what to expect on the isee - isee practice tests
TRANSCRIPT
piqosity
P a g e |1
WhattoExpectontheISEEERB’sOfficialPracticeTestAnswerExplanationsByStephenHayesforPiqosity.com®ISEEisaregisteredtrademarkoftheEducationalRecordsBureau,whichisneitheraffiliatedwithnorendorsesPiqosity.
P a g e |2
Contents
VerbalReasoning page3QuantitativeReasoning 10ReadingComprehension 20MathematicsAchievement 27
piqosity 2429BartlettSt.,Houston,Texas77098(713)2346098Piqosity.com©2017byPiqosityCorporation.Allrightsreserved.Thisdocumentmayonlybeusedand/orreprintedforpersonal,non-commercialuse.Allotherusesrequiretheprior,writtenpermissionofPiqosity.
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |3
VerbalReasoning-Synonyms1. INITIAL=existingoroccurringatthebeginningA. first B. mutual C. orderly D. propercomingbeforeallothersintimeororder
heldincommonbytwoormoreparties
neatlyandmethodicallyarranged
suitableorappropriate
2. MANNEQUIN=adummyusedtodisplayclothesinastorewindowA. actor B. aide C. leader D. modelonewhoperformsaroleinTV,movies,oronstage
onewhoassistssomeoneofimportance
onewhocommandsagroupororganization
oneemployedtodisplayclothing
3. AGENDA=aplanofthingstobedoneorproblemstobeaddressedA. accident B. composition C. duty D. programeventthathappensbychance
thewayinwhichsomethingismadeup
moralorlegalobligation;responsibility
aplannedseriesoffutureevents
4. ADVERSARY=one'sopponentinacontest,conflict,ordisputeA. agent B. coward C. opponent D. rascalonewhoactsonbehalfofanother
onewholackscouragetoendureunpleasantthings
onewhocompetesorfightsanother
mischievousorcheekyperson
5. PERSONIFY=representorembodya(usuallyhuman)quality,concept,orthinginphysicalformA. argue B. fulfill C. replace D. representexchangeorexpressopposingviews
bringtocompletionorreality;carryout
taketheplaceofsomething
beasymbolorembodimentofathing
6. EQUITY=thequalityofbeingfairandimpartialA. fairness B. harshness C. humor D. knowledgequalityofbeingfreefrombiasorinjustice
qualityofbeingdisagreeabletosenses
qualityofbeingamusingorcomic
facts/skillsgainedbyexperienceoreducation
7. ANTHOLOGY=apublishedcollectionofpoemsorotherpiecesofwritingA. agreement B. collection C. disease D. extensionharmonyinopinionorfeeling
assemblyofitems,suchaswrittenworks
conditionthatimpairsnormalfunctioning
continuation;partthatisaddedtoprolong
8. OPAQUE=notabletobeseenthrough;nottransparentA. antique B. clouded C. exhausted D. pretentiousbelongingtoancienttimes
madeunclearorlesstransparent
verytired;completelyusedup
actinggreaterthanoneistoimpressothers
9. PALPABLE=abletobetouchedorfelt;cleartothemindorplaintoseeA. docile B. political C. sluggish D. tangiblesubmissive;readytoacceptcontrol
interestedinoractiveinpolitics
slow-movingorinactive perceptiblebytouch;clearanddefinite;real
10. FATHOM=understand(adifficultproblemoranenigmaticperson)aftermuchthoughtA. comprehend B. hasten C. question D. trickgraspmentally;understand
causetohappensoonerthannormal
feelorexpressdoubtaboutsomething
deceiveoroutwitthroughcunning/skill
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |4
11. DIMINISH=makeorbecomeless;makeseemlessimpressiveorvaluableA. eliminate B. evade C. examine D. reducecompletelyremoveorgetridofsomething
escapeoravoid;avoidgivingadirectanswerto
inspectindetail;investigatethoroughly
makesmallerorlessinamount,degree,orsize
12. PERPETUATE=makeathing(undesirablesituationorunfoundedbelief)continueindefinitelyA. continue B. convince C. enclose D. introducepersistinanactivityorprocess
causeonetobelievefirmlyinatruth
surroundorcloseoffonallsides
bringintouse/operationforfirsttime
13. ADMONISH=warnorreprimandsomeonefirmlyA. delay B. organize C. suffer D. warnmakesomethinglateorslow
arrangeintoastructuredwhole
experiencesomethingbadorunpleasant
givesomeoneforcefulorcautionaryadvice
14. DEPICT=showorrepresentbyadrawing,painting,orotherartformA. describe B. discard C. include D. reversegiveanaccountinwordsofsomething
getridofsomethingasnolongeruseful/wanted
makepartofawholeorset
movebackward;makeoppositeofwhatis
15. EPITOME=apersonorthingthatisaperfectexampleofaparticularqualityortypeA. embodiment B. equilibrium C. resilience D. viewpointatangibleformofanidea,quality,orfeeling
astateofphysicalormentalbalance
capacitytorecoverquicklyfromdifficulties
wayofconsidering/one’spositiononamatter
16. TRANSITORY=lastingonlyforashorttimeA. active B. essential C. fleeting D. immediatereadytoengageinenergeticpursuits
absolutelynecessary;extremelyimportant
lastingforaveryshorttime
occurringordoneatonce;instant
17. INCITE=encourageorstirup(usuallyviolentorunlawfulbehavior)A. explain B. investigate C. provoke D. requestmakesomethingmoreclearthroughdescription
carryoutinquirytoestablishtruth
stimulateareactionoremotion(unwelcome)
politelyorformallyaskforsomething
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |5
VerbalReasoning-SentenceCompletions18. Poet-novelistRitaDove,formerUnitedStatesPoetLaureate,wastherecipientof
the1966HeinzAwardinthecategoryofartsandhumanities. D
Explanation
Workingwiththeinformationprovidedbythesentence,Dovewritespoetryandnovels(bothworksofarts/humanities)andwastheUnitedStatesPoetLaureate.YoudonothavetoknowwhataPoetLaureateis,butyoucanrecognizethefactthetitleincludes“UnitedStates,”whichindicatesthatDovewasaveryimportantpoetthroughoutthewholeoftheUnitedStates.Thus,itmakessensethatsuchanimportantpoetwouldreceiveanawardforherefforts.Plus,wewouldneedmoreinformationfortheotheranswerchoicestobetrue(didshemakeorbringabouttheaward?)
19. AlfredJarry’sfirstplay,UbiRoi,isconsideredthefirstworkofthetheaterofthe
absurd;althoughitcausedascandalwhenitopenedin1896,todayitisacclaimedforitsinnovativeplot.
A
Explanation
Focusingonthepartsofthesentencethatfollowthesemicolon,thecontextualstructureshiftsfromnegativetopositive.While“scandal”putstheplayinanegativelight,the“although”marksashiftfrom“scandal,”and“innovative”suggeststheplaywaswellreceived.Thus,“acclaimed”(praisedenthusiasticallyandpublically)makesthemostsense.
20. Manypeopleraisetheirvoicesinanargument,asthoughhighervolumeprovidesa
greaterabilitytopersuade. C
Explanation
“asthough”indicatesthatsecondpartofthesentenceisthereasonforthefirstpart—raisedvoiceshelpwithpersuasioninanargument.Thus,“provides”makesthemostsense.Thesentencedoesnotdiscussasecondaspectofvolumeorargumentfor“balances”tomakesense(lowvolumeorfighting,forexample,isnotmentioned).“necessitates”doesnotworkbecause“agreaterabilitytopersuade”isthereasonfor“highervolume”andnotitsconsequence.
21. Inthesecondhalfofthenineteenthcentury,thenumberofAmericanbison,which
wereonceabundant,begantodeclineasthebisonbecameasourceoffoodforwestward-movingpioneersandrailroadworkers.
A
Explanation
Boileddown,thesentencestatesthenumberofbisondeclined.However,“whichwereonce”indicatesthenumberofbisonweresomethingelsebeforethedecline.Wewantananswerchoicethatmeansthebisonweregreatinnumberorweresomethinggreaterthanbeforetheirdecline.Thus,“abundant”(existingoravailableinlargequantities)makesthemostsense.“vibrant”means“fullofenergyandenthusiasm,”whichtellsusnothingaboutthenumberofbisonbeforetheirdecline(justthattheyhadgreatpersonalities).
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |6
22. Unlikeothergreatapes,whicharesocial,orangutansaresolitarycreaturesexceptforplayfuljuvenilesandmotherswithbabies. D
Explanation
Thesentencedefinesgreatapesassocialthings,andthe“Unlike”indicatesthatorangutansaretheoppositeofsocial.Wewantananswerchoicethatmeanstheoppositeofwantingtointeractwithothers,likethejuvenilesandmotherswithbabies.Thus,“solitary”(wantingtoactalone)makesthemostsense.Wedonothaveenoughinformationinthesentencetosaywhetherornotothergreatapesareunhappy(“contented”)orstrange(“mysterious”),and“friendly”hasasimilarmeaningto“social.”
23. Thearticleongenesplicingwassoesotericthatonlyahandfulofthestudents
wereabletounderstandit. B
Explanation
Ifonlyasmallportionofagroupofpeopleunderstandsomething,thenthatsomethingisdifficultorabovetheheadsofmost.Whileyoumaynotknowthedefinitionof“esoteric,”youlikelyknowthedefinitionoftheotheranswerchoices.“contrite”meanstoshoworfeelremorse(feelingguilty).Ifthearticlewere“functional,”thenmorepeoplewouldunderstandit.Thereisnotenoughinformationinthearticletodetermineifthetruth(“genuine”)ofthearticlewouldhelpmakeitmoreunderstandable.Thus,ouronlypossibleansweris“esoteric”(onlyunderstoodbyafewpeople).
24. ThefirstAfricanAmericanactortoattaininternationalrenownwasIraAldridge,
oneoftheleadingShakespeareanperformersofthe1800s. D
Explanation
IraAldridgeisaleadingperformer,whichindicatesthatsheisimportant(apositiveconnotation).WewantananswerchoicethatmeansIraattainssomethinggoodregardingtheinternationalcommunity.Thus,“renown”(fame)makesthemostsense,since“rejection”isnegative.International“permanence”doesnotmakesense(whatisbecomingpermanent?Herfameorinfamy?),andwewouldneedtoknowwhatIrais“provoking”internationally(goodorbadthings?).
25. Ancientcavepaintingsofthesun,themoon,andwildanimalstestifytothe
inherenthumandesireandabilitytoportraytheenvironment. D
Explanation
Thesentencestatesthathumanswantandareabletodraworportraytheirenvironment,asevidencedorshownbythepaintings.Youmightthinkthat“cater”makesthemostsense,sinceitreferstotryingtosatisfyaparticularneedordemand.However,theblankisthesubject’sverb—thepaintings’verb.Thehumanscreatethepaintingstosatisfytheirdesire,butthatisnottheactiontakingplaceinthesentence.Instead,theactionistheexistenceofthepaintingsshowor“testify”tothisinherentdesire.
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |7
26. Eachafternoontheshepherdwoulddrivehisflockalongthenarrowroad,effectivelyobstructingthewayforanhour. A
Explanation
Thesentencestipulatesthattheroadis“narrow,”whichisenoughinformationforustodeterminethataflockofsheepwouldblock“theway”foranhour.Thus,“obstructing”(blocking)makesthemostsense.Wewouldneedmoreinformationtodetermineifthesheep/shepherdwere“plundering”(stealing)itemsfromtheroad.Iftheflockwere“renouncing”(declaringabandonmentofsomething)theroadforonlyanhour,it’snotmuchofarenouncement.Wewouldneedmuchmoreinformationfor“transplanting”(moveortransfersomethingtoanotherplace)tomakeanysortofsense.
27. Thecitycouncillookedattheproposalforanewlibrarywithanindifferencethat
borderedonscornfulness. C
Explanation
Theimportantwordinthissentenceis“indifference”(lackofconcern,interest,orcare).Becausethecitycouncildoesnotcareaboutorhaveanyinterestintheproposal,thedirectionthatindifference“borders”onmustmakesense.Nothinginthesentencesuggestsanythingthatwouldmakethecouncilinterestedintheproposal.Thus,“scornfulness”(deepcontemptforsomething)makesthemostsense.
28. TheartofFridaKahlowasstronglyinfluencedbyherlifelonginterestinand
fascinationwithMexicanfolkloreandculture. B
Explanation
Theconjunction“and”between“lifelonginterest”andthesecondblankindicatesthatthesecondblankmimicsthepositivecontextof“lifelonginterest.”IfKahlo’srelationshipwithMexicanfolkloreandcultureispositive,thentheaffectithasonKahlo’sartisalsopositive.“irritation,”“repelled,”andallofanswerchoiceDarenegative.Thus,“influenced”and“fascination”makesthemostsense.
29. Likemostotherchronicmedicalconditions,arthritisisnotcurable;physiciansdo
theirbest,however,toameliorateitssymptoms. A
Explanation
“notcurable”showsthatarthritisdoesnotend,andthefirstblankisawordthatmeansthisfact.“temporary”isthecompleteoppositeofwhatwewant,and“complicated”hasnobearingonwhetherornotsomethingwilleverend.Ifamedicalconditionis“imaginary,”itneverexistedinthefirstplace.Thus,“chronic”istheonlyanswerthatmakessenseforthefirstblank.IfyouwanttomakesureAisthebestanswer,youcanlooktotherelationshipbetween“physician”(ahealer)andthesecondblank.Evenifsomethingisn’tcurable,aphysicianwillwanttohelpasickpersonasmuchaspossible.Aphysicianwouldnotwantto“mimic”(imitate)or“extend”(causetolastlonger)arthritis’ssymptoms.Aphysicianwouldwantto“minimize”(reducetothesmallestamountordegree)thesymptoms,butwealreadyestablishedthat“imaginary”doesn’twork.
