【奇偶數(shù)】

Ifxisaneveninteger,whichofthefollowingisanoddinteger?

3x+2

7x

8x+5

x2

x3

Ifxandyareintegersandxy2isapositiveoddinteger,whichofthefollowingmustbetrue?

xyispositive.

xyisodd.

x+yiseven.

Ⅰonly

Ⅱonly

Ⅲonly

ⅠandⅡ

ⅡandⅢ

Ifthesumoftwointegersis6,thenitmustbetruethat

bothintegersareeven

bothintegersareodd

bothintegersarepositive

ifoneintegerisnegative,theotherispositive

ifoneintegerispositive,theotherisnegative

Ifnisaninteger,whichofthefollowingmustbeeven?

n+1

n+2

2n

2n+1

n2

Ifxisanevenintegerandyisanoddinteger,whichofthefollowingCANNOTbetrue?

xy

yx

isaneveninteger.isanoddinteger.

xisamultipleofy.

yisamultipleofx.

xyisaneveninteger.

【質(zhì)因數(shù)】

Ifnisanintegerand

k?

22

26

35

54

60

n23571113thenwhichofthefollowingcouldbethevalueof

77k

WhichofthefollowingintegersdoesNOThaveadivisorgreaterthan1thatisthesquareofaninteger?

75

42

32

25

12

Ifxistheproductofthepositiveintegersfrom1to8,inclusive,andifi,k,m,andparepositiveintegerssuchthatx=2i3k5m7p,theni+k+m+p=

4

7

8

11

12

Sixcardsnumberedfrom1to6areplacedinanemptybowl.Firstonecardisdrawnandthenputbackintothebowl;thenasecondcardisdrawn.Ifthecardsaredrawnatrandomandifthesumofthenumbersonthecardsis8,whatistheprobabilitythatoneofthetwocardsdrawnisnumbered5?

(A)1

6

(B)1

5

(C)1

3

(D)2

5

(E)2

3

TheproductofthefirsttwelvepositiveintegersisdivisiblebyallofthefollowingEXCEPT

210

88

75

60

34

Thesumoftheprimenumbersthataregreaterthan60andlessthan70is

67

128

191

197

260

Ifnisaninteger,whichofthefollowingCANNOTbeafactorof3n+4?

(A)4

(B)5

(C)6

(D)7

(E)8

Inacertaingame,alargecontainerisfilledwithred,yellow,green,andbluebeadsworth,respectively,7,5,3,and2pointseach.Anumberofbeadsarethenremovedfromthecontainer.Iftheproductofthepointvaluesoftheremovedbeadsis147,000,howmanyredbeadswereremoved?

(A)5

(B)4

(C)3

(D)2

(E)0

Howmanypositiveintegerskaretheresuchthat100kisafactorof(22)(3)(53)?

None

One

Two

Three

Four

Ifkandwarethedimensionsofarectanglethathasarea42,andifkandwareintegerssuchthatk>w,whatisthetotalnumberofpossiblevaluesofk?

Two

Three

Four

Five

Six

Ifthesumofasetoftendifferentpositiveprimenumbersisanevennumber,whichofthefollowingprimenumbersCANNOTbeintheset?

2

3

5

7

11

Ifxandyaredifferentprimenumbers,eachgreaterthan2,whichofthefollowingmustbetrue?

x+y≠91

x–yisaneveninteger.

xisnotaninteger.

y

IIonly

IandIIonly

IandIIIonly

IIandIIIonly

I,II,andIII

Whatisthesmallestpositiveintegernforwhich324isafactorof6n?

(A)2

(B)3

(C)4

(D)5

(E)6

Whichofthefollowingcouldbethesumofthereciprocalsoftwodifferentprimenumbers?

7

13

10

21

11

30

23

50

19

77

Ifnandparedifferentpositiveprimenumbers,whichoftheintegers(have)exactly4positivedivisors?

n4only

p3only

nponly

n4andnp

p3andnp

n4,p3,andnphas

Ifxy=165,wherexandyarepositiveintegersandx>y,whatistheleastpossiblevalueofx

–y?

2

4

8

15

28

Ifnandkareintegerswhoseproductis400,whichofthefollowingstatementsmustbetrue?

n+k>0

n≠k

Eithernorkisamultipleof10.

Ifniseven,thenkisodd.

Ifnisodd,thenkiseven.

