessthan5 5istheaverage. x=5+3=8

Useful Percentages to Know1/8=12.5%1/6=16.6%5/6=83.3%





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Group Problems Involving “Either/Or”SomeGMATwordproblemsinvolvegroupswithdistinct“either/or”categories(male/female,bluecollar/whitecollar,etc.).Thekeyistoorganizetheinformationintoagrid.

DivisorsYoucanfindallthedivisorsofanumberbyfindingalltheprimefactors.

PercentageTomakeapercentage,multiplyby100%:

CORRECT:

Todropapercent,divideby100%:

CORRECT:

Powers and RootsTomultiplyoneradicalbyanother,multiplyordividethenumbersoutsidetheradicalsigns,thenthenumbersinsidetheradicalsigns.

CORRECT: 12√15=(12)√15=6√3 2√5 2 √5

(6√3)2√5=(6×2)(√3√5)=12√15

1 =1%=0.25%400 4

1%×1 = 12 100 20,000

Doctors Dentists TotalMale 55 27 82

Female 39 9 48Total 48 36 130





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Multiple Event ProbabilityTwothingstodo:

•Findthetotalnumberofpossibleoutcomes.•Findthenumberofdesiredoutcomes.

Writethemoutifnecessary.

Sum of Angles in a Regular PolygonSumofinterioranglesinapolygonwithnsides=180(n–2)

Volume of a Sphere 4

∏r3 3

Factor Out and SimplifyImmediatelytryfactoring/simplifyingwhenpossible.

Is2x+24aninteger? 6 6

=>2x+24 6

=>x+4 3





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Balancing Method for Mixtures/Dilutions Example

Howmanylitersofasolutionthatis10%alcoholbyvolumemustbeaddedto2litersofasolutionthatis50%alcoholbyvolumetocreateasolutionthatis15%alcoholbyvolume?

CORRECT: n(15–10)=2(50–15) 5x=2(35)=>n=70/5=>14litersof10%

solutionmustbeadded.

Balancing Method for Mixtures/Dilutions

Added, DeletedNumberadded:(newsum)–(originalsum)Numberdeleted:(originalsum)–(newsum)Example:Theaverageof5numbersis2.Afteronenumberisdeleted,thenewaverageis–3.Whatnumberwasdeleted?

CORRECT: Originalsum:5x2=10Newsum:4x(-3)=–12Numberdeleted=10–(–12)=22

Group Problems Involving “Both/Neither”Mixedgroupformula:

Group1+Group2+Neither–Both=Total

(percent/pricedifferencebetweenweakersolutionanddesiredsolution ) (amountof

weakersolution )× =

(percent/pricedifferencebetweenstrongersolutionanddesiredsolution ) (amountof

strongersolution )×





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Factorial of Zero0!=1

A Common Digits Problem BA 47 83 +AB =>+74 or+38 CDC 121 121

Average RateAverageAperB=(TotalA)/(TotalB)AverageSpeed=(TotalDistance) (TotalTime)

Compound InterestUsuallyyoudon’tneedtocalculatecompoundinterest.Tryfindingsimpleinterestandlookingfortheanswerthatisalittlebitlarger.





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Sum of Consecutive NumbersSum=(average)(numberofterms)

Simple InterestSimpleinterest=(principal)(interestrate)(time)

decimal yearsExample:If$12,000isinvestedat6%simpleannualinterest,howmuchinterestisearnedafter9months?

CORRECT: ($12,000)(0.06)(9/12)=$540

Count Consecutive NumbersNumberofintegersfromAtoBinclusive=B–A+1Example:Howmanyconsecutiveintegersaretherefrom73through419,inclusive?

CORRECT: 419–73+1=347

Compound Interest(Finalbalance)=(principal)x(1+(interest)/C)^[(time)(C)]

• C=thenumberoftimescompoundedannuallyExample:If$10,000isinvestedat8%annualinterest,compoundedsemiannually,whatisthebalanceafter1year?

CORRECT: Finalbalance=(10,000)(1+(0.08)/2)^[(1)(2)] =10,000x(1.04)^2 =$10,816





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FactorsFactorsof18:1,2,3,6,9,18Factorsof6:1,2,3,6

PercentExample:15is3/5percentofwhatnumber?