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |8
30. AlthoughmuchoftheworstpollutionhasbeeneliminatedintheUnitedStates,tracesofmanytoxicchemicalsstillpersist. B
Explanation
“Although”indicatesthatthesecondblankwillbetheoppositeinsomewayofthefirstblank.Plus,thecombinationof“traces”(smallamounts)and“still”showsthatthepollutioniscontinuingsomethinginsomeway.Thus,ifthepollutioniscontinuing,thefirstblankisawordforstoppingorending.Only“eliminated”fitsthisdescription,and“persists”means“tostubbornlycontinueagainstallodds.”Also,AnswerchoiceBistheonlyoptionwithopposingmeanings.
31. QueenVictoriahadmixedopinionsontheemancipationofwomen;whileshe
fosterededucationforwomen,sheopposedtheirrighttovote. C
Explanation
“mixedopinions”indicatesthatthetwoblankswillbeopposinginmeaning—whatevershewantsforwomen’seducation,itwillbetheoppositeforwomen’svotingrights.AnswerchoicesA,B,andDarecomplimentaryinmeaningsomewayandcontext,butanswerchoiceChasopposingwords—“fostered”(promotethedevelopmentof)and“opposed”(disapproved).
32. Thecasualobserverofalichengrowingonarockwouldneversuspectthatitwasa
compositeoflife-formsinteractingwithoneanother. A
Explanation
Althoughthisisatwo-blanksentence,wereallyonlyneedthewordforthefirstblank.Anobserverthatwouldneversuspectsomethingisonewhoisnotlookingcarefullyatthings.An“inquiring”(showinganinterestinlearningnewthings)wouldwanttothoroughlyobservethelichenontherock,whilean“expert”or“knowledgeable”observerwouldalreadyknowthesecondpartofthesentenceorwhattolookfor.Thus,ouronlyoptionisa“casual”(relaxedorunconcerned)observerinanswerchoiceA.Youcancheckyouranswerwith“composite”(madeupofvariouspartsandelements),butitalsoistheonlywordthatworksfor“interactingwithoneanother.”
33. Iftheauthorshadwrittenwithmorerestraintandavoidedsuchsentimental
language,theirarticleswouldhavehadmorepower. D
Explanation
Theconjunction“and”betweenthefirstblankand“avoided”indicatesthatthefirstblankmimicstherelativemeaningof“avoided.”Plus,“wouldhavehadmorepower”indicatesthatthesecondblankisanegativeadjectivefor“language.”BothanswerchoicesAandBhavepositivewordsanddonotmatchwhatweneed.While“excess”matchesthenegativecontextthatweneed,itdoesnotmimicthemeaningof“avoided.”Thus,“restraint”(self-control)and“sentimental”(sadinanexaggeratedway)makethemostsense—iftheauthorshadrestrainedtheirlanguage,theywouldhaveavoidedlosingpower.
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |9
34. DespitetheapprehensionIfeltatthethoughtofmeetingLuisa,ourbusinesswastransactedinanatmospherethatwasclearlycongenial. A
Explanation
“Despite”indicatesthatthefirstblankisopposinginmeaningandcontexttothesecondblank—ifthefirstblankisnegative,thenthesecondblankmustbepositive.OnlyanswerchoiceAhaswordsthatopposeinmeaningandcontext.AnswerchoicesBandChavewordsthatarebothpositive,whileanswerchoiceDhaswordsthatarenegative.Thus,“apprehension”(fearthatsomethingbadwillhappen)and“congenial”(pleasantoragreeable)makethemostsense.
35. Becausethecaretakerhadledafrugallifestyleformostofhislife,hismilliondollar
bequesttothesettlementhouseamazedthetrustees. A
Explanation
“Because”and“amazed”indicatethatthefirstblankwillopposeinmeaningandcontexttothesecondblankinsomeway.Ifthecaretakerleda“lavish”(verygenerousorextravagant)lifestyle,thenamilliondollar“generosity”wouldnotamazethetrustees—nottomentionthefactthiswouldbeanimproperuseofgenerosityasanactualobjectandnotaquality.Ifthecaretakerleda“generous”lifestyle,anysortof“legacy”(amountofmoneyorpropertylefttosomeone)wouldnotamazethetrustees.Wewouldneedmoreinformationforwhata“unique”lifestyleisandwhya“milliondollarentreaty”(“entreaty”=humblerequest)wouldamazethetrusteesforanswerchoiceDtowork.Thus,“frugal”(sparingoreconomicalwithfoodormoney)and“bequest”(legacyorendowment)makesthemostsense.
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |10
QuantitativeReasoning1. 35 A
Tools: functionnotationSteps: (1) 𝑛∗isjustlike𝑓(𝑥),inthatyouinputaspecificvaluefornforthefunction
(equation)𝑛∗ = 4𝑛 + 3(theinputismultipliedby4andthenaddedto3)(2) Inthiscase,8isourspecificvalueà𝑛∗ = 4𝑛 + 3 → 4 8 + 3(3) 4 8 + 3 → 32 + 3 = 35
QuickTips: • Functionnotationcancomeinmanyformsandwithmultiplevariables• Example:𝑛∎𝑜∎𝑝 = 𝑛 + 𝑜 + 𝑝 → 4∎5∎6 = 4 + 5 + 6
2. 𝑥 − 3 B
Tools: balancingequationsSteps: (1) Inordertofindwhichexpressionisequaltoy,wemustgetybyitselfinthe
givenequation(2) 𝑥 − 𝑦 = 3 → −𝑦 = 3 − 𝑥 → −𝑦 = −𝑥 + 3(3) Since–yisnotthesamethingasy,weneedtomake–ypositivebymultiplying
bothsidesby–1(4) −1 −𝑦 = −1 −𝑥 + 3 → 𝑦 = 𝑥 − 3
QuickTips: • Paycloseattentiontoyoursignsasyourbalancetheequation• Remember,youmustperformthesameoperationtobothsidesofanequation
tokeepitbalanced3. 𝑥 − 1,999 A
Tools: algebrawordproblem,integersSteps: (1) Wearegiventhesumofallintegersfrom1to1000asx,whichcanbewritten
as1 + 2 + 3…+ 998 + 999 + 1000 = 𝑥(2) Youcanalsowriteoutthesumofallintegersfrom1to998inasimilar
manner:1 + 2 + 3…+ 996 + 997 + 998 =?(3) Noticethedifferencebetweenthetwoequations:thefirstequationincludesall
integersfrom1to998,andthenadds999and1000toachievex(4) Thus,thesecondequationissimplymissingthevalues999and1000(missing
canbeatranslationofsubtracting)(5) Ifthesumofthefirstequationisx,thenwecansubtract999and1000fromx
toachievethesumofallintegersfrom1to998(6) 1 + 2 + 3…+ 998 + 999 + 1000 = 𝑥 → 1 + 2 + 3…+ 998 = 𝑥 − 1000 − 999(7) 𝑥 − 1000 − 999 → 𝑥 − 1999
QuickTips: • Writeoutallinformationtothesideofthewordproblemsothatitisseparatefromthetext
4. 12% D
Tools: percentofchange,trianglesSteps: (1) Whilewearenotgivenanyvalues,wecanstillfindtheanswer
(2) Chooseavalueforthetriangle’sheightandbasethatiseasytomanipulatewithpercentages(suchas10or100forboth)
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |11
(3) Using10forbothmeasurements,theareaofthetriangleis50(=>×=>@
= 50)(4) Increasetheheightby10%:10 + 10×0.1 = 10 + 1 = 11(5) Decreasethebaseby20%:10 − 10×0.2 = 10 − 2 = 8(6) Findthenewtriangle’sarea: 11×8 ÷ 2 = 88 ÷ 2 = 44(7) Usethepercentofchangeformula:𝑃 = |EFGHGIJKLMNO|
EFGHGIJK
(8) 𝑃 = |P>LQQ|P>
= RP>→ =@
=>>→ 12%
QuickTips: • Percentageswillworkforwhatevervaluesyouchoosefortheoriginaltriangle• Itiseasiertoconvertfractionswithadenominatorof100topercentages(in
thiscasewemultipliedthedenominatorandnumeratorby2)5. 14 B
Tools: multiplyingpolynomials,balancingequationsSteps: (1) Startwiththeleftsideoftheequationbysquaring𝑥 + 7andfollowFOIL
(2) 𝑥 + 7 @ → 𝑥 + 7 𝑥 + 7 (3) First:(𝑥)(𝑥) = 𝑥@(4) Outside: 𝑥 7 = 7𝑥(5) Inside: 7 𝑥 = 7𝑥(6) Last: 7 7 = 49(7) 𝑥@ + 7𝑥 + 7𝑥 + 49 → 𝑥@ + 14𝑥 + 49(8) Now,lookattheplacementof14andmin𝑥@ + 14𝑥 + 49 = 𝑥@ + 𝑚𝑥 + 49(9) Ifyouremovesimilarelementsfrombothsides,14 = 𝑚remains
QuickTips: • IfyouareunfamiliarwithFOIL,youcanalsousethedistributiveproperty• 𝑥 + 7 𝑥 + 7 → 𝑥 𝑥 + 7 + 7 𝑥 + 7 → 𝑥@ + 7𝑥 + 7𝑥 + 49 → 𝑥@ + 14𝑥 + 49
6. 91.00 C
Tools: mean,multiplesSteps: (1) Findthesumof370and85,andthendividebythenumberoftests(5)
(2) 370 + 85 = 455(3) 455 ÷ 5 = 91
QuickTips: • Since370and85aremultiplesof5,theirsumwillalsobeamultipleof5• Theresultofdividingamultipleof5by5canonlybeaninteger,soanswer
choicesBandDcannotbetrue7. 42inches C
Tools: perimeter,wholenumbersSteps: (1) Sincethemeasurementsareinwholenumbers,wecanlooktothefactorsof
110tofindourmeasurements(2) 110 → 1, 2, 5, 10, 11, 22, 55, 110(3) Wecanquicklyeliminatetheperimetersof1and110and2and55(4) Ifweuse5and22,theperimeteris54inches,answerchoiceD(5) However,ifweuse10and11,theperimeteris42
QuickTips: • Sincethemeasurementsarewholenumbers,answerchoicesAandBcannotbetruesincethesumofall4sidesofarectanglewillbeanevennumber
• Thesumoftwoevennumbersisanevennumber
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |12
• Thesumoftwooddnumbersisanevennumber8. AnswerchoiceA’sgraph A
Tools: analyzingchartsandgraphs,temperatureSteps: (1) Sincethepotatostartsoutcool,answerchoicesBandCdonotworkbecause
theyplacethepotatoabove300°beforeanytimehaselapsed(2) Sincetheovenissetto350°,thepotatocannotgoabovethattemperatureasin
answerchoiceD(3) OnlyanswerchoiceAaccuratelyportraysthecookingofthepotatoovertime
QuickTips: • Paycloseattentiontotheinformationprovidedbythewordproblem• “coolpotato”and“hot(350°)oven”giveusourparametersfortheproblem
9. 6cm B
Tools: similartrianglesSteps: (1) Becausethetrianglesaresimilar,theysharethesamedegreevaluesand
proportionalsidelengths(2) IfyoulooktosidelengthsQRandTU,you’llnoticethatQRisincreasedbyV
@to
achieveV@𝑥;thus,ourproportionisV
@forthetriangles
(3) MultiplythesidelengthofQSbyV@tofindthelengthofTV
(4) 4× V@= =@
@= 6cm
QuickTips: • Similartriangleshavethesamedegreevaluesandproportionalsidelengths• Congruenttriangleshavethesamedegreevaluesandsidelengths
10. 1 B
Tools: exponents,distributivepropertySteps: (1) Thefastestwaytosolvethisquestionisbychangingallvaluesintotermsof3
(2) 9 → 3@;therefore,V(VWXVY)
VW(VXVW)
(3) Followingthedistributiveproperty,you’llnoticethatthesamethingishappeninginthenumeratorandthedenominatorV(V
WXVY)VW(VXVW)
→ VYXVZ
VYXVZ= 1
(4) Theresultofanumberdividedbyitselfisalways1(5) Youcanalsomultiplyeverythingout(reducewhereyoucantomakeiteasier)(6) V(V
WXVY)[(VX[)
→ =([X@\)V(=@)
→ = VRV =@
→ =(V)V(=)
→ 1QuickTips: • AnswerchoiceAcanbequicklyeliminatedbecausenopartoftheexpression
willresultin0• Inmanycases,youdonotneedtomultiplyeverythingouttoarriveatyour
answer11. 0.25miles A
Tools: analyzingchartsandgraphsSteps: (1) SincewearelookingforthepointduringJane’swalkwhereshewaitedforher
friend,weneedtofindaspotonthegraphwherethedistancefromJane’s
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |13
homeremainsthesamebutthetimestillincreases(2) Thevaluesonthex-axisandy-axisarethesame,butthex-axisisclearly
markedastimewhilethey-axisismarkedasdistance(3) Atthefirsthalf-hourmark,Jane’sdistanceis0.25milesfromherhome(4) Noticethatthisdistancestaysat0.25milesfrom0.50hourstoalittlebefore
the0.75hourmark—thisistheonlytimesomethinglikethishappens(5) Thus,theonlypossibleconclusionisJanewas0.25milesfromherhomewhen
shewaitedforherfriendQuickTips: • Sincethequestionislookingforapointwhereonevaluedoesnotincrease,
youcanquicklyobservethatthisonlyoccursatonepointforthewholegraph• Paycloseattentiontothedesignationsfortheaxes
12. range D
Tools: mean,median,mode,rangeSteps: (1) Muchoftheinformationinthisproblemissuperfluous(unnecessary)
(2) Thinkabouthowthemean,median,mode,andrangewillbeaffectedbyadding6pointstoeveryscore
(3) Themean,median,andmodewouldchangeinsomeway,butfocusontherange(thedifferencebetweenthelowestandhighestvalueinadataset)
(4) Ifthehighestscoreisa100,thenthelowestscoreisa36(rangeof64)(5) Ifyouincreasebothofthosescoresby6points,thehighestscorewouldbe
106andthelowestwouldbe42(6) Therangewillstillbe64withthepointincrease;thus,therangechangesthe
leastQuickTips: • Confirmwhatthequestionislookingforbeforewritingoutinformationtothe
sideoftheproblem(you’dsaveyourselfsometime)• KeepinmindthedefinitionsofconceptsintheQuantitativeReasoningsection
sincesomeofthequestionsaretestingthatknowledge13. Maud B
Tools: probabilitySteps: (1) Forprobability,itisimportanttounderstandtheoperationthatoccursfor
eventswithwordslike“or”(2) The“or”meansthattheprobabilityofrollingasumof6pointsisaddedtothe
probabilityofrollingasumof4pointsforMaud,givingherthegreaterprobabilityofreceivingapoint
(3) Jimonlyhasthefirstprobability,whileMaudhasboth(givinghertheedge)(4) Theprobabilityofrollingasumof6pointsis P
VRandtheprobabilityofrollinga
sumof4pointsis VVR; PVR+ V
VR= ]
VR
(5) Jim: PVR< ]
VR:Maud
QuickTips: • Youdonotneedtoknowtheactualprobabilitiestoanswerthisquestion• ThefactthatJimandMaudreceiveapointforthefirstprobabilitybutMaud
alsoreceivesapointforthesecondprobabilityisalltheinformationweneed
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |14
14. 14 DTools: mean,median,range,symmetry,analyzingchartsandgraphsSteps: (1) Themedian(ormiddle)ofthedatais7(thetallestbaronthegraph)
(2) Themode(orvaluethatappearsthemost)ofthedataisalso7(3) Ifthedataissymmetrical(onehalfisthesameastheotherhalf)aboutthe
valueof7,thenthefrequencyofthevaluesontheleftsideofthevalueof7willbemirroredforthevaluesontherightsideofthevalueof7(thebarswilllooklikeatriangle)
(4) Therange(differencebetweenthelowestandhighestvalue)ofthedatais8andthemaximumvalueis11,whichmeansthelowestvalueis3
(5) Wewantthenumberofdatapoints(totalnumberoffrequency)thatfallabovethevalueof7,whicharethedatapointsforthevaluesof8,9,10,and11
(6) Sincetheleftof7ismirroredontheright,thebarfor6isthesamefor8andthebarfor5isthesamefor9
(7) Countingeachpointoffrequency,8has7points,9has4points,10has2points,and11has1point
(8) 7 + 4 + 2 + 1 = 14QuickTips: • Thisquestionisthemostconvolutedquestiononthispracticetest,andmost
studentshavetroublewithit• YoucanwritealloveryourtestbookletontherealISEE(doso!)
