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Table of Contents 2 LetterfromtheFounder 3 TestPrepCompanyDiscounts
VerbalFlashcards 4SentenceCorrection26CriticalReasoning38ReadingComprehension
QuantitativeFlashcards49General74 DataSufficiency
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G M A T F L A S H C A R D S
L A S T U P D A T E D : J U N E 3 0 , 2 0 1 0
B E A T T H E G M A T
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Letter from the Founder
DuringmyGMATpreparation,ImadehundredsofflashcardstohelpmestayfreshonthestrategiesandmaterialsIhadstudiedoverthecourseofseveralmonths.Thisdocumentcontainsthedigitizedversionofmyflashcards—pleaseusethemasastudyaid.
Theseflashcardsareafreeresourceforeveryone.Theyareupdatedfrequently,sobesuretovisitthefollowingpagetomakesureyouhavethelatestversion:
http://go.beatthegmat.com/flashcards
AlsonotethattheseflashcardshavebeenreviewedandeditedbytopGMATinstructorsforqualitycontrol.Todatethisdocumenthasbeendownloadedover100,000times!
AllthebestinyourGMATprep,EricBahnFounderofBeatTheGMAThttp://www.beatthegmat.com
B E A T T H E G M A T
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GrockitDiscounthttp://www.beatthegmat.com/mba/partners/grockit-gmat-discount
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PrincetonReviewDiscounthttp://www.beatthegmat.com/mba/partners/the-princeton-review-gmat-discount
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Test Prep Company Discounts
Save BIG whenusingthesediscountcodesforonlinepurchasesatthefollowingtestprepwebsites.
AportionofeverypurchasemadeusingthesediscountcodeswillfundtheBeatTheGMATScholarships!
B E A T T H E G M A T
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Other Links 2 LetterfromtheFounder 3 TestPrepCompanyDiscounts
VerbalFlashcards 4SentenceCorrection26CriticalReasoning38ReadingComprehension
QuantitativeFlashcards49General74DataSufficiency
http://www.beatthegmat.com©BeatTheGMAT
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
Theseflashcardsarefreeandupdatedfrequently.Getthelatestversion:http://go.beatthegmat.com/flashcards
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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
V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
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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V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
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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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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V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
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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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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V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
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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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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V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
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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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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V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
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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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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V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
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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“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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V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
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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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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V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
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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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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V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
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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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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V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
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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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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V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
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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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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V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
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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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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V E R B A L S E N T E N C E C O R R E C T I O N
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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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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V E R B A L S E N T E N C E C O R R E C T I O N
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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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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V E R B A L S E N T E N C E C O R R E C T I O N
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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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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V E R B A L S E N T E N C E C O R R E C T I O N
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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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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V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
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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“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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V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
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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“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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V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
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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“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 S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
V E R B A L S E N T E N C E C O R R E C T I O N
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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B E A T T H E G M A T
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VerbalFlashcards 4SentenceCorrection26CriticalReasoning38ReadingComprehension
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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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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
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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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
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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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
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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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
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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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
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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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
Indicate FlawUsetheinformationthatispresentinthepassagetoanswer“IndicatetheFlaw”CRquestions.Notaboutnewinformationlike“Weaken”CRquestions.
AssumptionForassumptionquestions,findtheconclusionanddeterminewhichanswerchoiceneedstobetrueforaconclusiontobevalid.
InferenceForinferencequestions,determinewhichanswerchoicemustabsolutely,positivelybetruebasedonwhatyou’veread.
•Picktheobviousanswerchoice.•Avoidextremeanswers(toostrongortooweak)
Weaken/StrengthenWhenyoucomparetwoitems,youmustbesurethatthetwoitemsareindeedcomparable.
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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
Questions Involving SurveysConsider:Doesthesurveyaccuratelyrepresenttheviewsofthewholegroupsurveyed?Isthereastatisticsbaitandswitch?
StatisticsWhenanargumentisbasedonstatistics,itisusuallyassumedthatthepeoplepolledarerepresentativeofthewhole.
NegateForassumptionquestions,negateCRanswerchoicetoseeiftheconclusioncansurvive.
IrrelevantWatchforirrelevantoroverlystronganswerchoicesinCR.StaywithinSCOPEandTONEofpassage.
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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 G V E R B A L C R I T I C A L R E A S O N I N G
Scope ShiftsBewaryofscopeshifts.Lookfortestmakers’tricks:
•Sometimesapassagewillbeginwithonegroupanddrawaconclusionaboutanothergroup.Similarly,apassagemighthaveweakpremisesandthendrawanoverbroadconclusion.
•Othertimesthetoneofthepassagemovessofarthatthetesttakerisleftwondering,“Howdidthatconclusioncomeabout?”
Inference vs. AssumptionAninferenceisaconclusionthatcanbedrawnbasedononeormoreofthestatementsinthestimulus.Aninferencemustbetruebasedonsomethingthatyouread.Anassumptionisamissingbutnecessarypieceofevidence.Anassumptionissomethingthatmustbetrueinorderfortheargumenttobecomplete.
ExplanationWithexplanationquestions,reconcilethefactspresented.
•Staywithinscope.
PrephrasePrephraseananswerbeforelookingattheactualanswerchoices.
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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
Weaken2mostcommonwaystoweakenanargument:
• Breakdowncentralassumption.• Assertalternativepossibilitiesrelevanttotheargument.
Evaluate the ArgumentTestrelevance.Determinewhichachoicehelpstodeterminewhetheraconclusionisvalid.
For additional notesFor additional notes
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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
For additional notes
For additional notes
For additional notes
For additional notes
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Other Links
B E A T T H E G M A T
2 LetterfromtheFounder 3 TestPrepCompanyDiscounts
VerbalFlashcards 4SentenceCorrection26CriticalReasoning38ReadingComprehension
QuantitativeFlashcards49General74DataSufficiency
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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 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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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
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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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
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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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
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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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
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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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
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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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
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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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
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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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
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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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
For additional notes
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QuantitativeFlashcards49General74DataSufficiency
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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
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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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
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
How to Check Whether Number is Multiple of 9
Sumofdigitsismultipleof9.
How to Check Whether Number is Multiple of 6
Numberismultipleof3and2.
How to Check Whether Number is Multiple of 4
Lasttwodigitsaremultipleof4.Thenumbercanbedividedby2twice.
How to Check Whether Number is Multiple of 3
Sumofdigitsismultipleof3.
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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
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
Gross ProfitGrossprofit=SellingPrice–Cost
Simple Probability
Common FactorBreakdownbothnumberstotheirprimefactorstoseewhatfactorstheyhaveincommon.Multiplysharedprimefactorstofindallcommonfactors.
CORRECT: Whatfactorsgreaterthan1do135and225haveincommon?
135=3x3x3x5 225=3x3x5x5 Bothshare3x3x5incommon—findallcombinationsofthesenumbers: 3x3=9; 3x5=15; 3x3x5=45
How to Check Whether Number is Multiple of 12
Sumofdigitsismultipleof3,lasttwodigitsmultipleof4.
(#offavorableoutcomes)(#ofpossibleoutcomes)
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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
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
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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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
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
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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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
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
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 L
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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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
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
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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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
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
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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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
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
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 L
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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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
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
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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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
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
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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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
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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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
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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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
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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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
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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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
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
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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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
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
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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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
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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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
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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For additional notes
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QuantitativeFlashcards49General74DataSufficiency
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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
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
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
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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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
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
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
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
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
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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
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
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
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
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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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
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
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
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
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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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
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
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
For additional notes
For additional notes
For additional notes
For additional notes