CORRECT: 3/5percent=3/500 15=(3/500)xwhole whole=2500

Prime Numbers1isnotaprimenumber.Thefirsteightprimenumbersare:2,3,5,7,11,13,17,19

Average of Consecutive NumbersTheaverageofasetofevenlyspacedconsecutivenumbersistheaverageofthesmallestandlargestnumbersintheset.Example:Whatistheaverageofallintegersfrom13to77?

CORRECT: (13+77)/2=90/2=45





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Quadratics(x+y)2=x2+2xy+y2(x–y)2=x2–2xy+y2(x+y)(x–y)=x2–y2

Whenyouseeanequationinfactoredforminaquestion,immediatelyUNFACTORit;viceversa.

GuessingAccordingtosometestprepsources:Ifyouhavetoguessinaproblemsolvingquestion,gowith(D)or(E).Especiallywithproblemsthatforceyoutouseorplugintheanswerchoices

Work ProblemsConsiderworkdoneinonehour.Inverseofthetimeittakeseveryoneworkingtogether=Sumoftheinversesofthetimesitwouldtakeeachpersonworkingindividually.Example:YouhaveworkerAandworkerBdoingajob:

CORRECT:

Simple InterestA=P(1+r)n A=amountaccumulated P=principal r=annualrateofinterest n=numberofyears

1+1=1A B T





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Q U A N T I T A T I V E D A T A S U F F I C I E N C Y




Hard QuestionsSkipstatementsthatyoudonotunderstand.Eliminateasmuchaspossible.

RephraseAgooddatasufficiencystrategyistorephrasetheinformationinaquestion: z+z<z? =>z<0?(...or0<z<1)

Strategy1.Focusonthequestionstem—thinkingaboutthe

informationneededtoanswerthequestion.2.Lookateachstemseparately.3.Ifneitherstatementswassufficientalone,lookat

bothstatementsincombination.4.HalfoftheDataSufficiency(DS)answersonthe

GMATcomedowntostep3.

InsufficientHalfthetimestatements(A)and(B)arebothinsufficient.





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Common TrapDoNOTusetheinformationinonestatementasanassumptioninthesecondstatement.

•Statementsarenotnecessarilyrelated.•Viewseparately!

First Data Sufficiency (DS) QuestionsCalculateoutthefirstDSquestionstomakesuretheyarecorrect.Itisimportanttostartoutthesectionstrong.

StrategyImmediatelywriteouttheDSproblemtype(value,range,yes/no)onyourscratchpaperbeforeyoubeginaDSproblem.

What is Being Asked?InDataSufficiencyquestions,youareusuallybeingasked1of3things:

1.Aspecificvalue2.Arangeofnumbers3.Yes/No





77










Looking at Both Statements TogetherOnlyabouthalfthetimedoyouhavetolookatbothstatementsincombination.

“Yes/No”About1/3ofDSquestionsare“Yes/No”questions.

EquationsForasystemwithnvariables:

• Ifyouhaveasmanydistinctlinearequationsasyouhavevariables,youcananswerANYquestionaboutthesystem.

• Ifyouareonlyaskedtosolveforpartofthesystem,youdon’tnecessarilyneedallnequations.

• Ifyouareaskedtosolveforarelationshipinsteadofthevalueofvariables,youdon’tnecessarilyneedallnequations.

Hard QuestionsOnharderDSquestions,answerchoicestendtobemoresufficientthantheymightappear.

•DON’TCHOOSE(E)ifyouhavetoguess.•Pickbetween(A)or(C),ifyoucaneliminate(B).•Historically,(A)isslightlymorecommonasthe

rightanswer.





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StrategyADorBCE:Ifyoucandeterminethatchoice(A)iscorrectinyourDSquestion,thenyouknowthattheultimateanswermustbeeither(A)or(D).Ifyoucandeterminethatchoice(A)isnotcorrectinyourDSquestion,thenyouknowthattheultimateanswermustbe(B),(C),or(E).

Sufficiency in “Yes/No” QuestionsOn“Yes/No”DSquestions,ifastatementanswersthequestionconclusivelyintheaffirmativeorinthenegative,thenITISSUFFICIENT.

For additional notes For additional notes

Solving a System of Equations RuleTosolveasystemofnvariables,youneedndistinctlinearequations.Example:Whatisthevalueofy?

Given:x+y=1=>insufficientwithoutanotherdistinctequation





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