15. 9 C
Tools: functions,compoundinequalitiesSteps: (1) Thecompoundinequalityisstatingthatthesmallestvalueforxis–2andthe
largestvalueforxis1(2) Inputthesetwovaluestofindy(moststartwith1sinceitisthelargest)(3) 𝑦 = 2𝑥@ + 1 → 2 1 @ + 1 → 2 + 1 → 𝑦 = 3(4) 𝑦 = 2𝑥@ + 1 → 2 −2 @ + 1 → 2 4 + 1 → 8 + 1 → 𝑦 = 9
QuickTips: • Youcaninputtheanswerchoicesforyandsolveforxtofindtheanswer• AnswerchoiceDisachievedbyinputting 8,whichisnotapossiblevalueofx,
since 8isapproximately±2.8• AnswerchoiceAisachievedbyinputting0
16. 𝑔 0.9 < 𝑓 0.9 < 𝑓 1.1 < 𝑔(1.1) B
Tools: radicals,exponentsSteps: (1) Whileyouarenotallowedacalculatoronthistest,youdon’tneedtoknowthe
exactresultsforeachoftheinputsof0.9and1.1intofunctions𝑓(𝑥)and𝑔(𝑥),whichtakethesquarerootoftheinputandsquaretheinputrespectively
(2) Ifyousquareapositivedecimalnumberthatislessthan1,suchas0.9,thentheresultwillbelessthanbefore(0.9@ = 0.81)
(3) Ifyoutakethesquarerootofapositivedecimalnumberthatislessthan1,suchas0.9,thentheresultwillbegreaterthanbefore( 0.9 ≈ 0.95)
(4) Theoppositeistrueforadecimalnumberthatisgreaterthan1,suchas1.1,where1.1@ = 1.21and 1.1 ≈ 1.05
(5) 0.9@ < 0.9 < 1.1 < 1.1@QuickTips: • Consider [email protected] 𝑥and𝑥@
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |15
17. thedifferenceinJohn’sandErin’sspeeds DTools: distance,rate,andtimeSteps: (1) NotethatJohnandErinrunataconstantrateandonthesamepath
(2) Johnis500metersaheadofErinwhenshestartstorun,andJohnwillmaintainhisconstantratethewholetimeErinisattemptingtocatchup
(3) IfJohnandErinarebothrunningat20metersperminute,thenErinwillforeverremain500metersbehind
(4) IfJohnisrunning20metersperminuteandErinisrunning25metersperminute,Erininwillbeabletocatchupin100minutes(𝑡 = c
F→ 𝑡 = P>>
P= 100)
(5) IfweknowthedifferenceinJohnandErin’sspeeds,thenwecandeterminehowlongitwilltakeErintocatchuptoJohn
QuickTips: • Inputeasyvaluesforeachvariableinawordproblemtotestoutinformationtoseewhatwouldbetrue
• Multiplesof5or10workwellforinput18. answerchoiceA’sfigure A
Tools: geometricpatternsSteps: (1) Notethatthecubehasacirclewithonetrianglepointingawayfromitandthe
othertrianglepointingtoit(2) Foldedover,answerchoiceBwouldhavethepatternr¡r(3) Foldedover,answerchoiceCwouldhavethepatterns¡s(4) Foldedover,answerchoiceDwouldhavebothtrianglespointedawayfrom
thecircle(5) OnlyanswerchoiceAwouldhavethepatternofonetrianglepointingaway
fromthecircleandtheothertrianglepointingtothecirclewhenfoldedoverQuickTips: • AnswerchoiceAistheonlypatternwithatrianglepointingtowardsthecircle,
sotheotheranswerchoicesdonotwork19. Thetwoquantitiesareequal C
Tools: orderofoperationsSteps: (1) AllweneedtodoisfindthevalueofthequantityunderColumnA(ColumnBis
alreadysimplified)(2) Followtheorderofoperations:5 + 2× 4 + 3 → 5 + 2×(7)(3) 5 + 2× 7 → 5 + 14 → 19(4) 19 = 19
QuickTips: • Manystudentsmissthisquestionbecausetheyadd5and2firstandthenmultiplythatproducttothesumof4and3—don’tforgettheproperorder!
20. yisthegreatervalue B
Tools: area,perimeter,algebraicequationsSteps: (1) SincetheareaofrectangleQis18cm2,wecanfindxbyusingtheformulafor
theareaofarectangle(𝐴 = 𝑙𝑤)(2) 2𝑥 𝑥 = 18 → 2𝑥@ = 18 → 𝑥@ = 9 → 𝑥 = 3(3) SincetheperimeterofrectangleRis30cm,wecanfindybyusingtheformula
fortheperimeterofarectangle(𝑃 = 2𝑙 + 2𝑤)
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |16
(4) 2 2𝑦 + 2 𝑦 = 30 → 4𝑦 + 2𝑦 = 30 → 6𝑦 = 30 → 𝑦 = 5(5) 3 < 5
QuickTips: • Assoonasyouseeinformationregarding“area”or“perimeter,”quicklyjotdowntheappropriateformulasforthoseconcepts
21. Thetwoquantitiesareequal C
Tools: multiplyingpolynomialsSteps: (1) ThereisnothingtobedonewithColumnB,sowecanfocusonColumnA
(2) Usethedistributivepropertytocorrectlymultiplythepolynomials(3) 𝑥 − 𝑦 𝑥@ + 𝑥𝑦 + 𝑦@ → 𝑥 𝑥@ + 𝑥𝑦 + 𝑦@ − 𝑦 𝑥@ + 𝑥𝑦 + 𝑦@ (4) 𝑥 𝑥@ + 𝑥𝑦 + 𝑦@ − 𝑦 𝑥@ + 𝑥𝑦 + 𝑦@ → 𝑥V + 𝑥@𝑦 + 𝑥𝑦@ − 𝑥@𝑦 − 𝑥𝑦@ − 𝑦V(5) 𝑥V + 𝑥@𝑦 + 𝑥𝑦@ − 𝑥@𝑦 − 𝑥𝑦@ − 𝑦V → 𝑥V + 𝑥@𝑦 + 𝑥𝑦@ − 𝑥@𝑦 − 𝑥𝑦@ − 𝑦V →
𝑥V − 𝑦V(6) 𝑥V − 𝑦V = 𝑥V − 𝑦V
QuickTips: • Youcouldalsoinput1,0,and–1asvaluesforbothxandytotestthem,butdoingsomightactuallytakeyoulongerthansimplymultiplyingColumnA
22. $3.00isthegreatervalue B
Tools: substitutioninlinearequationsSteps: (1) Createanequationforthesumofthevalueofdimesandquartersinthe
parkingmeter:0.10𝑑 + 0.25𝑞 = $4.50(2) Iftherearetwiceasmanydimesastherearequartersintheparkingmeter,
thenwecanshowdas2q(𝑑 = 2𝑞)(3) Now,substitute2qfordinthefirstequation:0.10𝑑 + 0.25𝑞 = 4.50 →
0.10 2𝑞 + 0.25𝑞 = 4.50(4) Solveforq:0.10 2𝑞 + 0.25𝑞 = 4.50 → 0.20𝑞 + 0.25𝑞 → 0.45𝑞 = 4.50(5) 0.45𝑞 = 4.50 → 𝑞 = 10quarters(6) Thetotalvalueofthequartersinthemeteris$2.50(or0.25×10)(7) $2.50 < $3.00
QuickTips: • Inthefirstequation,youcannotsimplyadddtoqandsetitequalto4.50—thenumberofitemsdoesnotequateto$4.50,butthevalueoftheitemstimesthenumberoftheitemsdoes(10quartersat$0.25eachplus20dimesat$0.10eachmakes$4.50)
23. Theslopeoflinekisthegreatervalue A
Tools: parallellines,slopeoflinearequationsSteps: (1) Ifalineisparalleltoanotherline,thentheirslopesareequal
(2) Theslopeoflinejis3(𝑦 = 𝑚𝑥 + 𝑏;wheremistheslopeand𝑚 = 3)(3) 3 > −3
QuickTips: • Noticethatthelinesareatanincline;thus,theirslopesmustbepositive• Anypositivevalueisgreaterthananegativevalue—evenifyouweren’tgiven
theequationforlinejyoucouldfindtheanswerwiththisknowledgealone
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |17
24. Therelationshipcannotbedeterminedfromtheinformationgiven DTools: perimeter,areaSteps: (1) Whilewearenotgivenanyvaluesforthelengthandwidthoftherectangle,we
cantestsomepossibilitiesbyusingtheformulasforperimeter(𝑃 = 2𝑙 + 2𝑤)andarea(𝐴 = 𝑙𝑤)
(2) Ifthelengthis10,thenthewidthwouldbe15:2 10 + 2𝑤 = 50 → 20 + 2𝑤 =50 → 2𝑤 = 30 → 𝑤 = 15
(3) Theareaofthesedimensionswouldbe150: 10 15 = 150(4) Inthiscase,ColumnAisgreater(5) Ifthelengthis5,thenthewidthwouldbe20:2 5 + 2𝑤 = 50 → 10 + 2𝑤 =
50 → 2𝑤 = 40 → 𝑤 = 20(6) Theareaofthesedimensionswouldbe100: 5 20 = 100(7) Inthiscase,ColumnBisgreater(8) Becauseouranswerschange,theonlypossiblesolutionisanswerchoiceD
QuickTips: • Wheninputtingvalues,ifyouranswerchangesfromonecasetothenext,thentherelationshipcannotbedetermined(moreconcreteinformationisneeded)
25. Areaoftheshadedregionisthegreatervalue A
Tools: area,operationsonalgebraicexpressionsSteps: (1) Findtheareaofthelargersquareasifthesmallcutoutisnotthere
(2) 𝑥 𝑥 = 𝑥@(3) Findtheareaofthecutout(4) 𝑦 𝑦 = 𝑦@(5) Subtracttheareaofthecutoutfromtheareaofthelargersquare(6) 𝑥@ − 𝑦@(7) If𝑥 > 0and𝑦 > 0,thenxandyarepositivevalues(8) Input2forxand1forytotestColumnAandB(9) 𝑥@ − 𝑦@ → 2 @ + 1 @ = 4 + 1 = 5vs.𝑥@ − 𝑥𝑦 − 𝑦@ → 2 @ − 2 1 − 1 @ →
4 − 2 − 1 = 1(thiswillbetrueforallinputs)QuickTips: • NotethatthequantityunderColumnBisgenerallythesameasColumnA
exceptthatanadditionaltermissubtractedfrom𝑥@• Sinceweknowbothxandyarepositivevalues,wecansafelyconcludethatan
additionalpositivevalueissubtractedfromthequantityunderColumnB,makingColumnAlargerinallinstances
26. 10isthegreatervalue B
Tools: integers,consecutivenumbersSteps: (1) Althoughwedon’tneedtodoanythingwithColumnB,wecanstilluseit’s
quantitytodeterminethevalueofthequantityinColumnA(2) Ifweassumethatgreatestofthe3consecutiveintegersis10,wecanfindthe
productofthe3integersandcomparethattheproductoftheactual3consecutiveintegers
(3) If10isthegreatestinteger,thenitwouldbe8×9×10 = 720(4) 720ismuchlargerthan210,whichmeansthatthegreatestintegerforColumn
Acannotbegreaterorequalto10(itmustbeasmallerinteger)(5) Incidentally,theconsecutiveintegersare5,6,and7(5×6×7 = 210)
QuickTips: • Itwouldbeverychallengingtotrytofindthesolutionalgebraically
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |18
• 𝑥 𝑥 + 1 𝑥 + 2 → 𝑥@ + 𝑥 𝑥 + 2 → 𝑥@ 𝑥 + 2 + 𝑥 𝑥 + 2 → 𝑥V + 2𝑥@ +𝑥@ + 2𝑥 → 𝑥V + 3𝑥@ + 2𝑥 = 210(Goodlucksolvingthisinatimelymanner!)
