【小站教育】SAT数学难题汇总及答案

1/18SAT数学难题汇总及答案x^2表示x的平方，=！表示不等于。pi表示圆周率类型1：20.Theleastintegerofasetofconsecutiveintegersis-25.Ifthesumoftheseintegersis26,howmanyintegersareinthisset?(A)25(B)26(C)50(D)51(E)5214.Exactly4actorstryoutforthe4partsinaplay.Ifeachactorcanperformanyonepartandnoonewillperformmorethanonepart,howmanydifferentassignmentsofactorsarepossible?16.SetXhasxmembersandsetYhasymembers.SetZconsistsofallmembersthatareineithersetXorsetYwiththeexceptionofthekcommonmembers(k0).WhichofthefollowingrepresentsthenumberofmembersinsetZ?(A)x+y+k(B)x+y-k(C)x+y+2k(D)x+y-2k(E)2x+2y-2k20.Thereare75morewomenthanmenenrolledinLindenCollege.Iftherearenmenenrolled,then,intermsofn,whatpercentofthoseenrolledaremen?2/1817.Amerchantsellsthreetypesofclocksthatchimeasindicatedbythecheckmarksinthetableabove.Whatisthetotalnumberofchimesoftheinventoryofclocksinthe90-minuteperiodfrom7:15to8:45?18.Ifthe5cardsshownaboveareplacedinarowsoisneverateitheend,howmanydifferentarrangementsarepossible?20.When15isdividedbythepositiveintegerk,theremainderis3.Forhowmanydifferentvaluesofkisthistrue?(A)One(B)Two(C)Three(D)Four(E)Five17.Onthenumberlineabove,thereare9equalintervalsbetween0and1.Whatisthevalueofx?19.Ifa,b.c,andfarefournonzeronumbers,thenallofthefollowingproportionsareequivalentEXCEPT(A)a/f=b/c(B)f/c=b/a(C)c/a=f/b(D)a/c=b/f(E)af/bc=1/18.Ifaandbarepositiveintegersandwhatisthevalueofab?3/18(A)6(B)12(C)18(D)24(E)3616.Afterthefirstterm,eachterminasequenceis3greaterthan1/3oftheprecedingterm.Iftisthefirsttermofthesequenceandt=!0.whatistheratioofthesecondtermtothefirstterm?15.TheAcmePlumbingCompanywillsendateamof3plumberstoworkonacertainjob.Thecompanyhas4experiencedplumbersand4trainees.Ifateamconsistsof1experiencedplumberand2trainees,howmanydifferentsuchteamsarepossible?17.Ifp.r.andsarethreedifferentprimenumbersgreaterthan2,andn=p*r*s,howmanypositivefactors,including1andn.doesnhave?18.Ifthesumoftheconsecutiveintegersfrom-22tox,inclusive,is72,whatisthevalueofx?(A)23(B)25(C)50(D)75(E)9417.Forallpositiveintegersjandk.letj\R\kbedefinedasthewholenumberremainderwhenjisdividedbyk.If13\R\k=2,whatisthevalueofk?19,Inasetofelevendifferentnumbers,whichofthefollowingCANNOTaffectthevalueofthemedian?(A)Doublingeachnumber(B)Increasingeachnumberby10(C)Increasingthesmallestnumberonly(D)Decreasingthelargestnumberonly(E)Increasingthelargestnumberonly15.Astorecharges$28foracertaintypeofsweater.Thispriceis40percentmorethantheamountitcoststhestoretobuyoneofthesesweaters.Atanend-of-seasonsale,storeemployeescanpurchaseanyremainingsweatersat30percentoffthestore'scostHowmuchwoulditcostanemployeeto4/18purchaseasweaterofthistypeatthissale?(A)$8.40(B)$14.00(C)$19.60(D)$20.00(E)$25.2017.AliceandCorinnestandback-to-back.Theyeachtake10stepsinoppositedirectionsawayfromeachotherandstop.Alicethenturnsaround,walkstowardCorinne.andreachesherin17steps.ThelengthofoneofAlice'sstepsishowmanytimesthelengthofoneofCorinne'ssteps?(AllofAlice'sstepsarethesamelengthandallofCorinne'sstepsarethesamelength.)14.Ifnandpareintegersgreaterthan1andifpisafactorofbothn+3andn+10.whatisthevalueofp?(A)3(B)7(C)10(D)13(E)3016.Inamixtureofpeanutsandcashews,theratiobyweightofpeanutstocashewsis5to2.Howmanypoundsofcashewswilltherebein4poundsofthismixture?14.Howmanyintegersgreaterthan20andlessthan30areeachtheproductofexactlytwodifferentnumbers,bothofwhichareprime?(A)Zero(B)One(C)Two(D)Three(E)Four20.Ifkisapositiveinteger,whichofthefollowingmustrepresentanevenintegerthatistwicethevalueofanoddinteger?(A)2k(B)2k+3(C)2k+4(D)4k+1(E)4k+25/18类型2：18.Theshadedregioninthefigureaboveisboundedbythex‐axis,thelinex=4,andthegraphofy=f(x).Ifthepoint(a,b)liesintheshadedregion,whichofthefollowingmustbetrue?I.a4II.baIII.bf(a)(A)Ionly(B)IIIonly(C)IandIIonly(D)IandIIIonly(E)I.II,andIII19.Atabottlingcompany,machineAfills,abottlewithspringwaterandmachineBacceptsthebottleonlyifthenumberoffluidouncesisbetween1178and1218IfmachineBacceptsabottlecontainingnfluidounces,whichofthefollowingdescribesallpossiblevaluesofn?7.Dwaynehasanewspaperrouteforwhichhecollectskdollarseachday.Fromthisamounthepaysoutk/3dollarsperdayforthecostofthepapers,andhesavestherestofthemoney.Intermsofk,howmanydayswillittakeDwaynetosave$1,000?6/1817.Inthexy-coordinateplane,thegraphofx=y*y-4intersectslinelat(0,p)and(5,t).Whatisthegreatestpossiblevalueoftheslopeofl?18.Estherdrovetoworkinthemorningatanaveragespeedof45milesperhour.Shereturnedhomeintheeveningalongthesamerouteandaveraged30milesperhour.IfEstherspentatotalofonehourcommutingtoandfromwork,howmanymilesdidEstherdrivetoworkinthemorning?14.If(a+b)^0.5=(a-b)^-0.5,whichofthefollowingmustbetrue?(A)b=0(B)a+b=1(C)a-b=1(D)a^2+b^2=1(E)a^2-b^2=115.Thefigureaboveshowsthegraphsofy=x*xandy=a-x*xforsomeconstanta.IfthelengthofPQisequalto6,whatisthevalueofa?(A)6(B)9(C)12(D)1518.Duringasale,acustomercanbuyoneshirtforxdollars.Eachadditionalshirtthecustomerbuyscostszdollarslessthanthefirstshirt.Forexample,thecostofthesecondshirtisx-zdollars.Whichofthefollowingrepresentsthecustomer'scost,indollars,fornshirtsboughtduringthissale?7/1816.Letthefunctionhb