27. 25𝑛 − 1isthegreatervalue A
Tools: orderofoperationsSteps: (1) Althoughwearenotgivenanyvaluesforn,wecannotassumetheanswerisD
(2) Instead,testyourowninputsforn(1,0,and–1tostart)(3) If𝑛 = 1,thenAis25 1 − 1 = 24andBis25 1 − 1 = 0;24 > 0(4) If𝑛 = 0,thenAis25 0 − 1 = −1andBis25 0 − 1 = −25;−1 > −25(5) If𝑛 = −1,thenAis25 −1 − 1 = −26andBis25 −1 − 1 = −50;−26 >
−50(6) Inallcases,ColumnAisgreaterthanColumnBandwillremaintrueforall
otherinputsQuickTips: • Remember,ifyouaren’tgivenanyvaluesforvariables,inputsimpleto
calculatevalues(2,1,0,-1,and-2)28. Therelationshipcannotbedeterminedfromtheinformationgiven D
Tools: perimeterSteps: (1) Itmayseemlikewe’regivenadecentamountofinformation,butyou’llquickly
seewereallyneedtohavesomeparametersforxandytosolvethisone(2) If𝑥 = 1and𝑦 = 2,thenAis3andBis6(3) If𝑥 = 2and𝑦 = 1,thenAis6andBis3(4) Becauseouranswerschanged,theonlypossiblesolutionisD
QuickTips: • Wheninputtingvalues,ifyouranswerchangesfromonecasetothenext,thentherelationshipcannotbedetermined(moreconcreteinformationisneeded)
29. Thetwoquantitiesareequal C
Tools: probabilitySteps: (1) WhileitmayseemlikethefirstpartofeachstatementunderColumnAand
ColumnBmatter,therollofanumbercubehasnobearingontheprobabilityofacoinlandingheadsortailsup(theseeventsareindependent)
(2) Ifaneventisindependentofanotherevent,thenthereisnocorrelation(connection)totheevents’probabilities
(3) Thus,therealquantityunderColumnAistheprobabilityofthecoinlandingtailsupor=
@
(4) TherealquantityunderColumnBistheprobabilityofthecoinlandingheadsupor=
@
(5) =@= =
@
QuickTips: • Independenteventsdonotinfluenceeachother’sprobabilities(adieiscastandacoinflipped)
• Dependenteventsdoinfluenceeachother’sprobabilities(2marblesareremovedfromabag—theprobabilityofbothbeingred)
• Mutuallyexclusiveeventscannothappenatthesametime(coinlandingheadsandtailsup)
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |19
30. Themedianscoreisthegreatervalue ATools: median,range,analyzingchartsandgraphsSteps: (1) Youcouldspendagreatdealoftimefindingtheactualmedianforthegraph,
butitisfastertofindtherangeandcomparethattoapossiblemedian(2) Thehighestpossiblevalueofthisgraphis100andthelowestpossiblevalueis
51(3) Therangeisthedifferencebetweenthesetwovalues:100 − 51 = 49(4) Therangeofthisgraphis2lessthanthelowestpossibleexamscoreonthis
graph;thus,therangecannotbegreaterthanthemedian(middlevalue)ofthisgraph
QuickTips: • Ifaquestionseemslikeitwilltakealongtimetodeterminesomething,likethemedianofthisgraph,thenthereislikelyamoresimplewaytosolvingtheproblem
• Paycloseattentiontowhatthequestionislookingforandkeepinmindthedefinitionsforrange,median,mode,andmean
31. Theprobabilitythatthefirstcandyselectedisgreenisthegreatervalue B
Tools: probabilitySteps: (1) Sincethereare5candies,wecandeterminethatforasingleselectionthe
probabilityofselectinganorangecandyis@PandagreencandyisV
P
(2) ColumnBisprobabilityofselectingagreencandyonthefirstdraworVP
(3) ColumnAistheprobabilityofselectingagreencandy,puttingitback,andthenselectinganothergreencandy(dependentevents)
(4) ForColumnA,wemultiplytheprobabilityofthefirstdraw(VP)tothe
probabilityoftheseconddraw(VP)
(5) VP× VP= [
@P
(6) [@P< V
P
QuickTips: • Iftheeventsaredependent,thenyoumultiplytheprobabilityofeacheventtoeachother
• Ifthefirstdrawisnotreplaced,thenyoumustreducethenumeratoranddenominatoroftheprobabilityaccordingly(V
P→ @
Q)
32. $1.50isthegreatervalue B
Tools: algebrawordproblemsSteps: (1) FindtheincreasedpriceofapplesinMarch:𝐴 + 𝐴×% = 𝐵
(2) 1.50 + 1.50×0.10 = 1.50 + 0.15 = 1.65(3) FindthedecreasedpriceofapplesinAprilfromMarch’sprice(4) 1.65 − 1.65×0.10 = 1.65 − 0.165 = 1.485(5) $1.485 < $1.50
QuickTips: • Increasingavaluebyapercentageandthendecreasingtheresultingvaluebythesamepercentagewillresultinasmallervaluethantheoriginalvalue
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |20
ReadingComprehension-Passage11. Theprimarypurposeofthepassageistodescribeadiscoverythatexcitedthe
author’sinterest. B
Explanation
Thewholeofthepassagediscussestheauthor’sexperimentwithcaddislarvae,fromcollectingcreaturesinjarstoshowingoffhisexperiment’sresultstohisfriends.Whilethepassagestartsoffbymentioningtheauthor’sinterestinfreshwaterbiology,thepassagedoesnotdiscusswhyheisinterestedinit(answerchoiceA).Theauthordoesnotcomparethecaddislarvaetoanyothercreature(answerchoiceC)anddoesnotdiscussthecompletelifecycleofthecaddislarvae(answerchoiceD).
2. Inline4,“minute”mostnearlymeanstiny.
C
Explanation
Ifacreaturecanfitintoajar,evenalargeone,thenitissmallinsize.Thus,theauthoruses“minute”(mı̄̍ n(y)o͞otormy-noot)tomean“tiny”or“extremelysmall.”Evenifyoudonotknowthisdefinitionof“minute,”youdoknowthemeasurementoftimeforwhich“minute”stands.Youknowthataminuteisaveryshortorsmallamountoftime,soyoucanstillthinkofcreaturesinthatgeneralsense.Nothinginthesentenceoritssurroundingcontentsuggeststhatthecreaturesare“timely”(punctualoron-time),“timorous”(nervousorfearful),or“tireless”(nevertiring).
3. Theauthorcausedthelarvaetodecoratetheircocoonswithstripesbychanging
theirenvironmentatvariousstagesofcocoondevelopment. C
Explanation
Looktothesecondandthirdparagraphs.Theauthorfirststateshisfriendsaid,“…thatifyouremoveacaddislarvafromitscocoonandplaceitinajarofclearwater,itwouldspinitselfanewcocoonanddecoratetheoutsidewithwhatevermaterialsyousupplied.”Then,inthethirdparagraph,theauthorstates,“Idiscoveredthatbymovingthelarvaetoadifferentjarwithanewsubstance,theywouldproducenewmulticoloredcocoons.”Theauthormovesthelarvaefromjartojar(answerchoiceC).Hedoesnotkeepthelarvaeinasinglejarthroughoutthewholeprocess(answerchoicesA,B,andD).
4. Inline8,theauthordescribesthecaddislarvaeas“ratherdull”becausetheyhad
beenlivinginastagnantpool. C
Explanation
Looktoline7-11,“ThecaddisIhadcollectedlookedratherdull,forIhadcollectedthemfromastagnantpool…”Theauthordoesnotsaythatthelarvaewerestillinthecaterpillarstageorthatthelarvaewereremovedfromthepoolbeforefinishingtheircocoons(AandD).Whiletheauthordoesplacethelarvaeintoajar,hedoesnotsaythat’swhythelarvaeweredull(answerchoiceB).
5. Inthefinalsentence(lines33-36),theauthorsuggeststhatthecaddislarvaewere
annoyedbytheauthor’sexperiments. B
Explanation
Theauthorcontinuallymakesthelarvaecreatenewcocoonsdecoratedwithnewmaterialsagainandagainwithhisexperiments.Inlines33-36,theauthorstatesthe“poorcreatureswerereallyratherrelieved”whentheywereallowedtohatchandflyaway,insteadofconstantlybuildingcocoons.“relieved,”“forget,”and“problems”allindicatethatthelarvaewereinanegativesituationfromwhichtheywereeventuallyfreed.AnswerchoicesAandCreflectpositivereactionsthat
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |21
wouldnotresultfromnegativesituations,whileweneedmoreinformation(moreofareactionfromthecaddis)foranswerchoiceDtowork.
6. Aconversationwiththeauthor’sfriendledtheauthortoexperimentwithcaddis
larvae. B
Explanation
Looktolines12-18,“Ihadbeentoldbymyfriend…Decidingtoexperiment…”Theauthorhasaconversationwithhisfriendaboutthefriend’sobservationofcocoondevelopmentincaddislarvae,andtheauthorthendecidestoexperimentwithhisfriend’sobservation.Nobookorfamousnaturalistismentionedinthepassage(AandC).Whiletheauthordoesspendmostofhistimecollectingcreaturesfrompondsandstreams(answerchoiceD),itistheconversationwithhisfriendthatleadshimtoexperimentonthelarvae.WewouldneedproofthattheauthorexperimentsonhiscollectionbeforetheconversationforDtobetrue.
ReadingComprehension-Passage27. “NorthwestCoastIndiansarefamousforlarge,beautifultotempoles”best
expressesthemainideaofthispassage. D
Explanation
ThepassagediscussesthetotempolescreatedbytheNorthwestCoastIndians—thepoles’varyingstyles,howthepolesaremade,andthepoles’history,decline,andreturn.AnswerchoicesAandConlycoveronepartofthepassage,whileanswerchoiceBisnotmentionedinthepassage.
8. Theauthorimpliesthattotempolecarvingwasabandonedforalongperiod.
A
Explanation
Whilethepassagedoesmentionthe1800sandthe1950s,thereisnodirectconnectionbetweenthesedatesandtheabandonmentoftotempolecarving.However,looktolines23-26,“Inthe1950s,thefewremainingcarvers…reproduceoldanddecayingKwakiutlpoles.”Ifsomethingisoldanddecayingandnomentionofanynewerpolesismadeinthepassage,thenwehaveourevidenceforanswerchoiceA.Plus,theauthordoesnotmentionanythingaboutmakingalivingorrespectfortotempolecarvinganddoesnotmentionthepopulationofcedartreesinthepassage.
9. “Aprocessisdescribedinchronologicalorder”bestdescribestheorganizationof
lines8-17. B
Explanation
Lines8-17discusstheprocessofplanning,designing,carving,and(insomecases)paintingtotempoles(inthatorder).Plus,“before”and“After”areindicatorsoftime.Theauthordoesnotcontrastdifferenttotempoledesignsandisnotexpressinganopinion(AandC),whileanswerchoiceDismoreaboutthepassageasawholethanlines8-17.
10. Accordingtothepassage,totempoleswerecarvedbyNorthwestCoastIndian
tribes. D
ExplanationLooktolines1-3,“Totempoles…areatrademarkoftheNorthwestCoastIndians.”AnswerchoiceAisincontradictionwiththepassage’sfinalparagraph,whileanswerchoicesBandCareincontradictionwiththefirstparagraph.
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |22
11. TheauthorofthepassageappearstocaremostdeeplyaboutthefactthattheartisticheritageofNorthwestCoastIndianswassaved. D
Explanation
Sincethepassageisabouttheuniquenessoftotempoles(“Eachpoleisdifferent,andeachpoletellsitsownstory”),theauthorisdemonstratinghisinterestintheartoftotempolecarving.Plus,theauthordevotesafullparagraphtothenearextinctionandrevivaloftotempolecarving.AnswerchoicesAandCarenotgivennearlyasmuchemphasisasanswerchoiceD.AnswerchoiceBisnotevenmentionedinthepassage.
12. Accordingtothepassage,amuseumhelpedpreservetheartoftotempolecarving
bycommissioningcarverstoduplicateexistingtotempoles. B
Explanation
Looktolines23-26,“…fewremainingcarverswerehiredbyUniversityofBritishColumbiaMuseumofAnthropologytoreproduceoldanddecayingKwakiutlpoles.”“commissioning”isthesamethingas“hired”and“reproduce”isthesamethingas“duplicate.”“reproduce”isnotthesamethingas“preserve”(answerchoiceA),andanswerchoicesCandDarenotmentionedinthepassage.
ReadingComprehension-Passage313. Theprimarypurposeofthispassageistosuggestthatreportsexpressingconcern
overthestateofeducationalpreparednessintheUnitedStatesmaybeunnecessarilyalarming.
A
Explanation
Thepassageopenswithastatementabouthow“newsmediaseemtobefilledwithalarmingeditorials”aboutthestateofeducationalpreparedness.Theauthorthendiscussestwostudiesthatcountertheclaimsofthenewsmedia.Finally,theauthorcloseswithstatingthatthenewsmediamisunderstandsjobsandtheirgrowthrate.AnswerchoiceBiscountertowhatisstatedinthepassage,whiletheauthordoesnotexpressanylamentationforhighschooldropouts(answerchoiceD).AnswerchoiceCdoesnotappearanywhereinthepassageeither.
14. Inline6,“pundits”mostnearlymeansexperts.
B
Explanation
The“pundits”inlines5-11aredeclaringthat“lasertechnology,robotics,andcomputer-controlledequipment”willbesoinfluentialinourlivesthatstudentsmusthave“advancedtrainingorevencollegedegrees.”Inotherwords,the“pundits”inthenewsmedia“know”somethingtobetrueandaremakingrecommendationsbasedonthatknowledge.Ifyouwantadviceaboutsomething,yougenerallyseekan“expert”onthematter,orapersonwhohasacomprehensiveorauthoritativeknowledgeofsomething.Thus,answerchoiceBbestmatches“pundit”(anexpertinaparticularsubjectorfieldwhoisfrequentlycalledontogiveopinionsaboutittothepublic).AnswerchoiceAwouldonlyworkifthepeopleinthenewsmediawerestatingafactinsteadofanopinion(“editorials”areopinionpieces).
15. TheauthorofthepassagedoesallofthefollowingEXCEPTcomparetrendsin
differentcountries. C
Explanation Theauthorprovidesdata(answerchoiceA)throughoutthesecondparagraphandtheendofthethirdparagraphanddescribestheresearchoftwostudiesinthe
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |23
secondparagraph(answerchoiceB).Theauthorcitesthestatementsofcommentatorsfromthenewsmediainthefirstparagraph(answerchoiceD).NowhereinthepassagedoestheauthorcomparetheUnitedStatestoanothercountry.
16. Theworkforcebeingpreparedbyourschoolstodaymatchesfairlycloselythe
workforcelikelytobeneededbyoursocietyinthenearfuture. B
Explanation
AnswerchoiceAandDcontradictthefindingsofthetwostudies,whichstatethattheupcomingworkforcewillmatchfutureworkforceneeds.Whilethestudiesdoincludedataabouthighschooldropouts,nowhereinthepassagedoestheauthordiscusstheneedforthepublicandeducatorstobandtogethertopreventthedropouts.OnlyanswerchoiceBistheonlyconclusionthatcanbedrawnfromthestudiesinthesecondparagraphofthepassage.
17. Theauthor’stonewhendiscussingthenewsmediaisbestdescribedascritical.
B
Explanation
Theauthorpresentsevidencethatcontradictsthecommentsmadebythenewsmediaandsuggeststhatthenewsmediaisconfusedaboutthedata.Thus,theauthorisplacingtheblameforthe“discrepantconclusions”uponthemediaandnottheresearchers.Theauthorwouldhavepresenteddatathatconfirmedthestatementsmadebythenewsmediaifhe“admired”themorhewas“worried”abouttheirstatements(answerchoicesAandD).Althoughhumorissubjective,nowhereinthepassagedoestheauthormakelightofthenewsmedia’scommentsorcrackjokesatthenewsmedia’sexpense(answerchoiceB).
18. Thepurposeofthelastparagraph(lines40-55)istoprovideanexplanationforthe
differingpointsofview. A
Explanation
Looktolines43-47,“Onepossibleexplanationforthediscrepantconclusions…”Theauthorisattemptingtoexplainthedifferingpointsofviewbystatingthatthenewsmediaispossiblyconfusedaboutthe“ratesofgrowthwithactualnumbersofjobs.”Nowhereinthethirdparagraphdoestheauthorexpressconcernforthefuturewelfareoftheeconomy(answerchoiceB)orproposethatadditionalresearchisneeded(answerchoiceC).Theauthoronlycriticizestheshortcomingsofthenewsmedia’sargumentandnottheresearchers’(answerchoiceD).
ReadingComprehension-Passage419. Thepassageisprimarilyconcernedwithprovidingbackgroundinformationfora
discussionofthemedievalhomeanditscomforts. C
Explanation
Theauthoropenswiththestatement,“Anydiscussionaboutdomesticlife…cannotrefertomostofthepopulation,whowerepoor.”Theauthorlaysthegroundworkfordiscussingthemedievalhomeanditscomfortsbyfirstdiscussingwhythepoor,aristocracy,andtheclergycannotbeincludedinthediscussion.Theauthorisleavingouttherichfromthediscussion,soanswerchoiceAdoesn’twork.Medievalartismentionednotasimportantforthe“bourgeoisandtherich”butasanantidoteforthepoor,soanswerchoiceBdoesn’twork.Thepoliticalviewsintownsareonlybrieflymentionedinthethirdparagraph(answerchoiceD).
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |24
20. Accordingtothepassage,medievalpageantsandfestivalsforthepoorwereappealingbecausetheyprovidedrelieffromahard,bleakexistence. D
Explanation
Looktolines19-23,“Theextravagantpageantsandreligiousfestivals…butalsoasantidotestothemiseriesofeverydaylife.”Thepageantsandfestivalsactedasanescapefromthe“wretchedconditionsunderwhichtheylived.”Thepassagedoesnotmentionthatthepageantsandfestivalswerefree,hadmuchreligiousimportance,orthattheycreatedanexcusetocelebrate.Instead,thefocusofthepassageisontheterriblelivingconditionsofthepoorandhowthesepageantsandfestivalsprovidedrelieffromthoseconditions.
21. Theauthorsuggeststhatwedonotunderstandthe“keenness”(line10)ofcertain
pleasuresenjoyedbymedievalpeoplebecauseweenjoythepleasuresmentionedfairlyfrequently.
D
Explanation
Inlines9-12,theauthorcitesaprominent(importantorfamous)historian,“We,atthepresentday…wereformerlyenjoyed.”Thehistorianisstatingthatpresentdaypeoplecannotappreciatethelevelofjoymedievalpeoplefeltfortheeverydaycomfortswenowenjoy.Plus,thehistorianstatesthat“health,wealth,andgoodfortune”werea“rarity”duringthattime.Whilethisquestionrequiresalittlemorereadingbetweenthelines,youcanalsosafelyeliminateanswerchoicesA,B,andCbecausetheyaren’tevenmentionedinthepassage.
22. Inthesecondparagraph(lines24-34),theauthorstatesthattheconceptof
“family”didnotexistbecausechildrenweresentawayassoonastheywereoldenoughtowork.
D
Explanation
Looktolines28-31,“Therewasroomonlyfortheinfants—theolderchildrenwereseparatedfromtheparentsandsenttoworkasapprenticesorservants.”Becausetheirhomesweretoosmalltohousethem,thechildrenweresentofftoworkassoonaspossible—thesechildrenwereneverabletogrowupwiththeirparentsandsiblingsasa“family.”Thus,theideaof“family”and“home”hadnomeaningforthepoor.Again,answerchoicesA,B,andCarenotmentionedinthepassage.
23. Theauthormostlikelyusessimilartermsfromdifferentlanguages(lines38-42)in
ordertoemphasizethewidespreadnatureofasimilarconcept. B
Explanation
Looktolines36-38,“Thefreetown…wasuniquelyEuropean.”Tofurtherprovethisstatement,theauthorpresentsthenamesfortheinhabitantsofthefreetownsfromvariouspartsofEurope(France,Germany,Italy,andEngland)toshowhowwidespreadtheconceptwas.Thesetermsareallrelatedtoasingleideaanddonotrepresentarangeorbreadthofideas(answerchoiceA).AnswerchoiceCdoesn’tworkbecausetheauthoristryingtoshowhowsimilarinstructureandmeaningthedifferenttermsaretooneanother.Theoriginofmedievallanguagesisn’tevendiscussedinthepassage(answerchoiceD).
24. Thepassagesuggeststhatloyaltytoakingratherthanalordhastheadvantageof
morepotentialforself-government. C
Explanation
Looktolines44-48,“Itdescribed…electedcouncils…allegiancedirectlytothekinginsteadofalord.”Sincethe“bourgeois”inmostcasesalliedthemselvesdirectlytothekingandnotalord,theywereabletogovernthemselveswithelectedcouncils.AnswerchoicesA,B,andDaren’tevenmentionedinthepassage.
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |25
ReadingComprehension-Passage525. TheprimarypurposeofthepassageistoshowhowWrightmethisbusiness
partner. B
Explanation
Honestly,thisquestionisansweredbytheitalicizedtextabovethepassage,“…describesanincidentfromhisyouththatwastoleadtoabusinesspartnershipinlaterlife.”Plus,thepassagetalksaboutWrightmeetingLampandtheirmanyactivitiestogether.AnswerchoiceAdoesn’tworkbecauseonlyLamp’scourageisshown,andwedon’tknowifthebulliesbackeddownornot(answerchoiceD).Plus,answerchoiceCisn’tevendiscussedinthepassage.
26. Themoodofthefirstparagraph(lines1-10)canbestbedescribedasoneof
youthfulenthusiasm. C
Explanation
Thefirstparagraphisfilledwithpositivewordsandphrases—quick,“couldworkalmostashardasaman,”“wasn’tafraidofanything,”buoyantly,exclaimed.Theauthorisillustratinghowmuchheaccomplishedandgrewonhisuncle’sfarm.Heisnotdemonstrating“overbearingpride”becausehecountershis“wasn’tafraidofanything”statementwith“—well,maybealittleafraidofstormsandofpeople”(answerchoiceA).Heisnotshowinghowhis“adolescentshyness”kepthimfromperformingtasksathisuncle’sfarm(answerchoiceB),andhislongingforSeptemberisonlybrieflymentionedatthebeginningoftheparagraph(answerchoiceD).
27. ItcanbeinferredthatWrightandLamprequiredCharlieDoyontogivethem
moneybeforejoiningtheirbusinessbecausetheythoughtthatthebusinesswouldbenefitfromalargermodelpress.
D
Explanation
WrightandLampcreatedthingstogetherinlines26-28,includingthejointeffortofsettingtypeontheirsmallprintingpressinlines28-29.SincebothWrightandDoyonputineffortintotheirprojects,itcanbeinferredthatDoyonwouldneedtodothesame—hemustprovidealargerpress.ThefactthatWrightusedtheword“more”indescribingthelargerpressalsoindicatesWrightandLampthoughtthelargerpresswouldhelpmorethantheirsmallerpress.AnswerchoiceCisaveryenticingchoice,butwedonothaveanyevidencefromthepassagethatsuggestsWrightandLampwerecommittedtotheirbusiness.WealsodonothaveanyevidenceinthepassageforanswerchoicesAandB.
28. Thephrase“myforayintotheunknown”(line15)referstoWright’sentranceinto
anewschool. A
Explanation
Looktolines11-12,thesentencebefore“myforayintotheunknown,”“OnthedayIapproachedtheforbiddingSecondWardSchool,Iwaslesssureofmyself.”Wrightisunsureofhimselfasheentersthisnewschoolbecausehehadn’tmadeanyfriendsduringthesummeronhisuncle’sfarm.HisencounterwithRobieLamp(answerchoiceB)occursinaseparateparagraph,andWright’sexperiencesonhisuncle’sfarmswereknowninthefirstparagraph(answerchoiceC).AnswerchoiceDisnotevenmentionedinthepassage.
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |26
29. Thesentence“IsoadmiredRobie’scourageandresourcefulnessthatwebecamefriendsoftheheart”(lines24-26)isincludedinordertoexplainwhyWrightandLamp’sfriendshipwasalastingone.
C
Explanation
Thephrase“friendsoftheheart”indicatesthatWrightsawakindredspiritinLampandWright’sgreatadmirationforLampcreatedalinkbetweenthemasimportantasthelinkbetweentheheartandthebody.WedonotknowifWrightwantedtotormentLamp(answerchoiceA)orifLampwasolderthanWright(answerchoiceD).Plus,answerchoiceBdoesn’tworkbecauseLampdemonstratesuttercouragewhileWrightis“lesssureofhimself”—whywouldLampbeluckytowinWright’sfriendship?
30. Inline31,“inveigle”mostnearlymeansacquire.
A
Explanation
Theword“inveigle”meanstopersuadesomethingtodosomething,usuallythroughflatteryordeception.Whilewedon’tknowwhatDoyondidtoobtaintwohundreddollarsfromhisfather,wedoknowthathedidobtainitandtheboyswereabletobuythelargerpress.Thus,“acquire”bestmatcheswhathappensinthepassage.“dismiss”and“return”havetheoppositeeffectofobtainingthetwohundreddollars,andDoyonwouldnot“purchase”twohundreddollarsfromhisfather.
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |27
MathematicsAchievement1. 40cm2 A
Tools: area,evaluatingshapesSteps: (1) Sinceeachshadedgridsquare’sareais5cm2,wesimplyneedtocounthow
manyshadedgridsquaresthereareandmultiplythatamountby5(2) 8shadedgridsquares×5cm2=40cm2
QuickTips: • YouareallowedtowriteonyouractualISEEtestbooklet• Drawlinesthroughtheshadedregiontohelpaccuratelycountthenumberof
shadedgridsquares2. P
=[× P=[ DTools: probabilitySteps: (1) Determinetheprobabilityofchoosingaredballfromthejarforthefirst
drawing(IpqrNFstusvGwGxNspwysqNvtsFwzNNxNIwwswJKIpqrNFstusvvGrKNspwysqNv
)
(2) 5redballsoutofatotalof19balls= P=[
(3) Sincetheballisreturned,theprobabilityforchoosingaredballforthesecondeventisalso P
=[
(4) Todeterminetheprobabilityofbotheventsresultinginaredball,wemustmultiplythetwoprobabilities: P
=[× P=[
QuickTips: • Beforestartingyourcalculations,seehowtheanswerchoicesareformatted—sometimestheanswersarepresentedasastepintheprocessandnotthefinalresult
3. 3.241×10\ C
Tools: scientificnotationSteps: (1) Convertthevaluesintostandardnotation
(2) 3.2×10\ = 32,000,000and4.1×10P = 410,000(3) Findthesumofthesevalues:32,000,000 + 410,000 = 32,410,000(4) Convertthissumintoscientificnotation(5) 32,410,000 = 3.241×10\
QuickTips: • Inconvertingvaluesinstandardnotationtoscientificnotation,bringthedecimaltotherightofthelargestplacevalue
• Inaddinganumberwithmoreplacevaluestoanumberwithfewerplacevalues,suchas10\and10P,thenotationwillmostlikelynotchange(10\willremain10\)
4. 0.6666667 A
Tools: fractions,decimalsSteps: (1) Compareeachanswerchoiceto@
V
(2) D)@.QV.R= @
V;2.4and3.6aremultiplesof1.2—ifyoudividebothvaluesby1.2,
youget@V
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |28
(3) C) ==.P= @
V;ifyoumultiply1and1.5by2,youget@
V
(4) B)0. 6 = @V;ifyouconvert@
Vtoafraction,youget0.666666repeating
(5) A)0.6666667 > @V;answerchoiceAis@
Vroundeduptothetenmillionthsplace
value,whichisnotthesamethingas@V
QuickTips: • Comparefractionsbymultiplyingthedenominatorofonetothenumeratoroftheother
5. 0 D
Tools: zeroproductpropertySteps: (1) Noticethattheequationisavaluetimestisequaltot,or10𝑡 = 𝑡
(2) Ifyousubtracttfrombothsides,yournewequationis9𝑡 = 0(3) Thezeroproductpropertystatesthatiftheproductoftwovaluesiszero,one
ofthevaluesiszero—inthiscase,tmustbezeroQuickTips: • Whateveractionyoutaketobalanceanequationmustmakesense
• Ifyoudividebothsidesbyt,youget10 = 1(whichisnottrue)6. Therearenovaluesforxthatwouldmaketheequationtrue. D
Tools: divisionproperties,commutativepropertySteps: (1) Whenaddingvalues,thecommutativepropertystatesthatyoucanchangethe
orderwithoutchangingtheresult(2) Ifyouswitchtheorderofthevaluesinthedenominator,you’llnoticethatitis
thesameastheexpressioninthenumerator:{XVVX{
→ {XV{XV
(3) Wheneveranumberisdividedbyitself,thequotientis1(exceptfor0);thus,
theresultfor{XV{XV
= 1andnot0(4) Novaluesforxwillmaketheoriginalequationtrue
QuickTips: • Keepallmathematicalpropertiesinmindwhendealingwiththeseproblems• Ifyouinputvalues,you’llnoticethatDistheonlypossibleansweraswell
7. 13 B
Tools: orderofoperationsSteps: (1) Youmustfirstaddthevaluestogetherundertheradicalin 25 + 144before
takingthesquareroot(2) 25 + 144 = 169 → 169 = 13(3) Youcannottakethesquarerootofeachvaluefirstandthenaddtheresulting
values: 25 + 144 ≠ 25 + 144 → 5 + 12 → 17QuickTips: • Treatthevaluesundertheradicalasiftheyaresurroundedbyparentheses:
(25 + 144)—youmustcompleteoperationsintheparenthesesbeforetakingthesquareroot
• However,inmultiplicationofvaluesunderaradical,youcantakethesquarerootfirst: (25)(144) = 3600 = 60 → 25 144 = 5 12 = 60
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |29
8. 185 CTools: median,analyzingchartsandgraphsSteps: (1) Arrangethedogs’scoresinorderfromleasttogreatest
(2) 155,160,175,175,180,190,195,195,195,200(3) Themedianisthemiddlevalueofarangeofvalues,butwhentwovaluesshare
themiddle(180and190)youmustfindtheaverageofthosevalues(4) =]>X=[>
@= V\>
@= 185
QuickTips: • Ifarangeofvalueshasanoddnumberofvalues,aspecificvaluefromthatrangewillbethemedian
• Ifarangeofvalueshasanevennumberofvalues,thentwovalueswillsharethemiddleandtheaverageofthesetwovaluesistheactualmedian
9. 2 A
Tools: systemoflinearequations(orproportion)Steps: (1) Createanequationthatrepresentstherelationbetweenthenumberof
defectivepartseachmachinemakes:𝐴 = 2𝐵(2) Createanotherequationtherepresentsthetotalnumberofdefectiveparts
madeyesterday:𝐴 + 𝐵 = 6(3) SincewearelookingforthenumberofdefectivepartsmadebyMachineB,
substituteAwith2BsothatthesecondequationonlyhastheBvariable(4) 𝐴 + 𝐵 = 6 → 2𝐵 + 𝐵 = 6 → 3𝐵 = 6 → 𝐵 = 2
QuickTips: • Youcouldalsosetupaproportionforthefirstequation:2to1or2:1(whereMachineAmakes2defectsforevery1defectmadebyMachineB)
• Fromthisproportion,youcanevaluatehowmanydefectivepartscreatedbyeachmachinewouldaddupto6andstillkeeptheproportiontrue
• 2: 1 = 3parts;thus, 2 2 : 1 2 = 3 2 → 4: 2 = 6parts10. 94 B
Tools: meanSteps: (1) Wedonotknowtheexactfinalexamscore,butwecansetupameanequation
withthefinalexamscoreas2𝑥(thefinalexamismultipliedby2becauseitiscountedtwiceinhermean)setequaltothedesiredmeanof93
(2) [VX][X[PX@{P
= 93 → @{X@\\P
= 93 → 2𝑥 + 277 = 93 5 → 2𝑥 + 277 = 465(3) 2𝑥 + 277 = 465 → 2𝑥 = 188 → 𝑥 = 94
QuickTips: • AlthoughLisaisonlytaking4tests,wedividethesumofherscoresby5becausethefinalexamisbeingcountedtwicetowardshermean
11. 1 A
Tools: dataanalysis,modeSteps: (1) Modeisthevaluethatappearsthemostfrequentlyinarangeofvalues,butwe
mustmakesurewearechoosingthemodefromthecorrectrangeofvalues(theoutputs)
(2) Whiletheleftcolumnofthedatatabledoeshavevalues,thosevaluessimplyrepresentthenumberoftimestherightcolumn’svaluesoccur—theleftcolumnisourinputswhiletherightcolumnisouroutputs
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |30
(3) Ifyouwriteoutallofthevaluesfromtherightcolumnaccordingtotheirfrequencyfromtheleftcolumn,thenyouhavethedataset{0,0,0,0,0,1,1,1,1,1,1,2,2,2,2,2,3,3,4,4}
(4) Thevalue1(1pet)occursthemostinthissetofdataandisourmodeQuickTips: • AnswerchoicesCandDcanbequicklyeliminatedbecausenostudenthas
morethan4pets• Ifyouweretoconvertthisdatatableintoagraph,thex-axiswouldbethe
NumberofPets(ourinputs)whilethey-axiswouldbetheNumberofStudentsOwningThatNumberofPets(ouroutputs)
12. 24𝑛@𝑚 D
Tools: primenumbers,multiplesSteps: (1) Weneedavaluethateachofthealgebraicexpressions8𝑛, 6𝑛𝑚, and4𝑛@can
divideintowithoutanyremainders(2) While6𝑛𝑚candivideintoanswerchoiceA,theothertwoexpressionscannot(3) While6𝑛𝑚candivideintoanswerchoiceB,theothertwoexpressionscannot(4) While6𝑛𝑚and8𝑛candivideintoanswerchoiceC,4𝑛@cannot(5) AllthreeexpressionscandivideintoanswerchoiceD
QuickTips: • AnswerchoicesAandBcanbequicklyeliminatedbecause6isnotamultipleof4or8
• AnswerchoiceCcanbequicklyeliminatedbecause𝑛isnotamultipleof𝑛@—instead,𝑛isafactorof𝑛@
13. 3 D
Tools: balancingequationsSteps: (1) Lookattheplacementofthe3sontheleftsideandtheysontherightsideof
theequation—theysharethesameplacesineachterm(2) 3𝑥 − 3 = 𝑥𝑦 − 𝑦 → 3𝑥 − 3 = 𝑦𝑥 − 𝑦;thus,𝑦 = 3becausetheequationis
balanced(3) Youcanalsoinputsomepossiblevaluesforx,suchas0(4) 3𝑥 − 3 = 𝑥𝑦 − 𝑦 → 3 0 − 3 = 0 𝑦 − 𝑦 → −3 = −𝑦 → 3 = 𝑦
QuickTips: • Youcanalsoinputtheanswerchoicesinforytoseeiftheequationremainsbalanced,butbemindfulofsubtractionsignscoupledwithnegativeinputs
14. 5𝑥@𝑦Q − 𝑥Q𝑦@ C
Tools: operationsonalgebraicexpressionsSteps: (1) Addandsubtractliketermsintheexpression—“liketerms”referstoterms
withthesamevariablessettothesameexponents,suchas3𝑥Q𝑦@ − 4𝑥Q𝑦@(2) 2𝑥@𝑦Q + 3𝑥Q𝑦@ − 4𝑥Q𝑦@ − 3𝑥@𝑦Q → 2𝑥@𝑦Q + 3𝑥Q𝑦@ − 4𝑥Q𝑦@ + 3𝑥@𝑦Q(3) 2𝑥@𝑦Q + 3𝑥@𝑦Q + 3𝑥Q𝑦@ − 4𝑥Q𝑦@ → 5𝑥@𝑦Q − 𝑥Q𝑦@
QuickTips: • Besuretodistributethenegativesigntothetermsinsideoftheparentheses• 𝑥@𝑦Qand𝑥Q𝑦@arenotliketermsbecauseeachxandyinthetermsareraised
todifferentexponents
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |31
15. 𝑥 = −5and𝑥 = 5 CTools: factoringquadraticequations,definitionofzero,zeroproductpropertySteps: (1) Noticethattherationalequationissetequaltozero—since0dividedbyany
othernumber(except0)isequaltozero,theresultoftheexpressioninthenumeratormustbe0
(2) Setthenumeratorequaltozeroandsolveforx:𝑥@ − 25 = 0 → 𝑥@ = 25 →𝑥 = 5
(3) However,thesquareof5and–5bothresultin+25,so𝑥 = ±5(4) Ifthedenominatorwereequalto0,theequationwouldbeundefined—we
mustmakesurethat5and–5won’tmakethedenominatorequalto0(5) Seteachterminthedenominatorequaltozeroandfollowthezeroproduct
property(iftheproductoftwotermsisequaltozero,thenoneofthetermsiszero)
(6) 𝑥 + 2 = 0 → 𝑥 = −2(7) 𝑥 − 3 = 0 → 𝑥 = 3(8) Thus,𝑥 ≠ −2or3(our5and–5remaintrue)
QuickTips: • Itmightbefastertosimplyinputtheanswerchoicesintotheequationandseewhathappens
• Ifyouseeacomplicatedrationalequation,thequestionislikelytestingasimplepropertythatsolvesthequestionquickly
16. 𝑥@ + 𝑥 − 6 D
Tools: multiplyingpolynomials(FOIL/distributiveproperty)Steps: (1) FollowFOILtosolvetheexpression(𝑥 − 2)(𝑥 + 3)
(2) First: 𝑥 𝑥 = 𝑥@(3) Outside: 3 𝑥 = 3𝑥(4) Inside: −2 𝑥 = −2𝑥(5) Last: −2 3 = −6(6) Addalltermstogether:𝑥@ + 3𝑥 − 2𝑥 − 6 → 𝑥@ + 𝑥 − 6
QuickTips: • Youcanalsousethedistributivepropertyifyouaremorecomfortablewithit• 𝑥 − 2 𝑥 + 3 → 𝑥 𝑥 + 3 − 2 𝑥 + 3 → 𝑥@ + 3𝑥 − 2𝑥 − 6 → 𝑥@ + 𝑥 − 6
17. –2 B
Tools: graphsoflinearequations(slope)Steps: (1) Graphsoflinearequationswithadownwardslope,liketheonepresentedin
thequestion,representanegativeslope(2) SlopeisthesamethingasFGvN
FpIor yzJIHNGI�
yzJIHNGI{or �WL��
{WL{�
(3) Selecttwopointsonthegraph,suchasthey-intercept(0,5)and(2,1)(4) =LP
@L>= LQ
@= −2;thus,theslopeis–2forthisline
QuickTips: • Ifyoustartwiththey-intercept,youcanseethatthelineslopesdown2(–2)andtotheright1(+1)(aslopeofL@
== −2)
18. 5gridunits C
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |32
Tools: distanceformula(graphs),circleSteps: (1) Youaregiventwopoints—oneinthecenterofthecircleandoneontheedge
ofthecircle(2) Thedistancebetweenthesetwopointsisthesamethingastheradiusofthe
circle(thelengthfromthecentertotheedgeofthecircle)(3) Usethedistanceformulatosolve:𝑑 = 𝑥= − 𝑥@ @ + 𝑦= − 𝑦@ @(4) 𝑑 = 1 − (−2) @ + 8 − 4 @ → 1 + 2 @ + 4 @ → 3 @ + 4 @(5) 3 @ + 4 @ → 9 + 16 → 25 = 5gridunits
QuickTips: • Ifyouforgetthedistanceformula,youcandrawoutthegraphofthiscircleandapproximatethedistancebetweenthetwopoints
• Youcanevenusethepreviousquestion’sgraphtodrawyourcircle19. arandomsampleofallthestudentsintheschool B
Tools: dataanalysisSteps: (1) Considerthebias(one-sidedness)ofeachanswerchoiceandtheprobabilityof
hoursspentwatchingTVbythegroups(2) ForanswerchoiceA,Terri’sfriendswilllikelywatchthesameshowsasTerri
andforthesamenumberofhours,sothisgroupwillnotaccuratelyreflectthestudentbody
(3) ForanswerchoiceB,arandomselectionassurestheleastamountofbiasandanunknownprobabilityofhoursspentwatchingTV,sothisgroupwillbestreflectthestudentbody
(4) ForanswerchoiceC,ifthewholegrouphasshownuptowatchafootballgame,thentheyshareabiasandschedulethatonlyreflectstheirgroup,sothisgroupdoesnotaccuratelyreflectthestudentbody
(5) ForanswerchoiceD,ifthewholegroupisinthelibrarybeforeschool,thentheyshareabiasandschedulethatonlyreflectstheirgroup,sothisgroupdoesnotaccuratelyreflectthestudentbody
QuickTips: • Arandomsampleofthepopulation(freefrombiasandcategorization)providesthebestrepresentationofthatpopulation
• Specificgroupswillsharebiasesthatwarpthecollecteddatatowardstheirinterestsandwillnotreflectthevarietyanddiversityofapopulation
20. 45° A
Tools: anglesinaquadrilateralSteps: (1) Aquadrilateralisapolygonwith4straightsides—squaresandrectanglesare
quadrilaterals(2) Ifthesumoftheinterioranglesofasquareorrectangleequal360°,thenso
mustotherquadrilaterals(3) Findthesumoftheinterioranglesofthisquadrilateralandsetitequalto360°(4) 110° + 75° + 130°+? ° = 360° → 315°+? ° = 360° →? ° = 45°
QuickTips: • Thesumofanyquadrilateral’sinterioranglesisalways360°nomatterhowitlooks
21. 20 B
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |33
Tools: combinationsSteps: (1) WhileyoumightbetemptedtousetheFundamentalCountingPrinciplefor
thisproblem,weareonlydealingwithonesetofdata—thedebateteammembers
(2) Wemustusethecombinationformulatosolvethisproblem,sincetheorderoftheselectiondoesn’tmatter:nCr=
I!F! ILF !
(3) nisthenumberofitemsinaset(6debateteammembers)andristhenumber
ofselectionsbeingmadefromthatset(3)—the!symbolistheproductofthenandallpositiveintegersbelowit(indescendingorder)
(4) I!F! ILF !
→ R!V! RLV !
→ R×P×Q×V×@×=(V×@×=)(V×@×=)
→ R×P×Q×V×@×=(V×@×=)(V×@×=)
→ R×P×QV×@×=
→ =@>R= 20
QuickTips: • Combinationshasasecondformulathatyoucanuseiffactorialsseemtooconfusing:I IL= IL@ …
F FL= FL@ …wherethenumberofvaluesmultipliedinthe
numeratormatchersthenumberofvaluesinthedenominator• Ifyouhave3choicesorselectionsinacombinationsquestion,thenyouwill
have3values(ex.6×5×4)inthenumeratorand3values(ex.3×2×1)inthedenominator
22. (7,2) D
Tools: parallelogram,xy-coordinateplaneSteps: (1) Aparallelogramisapolygonwithparallelsides,suchasarhombus
(2) Thefastestwaytodeterminewhichofthefollowinganswerchoicesinthefourthvertex,orpoint,oftheparallelogramisbyplottingthemonthegraph
(3) Ifyoulookatpoints(–2,3)and(1,2),you’llnoticethat(1,2)is4totherightandtwodownfrom(–2,3);thus,thefourthvertexshouldmatchthispattern
(4) (7,2)is4totherightand2downfrompoint(3,4)QuickTips: • Afteryouplotthepoints,youcandrawfaintlinesbetweenthepointsto
visuallyevaluatewhichoftheanswerchoicesisthefourthvertex23. 𝑥 ≤ − =
@or𝑥 ≥ 4 D
Tools: absolutevalue,algebraicinequalitiesSteps: (1) Tosolveforabsolutevaluewithalgebraicinequalities,yousolvetheequation
twice—1)withtheinequalityasisbutwithoutthebarsand2)againwithoutthebarsbytherightsideoftheinequalitymultipliedby–1
(2) 4𝑥 − 7 ≥ 9 → 4𝑥 − 7 ≥ 9 → 4𝑥 ≥ 16 → 𝑥 ≥ 4(3) 4𝑥 − 7 ≥ 9 → 4𝑥 − 7 ≤ −9 → 4𝑥 ≤ −2 → 𝑥 ≤ − @
Q→ 𝑥 ≤ − =
@
(4) Youcanchecktheseanswersbyinputtingthembackintotheinequalitywiththeabsolutevaluebars
QuickTips: • Whenyoumultiplyordivideasideoftheinequalitybyanegativenumber,theinequalitysignmustswitchdirections
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |34
24. complexnumber CTools: numbertypesSteps: (1) Thisquestionrequiresthatyouknowthedefinitionsofintegers,rational
numbers,complexnumbers,andirrationalnumbers(2) Irrationalnumbersarevaluesthatcannotberepresentedasfractions(ex.𝜋)(3) Anintegerisavaluethatcanbeapositiveornegativenumberorzero,butit
cannotbeafractionordecimal(4) Arationalnumberisavaluethatcanberepresentedasafraction(5) Acomplexnumbercontainsarealnumberandanimaginarynumber—an
imaginarynumberisavaluethatdoesnotexist,suchas −1(6) Thedifferencebetweentwoirrationalnumberscouldresultinaninteger,
rationalnumber,orirrationalnumberbecauseallthreeofthesenumbertypesarerealnumbers
(7) Becauseirrationalnumbersarerealnumbersandhavenoimaginarypart,thedifferencebetweentwoirrationalnumberscannotresultinacomplexnumber—𝑎 + 𝑏𝑖isacomplexnumberwhereaisarealnumberwhilebiisanimaginarynumber(bisarealnumber,but𝑖 = −1)
QuickTips: • Whileyoumaynotknowthedefinitionofacomplexnumber,youshouldknowthedefinitionsoftheotherthreenumbertypesandcanreasonouttheresultofsubtractingtwoirrationalnumbers
25. 3.25 B
Tools: mean,analyzingchartsandgraphsSteps: (1) Identifythenumberofbooksreadfromthedata
(2) 5studentseachread1book(5books),4studentseachread2books(8books),2studentseachread3books(6books),1studentread4books(4books),6studentseachread5books(30books),and2studentseachread6books(12books)
(3) Findthesumofthebooksreadanddividethatsumbythetotalnumberofstudents
(4) 5 + 8 + 6 + 4 + 30 + 12 = 65books(5) 5 + 4 + 2 + 1 + 6 + 2 = 20students(6) RP
@>→ =V
Q→ 3 =
Q→ 3.25booksperstudent
QuickTips: • AnswerchoicesAandDcanbequicklyeliminatedbecausedividing65by20willnotresultinaninteger
• Sincemultiplicationcanbeeasierforsomestudentsthandividing,youcanmultiplyanswerchoicesBandCby20toseeiftheyequal65(totalbooks)
26. 𝑥 + 3 < 4 D
Tools: absolutevalue,inequalities,numberlinesSteps: (1) Theopencirclesindicatethatthepossibleinputsforxarelessthan1but
greaterthan–7,suchas0or–6,buttheinputscannotbe1or–7(2) Input0foreachanswerchoice(3) A) 0 − 4 < 3 → −4 < 3 → 4 < 3(nottrue,soeliminateit)(4) B) 0 + 4 < 3 → 4 < 3 → 4 < 3(nottrue,soeliminateit)(5) C) 0 − 3 < 4 → −3 < 4 → 3 < 4(true,sowemusttestitagain)(6) D) 0 + 3 < 4 → 3 < 4 → 3 < 4(true,sowemusttestitagain)
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |35
(7) Input–6foreachremaininganswerchoice(8) C) −6 − 3 < 4 → −9 < 4 → 9 < 4(nottrue,soeliminateit)(9) D) −6 + 3 < 4 → −3 < 4 → 3 < 4(true,thisisouranswer)
QuickTips: • Usesimpleintegersfromarangeofinputswhenpossible• Youcanalsosolveeachanswerchoice,butthismaytakesomestudentslonger
thansimplytestinginputs• 𝑥 + 3 < 4 → 𝑥 + 3 < 4 → 𝑥 < 1• 𝑥 + 3 < 4 → 𝑥 + 3 > −4 → 𝑥 > −7;thus,Dis−7 < 𝑥 < 1
27. V
@ B
Tools: probabilitySteps: (1) Eachtossofthecoinisanindependentevent,whichmeansthattheoutcome
ofonetossdoesnotaffecttheoutcomeoftheothertosses(2) Theprobabilityofcointosslandingheadsupis=
@;thus,theprobabilityof
tossing3headsinarowis=@× =@× =@= =
](thesameistruefornoheadstossed)
(3) Therearethreepossibilitiesforcointosslandingheadsup2times—thefirsttwotossesorthefirstandthirdtossorthesecondandthirdtoss(the“or”isveryimportant)
(4) The“or”signifiesthatwewilladdeachpossibilities’probabilitytogethertofindtheactualprobabilityofacoinlandingheadsuptwice:=
]+ =
]+ =
]= V
](the
sameistrueforthecoinlandingheadsuponce)(5) Hereisavisualrepresentationofallthepossibleoutcomes:HHH,HHT,HTH,
THH,HTT,THT,TTH,TTT(8possibleoutcomes)(6) Thereareatotalof12Hsoutofthe8possibleoutcomes,whichcanbe
representedas=@]→ V
@
(7) Thequestioncanalsobereadtosay“Whatistheprobabilityofthefirstcointosslandingheadsup,thesecondtosslandingheadsup,ORthethirdtosslandingheadsup?”Inthiscase,youfindthesumoftheprobabilityofeachevent:=
@+ =
@+ =
@= V
@
QuickTips: • Youcanalsomultiplythenumberofheadstotheirrespectiveprobabilities• 3 =
]+ 2 V
]+ 1 V
]+ 0 =
]= V
]+ R
]+ V
]+ 0 = =@
]→ V
@
• Paycloseattentiontohowprobabilityeventsinfluenceoneanother(ifatall)28. Q>>×R>
>.V>P×P,@]> A
Tools: convertingmeasurementsSteps: (1) Sincethequestionisaskingforthehorse’sspeedinmilesperhour,weneedto
writeoutratiosforeachmeasurementprovided(2) >.V>PqNwNFv
=tssw,P,@]>tNNw
=qGKN,R>qGIpwNv
=zspF,Q>>qNwNFv=qGIpwN
(theratioscanbeflippedtoaccuratelyconvertmeasurements)
(3) OurfinalratioshouldbeqGKNvzspF
—startwiththehorse’srate
(4) Convertmeterstofeet:Q>>qNwNFv=qGIpwN
→ Q>>qNwNFv=qGIpwN
× =tssw>.V>PqNwNFv
(weflippedtheratiotoeliminatemetersfromtheconversion
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |36
(5) Convertfeettomiles: Q>>=qGIpwN
× =tssw>.V>P
× =qGKNP,@]>tNNw
(weflippedtheratiotoeliminatefoot/feetfromtheconversion)
(6) Convertminutestohours: Q>>=qGIpwN
× R>qGIpwNv=zspF
× =>.V>P
× =qGKNP,@]>
(eliminateminutes)
(7) AllthatremainsisqGKNvzspF
:Q>>=× R>=zspF
× =>.V>P
× =qGKNP,@]>
→ Q>>×R>>.V>P×P,@]>
QuickTips: • Lookattheanswerchoicestoseehowfaryouneedtogoinyour
calculations—thisproblemjustwantstoseeifyouknowhowtosetupconversions
29. 12feet B
Tools: proportionSteps: (1) Thequestionisstatingtheheightofanobjectisproportionaltothelengthof
itsshadow—theratioofthepole’sheighttoitsshadowisVP(thenumeratoris
theheightandthedenominatoristheshadowlength)(2) Wecancreatethesameratioforthetree’sheightandshadowlength: {
@>(the
numeratoristheheightandthedenominatoristheshadowlength)(3) Setthetworatiosequaltooneanothertocreatetheproportionandsolvefor
x:VP= {
@>
(4) Crossmultiply:VP= {
@>→ 5𝑥 = 60 → 𝑥 = 12feet
QuickTips: • Thetypeofvalueinthenumeratorofoneratiomustmatchthetypeofvalueinthenumeratoroftheotherratioinaproportion(thesameistrueforthedenominators)—inthiscase,bothnumeratorsaretheheightoftheobjectswhilebothdenominatorsaretheshadowlengths
30. centimeters A
Tools: measurementsSteps: (1) AnswerchoicesBandCaremeasurementsforweightandwillnotmeasure
thelengthoftheleaf(2) AnswerchoicesAandCaremeasurementsforlength,butameterisagreater
degreeofmeasurementthanacentimeter(100centimetersfor1meter)(3) Sincethequestionisaskingforareasonablemeasurementforaleaf,imagine
ordrawastandardsizedleaf—whiletherearesomeleavesthatcouldbemeasuredusingmeters,theseleaveswouldlikelybenogreaterthanameter
(4) Thus,themostreasonablemeasurementformeasuringthelengthofaleafiscentimeters
QuickTips: • TheISEErequiresthatyouunderstandmetricmeasurements(conversionsandapplicationintherealworld)
31. 25 − 4 C
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |37
Tools: radicals,numbertypesSteps: (1) Anintegerisapositiveornegativenumber(includingzero)thatcannot
includeafractionordecimal(2) AnswerchoiceA: 4 − 25 → 2 − 5 = −3(integer)(3) AnswerchoiceB: 4× 25 → 2×5 = 10(integer)(4) AnswerchoiceC: 25 − 4 → 21 = 4.582…(notaninteger)(5) AnswerchoiceD: 4×25 → 100 = 10(integer)
QuickTips: • AnswerchoicesBandDcanimmediatelybeeliminatedbecausetheyaretheexactsame,justpresentedinaslightlydifferentway: 4× 25 = 4×25
32. (100 − 25𝜋)cm2 C
Tools: circle(area),square(area)Steps: (1) Findtheareaofthesquare(𝑠@ = 𝐴v)
(2) 10@ = 100(3) Findtheareaofthecircle(𝜋𝑟@ = 𝐴y)(4) Theradiusishalfthediameterofthecircle,andthediameteristhesame
lengthasthewidthofthesquare(10);thus,𝑟 = c@→ 𝑟 = =>
@→ 𝑟 = 5
(5) 𝜋𝑟@ → 𝜋 5 @ → 25𝜋(6) Theareaoftheshadedregionistheareaofthecirclesubtractedfromthearea
ofthesquare:100 − 25𝜋QuickTips: • Looktotheanswerchoicestoseehowfaryouneedtogowithyour
calculations—thisquestiondoesnotneedyoutofinishsubtractingtheareaofthesquarefromtheareaofthecircle
33. 108𝜋 B
Tools: volume(cylinder)Steps: (1) Findtheheightofthecylinder,whichistwotimesthecylinder’sdiameter
(2) ℎ = 2𝑑 → ℎ = 2 6 → ℎ = 12(3) Usethegivenformulaforthevolumeofacylindertosolve(risthecylinder’s
radius,orhalfofthecylinder’sdiameter(3inches))(4) 𝑉 = 𝑟@ℎ𝜋 → 3 @ 12 𝜋 → 9 12 𝜋 → 108𝜋
QuickTips: • Looktotheanswerchoicestoseehowfaryouneedtogowithyourcalculations—wedonotneedtomultiplythevaluestotheactualvalueofpi
34. 55 B
Tools: box-and-whiskerplot,numberlines,rangeSteps: (1) Whileyoumayormaynotknowwhatabox-and-whiskerplotis,youshould
knowrange(thedifferencebetweenthesmallestandlargestvalueinasetofdata)andnumberlines
(2) Thesetofthedatafallsbetween25degreesand80degrees,statingthatatsomepointover50years,thesamedayinthemonthofMaywas25degreesatleastonceand80degreesatleastonce
(3) Thus,25degreesisoursmallestvaluewhile80degreesisourlargestvaluefromthesetofdata
(4) 80 − 25 = 55
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |38
QuickTips: • Abox-and-whiskerplotrepresentsthemedian,lowerandupperquartiles,andtheextremesofasetofdataonanumberlinetodemonstratethedistributionofthesevalues
• Thefarleftandrightpointsofthethinlineindicatetheextremevalues(lowestandhighestamount)—whatweneededforthisproblem
• Theboxrepresentsthequartiles,wherethefarleftlineindicatesthefirstquartile,the“middle”lineindicatesthemedian,andthefarrightlineindicatesthethirdquartile
• Quartilesarethreepointsthatdividethesetofdataintofourgroups,witheachgroupcomprisingaquarterofthedata(thedataisalsoranked)
35. Q
=Q A
Tools: probabilitySteps: (1) BecauseKateremovedayellowmarblefromthebag,theprobabilityof
Joanne’sselectionisinfluenced;however,weareonlylookingfortheprobabilityofJoanne’sselectionforthisproblem( #stusvGwxNspwysqNv
wswJKusvvGrKNspwysqNv)
(2) Thebagcontains15marbles—4green,5blue,2yellow,and4orange(3) SinceKatehasremovedayellowmarble,thebagnowcontains14marbles(4) Thebagnowcontains4greenmarblesoutof14marbles,andtheprobability
ofJoannedrawingagreenmarbleis Q=Q
QuickTips: • Looktotheanswerchoicestoseehowfaryouneedtogowithyourcalculations—wedonotneedtoreduce Q
=Q→ @
\
• AnswerchoicesCandDrepresenttheprobabilityofKateANDJoanne’sselection,whileanswerchoiceBdoesnotreflectKatekeepinghermarble
36. 4𝑥] B
Tools: radicals,operationsonalgebraicexpressions,commutativepropertySteps: (1) 16and𝑥=Rarecommutative;thus,youcanplaceeachvalueunderitsown
radical: 16𝑥=R → ( 16 𝑥=R → ( 16)( 𝑥=R)(2) 16 𝑥=R → (4)( 𝑥=R)(3) Whenyoumultiplyvalueswiththesamebase,suchas𝑥Pand𝑥](xisthe
base),thenyousimplyaddtheexponentstogether((𝑥P) 𝑥] → 𝑥=V)(4) Inthiscase,youneedtwoofthesamevariablewhoseproductis𝑥=R—inother
words,twoofthesamevariablewiththesameexponentsthataddupto16(5) Ifyoudivide16inhalf,youfindthatyouneedxraisedtothepowerof8(6) 𝑥=R → 𝑥](ifyoumultiply𝑥]and𝑥],youget𝑥=R)(7) 4 𝑥] → 4𝑥]
QuickTips: • Thesquarerootofavaluecanalsobewrittenasthevaluetakentothe½power: 𝑥 = 𝑥
�W(numeratoristhepowerwhilethedenominatoristheroot)
• Youcanconvert 𝑥=Rthesameway: 𝑥=R → 𝑥��W → 𝑥]
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |39
37. @��� @>°
ATools: trigonometrySteps: (1) Sine(sine),cosine(cos),andtangent(tan)aretrigonometricfunctionsof
anglesinthecontextofrighttriangles.Thesefunctionsrepresentaparticularratiooftwosidelengthsofthetriangleinrelationtoaknownangle(notthe90°angle)
(2) Sinrepresentstheratioofthesidelengthoppositeoftheknownangleandtherighttriangle’shypotenuse( suusvGwN
z�uswNIpvN)
(3) Tanrepresentstheratioofthesidelengthoppositeoftheknownangleandthesidelengthadjacent(nextto)theknownangle(suusvGwN
Jc�JyNIw)
(4) Inthisrighttriangle,wearegiventheangle20°,thesidelengthof2cm(whichisoppositetheknownangle),andthefactwearelookingforthelengthofthetriangle’shypotenuse(x)
(5) Sincetheinformationincludestheoppositelengthandthehypotenuse,weneedtousesine’sratioof suusvGwN
z�uswNIpvN
(6) sin 20° = @{→ 𝑥 sin 20° = 𝑥 @
{→ 𝑥 sin 20° = 2 → ({)(��� @>°)
��� @>°= @
��� @>°
(7) 𝑥 = @��� @>°
QuickTips: • Youcanremembertheratiosofsine,cosine,andtangentusingthemnemonic
deviceSOH-CAH-TOA• sin 𝜃 = suusvGwN
z�uswNIpvN;cos 𝜃 = Jc�JyNIw
z�uswNIpvN;andtan 𝜃 = suusvGwN
Jc�JyNIw
38. AnswerchoiceA’snumberlinegraph A
Tools: compoundinequalities,numberlinesSteps: (1) Simplify41 ≤ 2𝑥 − 1 ≤ 51sothatxisbyitself
(2) Startwiththeleftpartofthecompoundinequality:41 ≤ 2𝑥 − 1(3) 41 ≤ 2𝑥 − 1 → 42 ≤ 2𝑥 → 21 ≤ 𝑥(4) Solveagainfortherightpartofthecompoundinequality:2𝑥 − 1 ≤ 51(5) 2𝑥 − 1 ≤ 51 → 2𝑥 ≤ 52 → 𝑥 ≤ 26(6) Rewrite21 ≤ 𝑥and𝑥 ≤ 26asacompoundinequality:21 ≤ 𝑥 ≤ 26(7) OnlyanswerchoiceA’snumberlinegraphrepresentsthesmallestpossible
valueforxas21andthelargestpossiblevalueforxas26QuickTips: • AnswerchoiceBrepresentsanestimationof41 ≤ 2𝑥 − 1 ≤ 51,where41and
51aredividedby2.Theproblemisthat51dividedbytwofallsbelow30,sothisestimationistoolargeofarangeofvalues
• AnswerchoiceCrepresents41 ≤ 𝑥 ≤ 51,butnot41 ≤ 2𝑥 − 1 ≤ 51• AnswerchoiceDrepresentsanestimationof41 ≤ 2𝑥 − 1 ≤ 51,where41is
dividedby2and51isdoubled.Theproblemisthat51shouldbedividedby2justas41is,sothisestimationdoesn’tfollowproperoperationprocedures
39. 78 C
ERB’sOfficialPracticeISEE–AnswersandExplanations
P a g e |40
Tools: median,stem-and-leafplotSteps: (1) Ifyoudonotknowhowastem-and-leafplotworks,thenlooktotheanswer
choices—eachvalueisdoubledigit(2) Youcanthenreasonthattheleafistheone’splacevalueofasinglevalueand
thestemisthehigherplacevaluesofthatsamevalue(3) Ifthestemis5andtheleafis7,thenthevalueis57.Ifthestemis10andthe
leafis0,thenthevalueis100(4) Writtenout,thedatapointsare55,57,58,62,62,62,64,66,67,68,74,76,76,
76,77,78,78,79,79,83,83,83,84,84,85,91,92,92,93,97,98,99,and100(5) Inall,thereare33datapoints,whichmeansthatthemedianwillbeoneof
thesepoints—ifthedatasetcontainsanoddnumberofvalues,thenoneofthevalueswillbethemedian;ifthedatasetcontainsanevennumber,thentheaverageofthetwomiddlenumbersisthemedian
(6) Whileyoucanspendyourtimecrossingoutnumbersuntilyoureachthemiddlenumber,youcanalsorecognizethat70,75,and80arenotdatapointsthatexistinthisdataset
(7) Thus,onlyanswerchoiceCcanbecorrectsinceitistheonlydatapointthatexistsintheset
QuickTips: • Ifaproblemseemslikeitwilltakealongtimetofigureout,thereislikelyaneasierwaytosolvetheproblem
• Inthiscase,weknowthatthemedianwillbeoneoftheexistingdatapointsinasetofdatathatcontainsanoddnumberofdatapointsorvalues
40. ±7𝑖 D
Tools: imaginarynumbers,commutativeproperty,associativepropertySteps: (1) Ataquickglance,youcanrecognizethattheonlywayfor49tobecome0isby
subtracting49(oradding–49)toit;however,youalsoknowthatnosquaredrealnumbercanresultinanegativenumber
(2) Somehow,weneedthesquareof7or–7tomake–49forthisequationtobetrue—entertheimaginarynumber −1or𝑖
(3) Setxbyitselfintheequation:𝑥@ + 49 = 0 → 𝑥@ = −49 → 𝑥 = −49(4) −49isalsoimaginary,butwecanwriteitinadifferentwayusingthe
commutativeandassociativeproperties(5) −49 → −1 49 → −1 49 → −1 7 → 7 −1(6) Sincethesquareofboth7and–7make49,wemustincludebothnumbersas
squarerootsof49:±7 −1(7) Ifweuse𝑖for −1,then±7 −1is ± 7𝑖
QuickTips: • Ifyousquare −1,thenyouget–1(justlikesquaring 8: 8@= 8)
• −1@→ −1 −1 → −1
• Convertingtheradicaltoapowerdemonstrateswhytheradicalsarecanceled
out: −1@→ −1
�W@→ −1
WW → −1
�� → (−1)
41. 7 6
2 5 A
ERB’sOfficialPracticeISEE–AnswersandExplanations piqosity
P a g e |41
Tools: matrices(addition)Steps: (1) Whenaddingmatrices,theseboxeswithcolumnsandrowsofvalues,you
simplyaddthevalueslocatedinthesamecolumnandrowinonematrixastheothermatrix
(2) Inthiscase,2inthefirstmatrixand5inthesecondmatrixarelocatedinthefirstrowandfirstcolumn;thus,wefindthesumofthesetwovaluesandplaceitinthesamespotintheresultingmatrix(andsoonfortheothervalues)
(3) 2 30 4 + 5 3
2 1 = 2 + 5 3 + 30 + 2 4 + 1 = 7 6
2 5 QuickTips: • AnswerchoicesCandDdonothave6inthefirstrowandsecondcolumnspot,
sowecaneliminatetheseanswers• AnswerchoiceBdoesnothave2inthesecondrowandfirstcolumnspot,so
wecaneliminateitasananswer• Inadditionofmatrices,thetwoormorematricesmusthavethesamenumber
ofrowsandcolumns—youcannotaddtogetheramatrixwith2rowsand2columnstoamatrixwith3rowsand3columns
42. 2cm A
Tools: surfacearea(sphere)Steps: (1) Wearegiventheformulaforthesurfaceareaofasphere(𝑆𝐴 = 4𝜋𝑟@)andthe
actualsurfaceareaofaparticularsphere(16𝜋cm2)(2) Inputtheknownsurfaceareaintotheformulaandsolvefortheradius(3) 16𝜋 = 4𝜋𝑟@ → 16 = 4𝑟@ → 4 = 𝑟@ → 𝑟 = 2
QuickTips: • Sincebothsidesoftheequationcontain𝜋,wecancancelitoutandtheequationwillremainbalanced
• Youcanestimatethattheradiuswillbeamuchsmallernumberthan16becauseitwillbedividedby4andthentakentoitssquareroot(wecanquicklyeliminateanswerchoicesCandD)