【公約數(shù)公倍數(shù)】

ThenumbersinwhichofthefollowingpairsdoNOThaveapairofdistinctprimedivisorsincommon?

10and20

12and18

24and32

21and63

22and88

If3isthegreatestcommondivisorofpositiveintegersrands,whatisthegreatestcommondivisorof2rand2s?

2

3

4

6

12

Agymclasscanbedividedinto8teamswithanequalnumberofplayersoneachteamorinto12teamswithanequalnumberofplayersoneachteam.Whatistheleastpossiblenumberofstudentsintheclass?

20

24

36

48

96

Ifx,y,andzarepositiveintegersand3x=4y=7z,thentheleastpossiblevalueofx+y+zis

33

40

49

61

84

SetSconsistsofndistinctpositiveintegers,noneofwhichisgreaterthan12.WhatisthegreatestpossiblevalueofnifnotwointegersinShaveacommonfactorgreaterthan1?

4

5

6

7

11

Ifanintegernisdivisiblebyboth6and8,thenitmustalsobedivisiblebywhichofthefollowing?

10

12

14

16

18

Jaimeearnedenoughmoneybysellingseashellsat25centseachtobuyseveralusedpaperbackbooksat55centseach.Ifhespentallofthemoneyheearnedsellingseashellstobuythebooks,whatistheleastnumberofseashellshecouldhavesold?

5

11

17

25

30

【余數(shù)】

Whentheintegernisdividedby17,thequotientisxandtheremainderis5.Whennisdividedby23,thequotientisyandtheremainderis14.Whichofthefollowingistrue?

23x+17y=19

17x–23y=9

17x+23y=19

14x+5y=6

5x–14y=-6

Ifnisaprimenumbergreaterthan3,whatistheremainderwhenn2

(A)0

(B)1

(C)2

isdividedby12?

(D)3

(E)5

Iftheintegerkisamultipleof3,whichofthefollowingisalsoamultipleof3?

k+2

2k+8

3k+5

4k+4

5k+12

IfMandNarepositiveintegersthathaveremaindersof1and3,respectively,whendividedby6,whichofthefollowingcouldNOTbeapossiblevalueofM+N?

86

52

34

28

10

Therearebetween100and110cardsinacollectionofcards.Iftheyarecountedout3atatime,thereare2leftover,butiftheyarecountedout4atatime,thereis1leftover.Howmanycardsareinthecollection?

101

103

106

107

109

Whentheintegernisdividedby6,theremainderis3,WhichofthefollowingisNOTamultipleof6?

n–3

n+3

2n

3n

4n

Howmanyintegersfrom0to50,inclusive,havearemainderof1whendividedby3?

15

16

17

18

19

Iftheremainderis7whenpositiveintegernisdividedby18,whatistheremainderwhennisdividedby6?

(A)0

(B)1

(C)2

(D)3

(E)4

When20isdividedbythepositiveintegerk,theremainderisk–2.Whichofthefollowingisapossiblevalueofk?

8

9

10

11

12

【小數(shù)分?jǐn)?shù)】

Whichofthefollowingfractions,ifwrittenasadecimal,wouldhavea2inthethousandthsplace?

(A)3

11

(B)7

9

(C)1

8

(D)4

7

(E)1

6

Onascalethatmeasurestheintensityofacertainphenomenon,areadingofn+1correspondstoanintensitythatis10timestheintensitycorrespondingtoareadingofn.Onthatscale,theintensity correspondingtoareadingof8ishowmanytimesasgreatastheintensitycorrespondingtoareadingof3?

5

50

105

510

810310

Onacertainscaleofintensity,eachincrementof10inmagnituderepresentsatenfoldincreaseinintensity.Onthisscale,anintensitycorrespondingtoamagnitudeof165ishowmanytimesanintensitycorrespondingtoamagnitudeof125?

40

100

400

1,000

10,000

Whatistheleastnumberofdigits(includingrepetitions)neededtoexpress10100indecimalnotation?

4

100

101

1,000

1,001

Whichofthefollowingfractionshasadecimalequivalentthatisaterminatingdecimal?

(A)

(B)

(C)

(D)

10

189

15

196

16

225

25

144

(E) 39

128

Whichofthefollowingproceduresisalwaysequivalenttoadding5givennumbersandthendividingthesumby5?

Multiplyingthe5numbersandthenfindingthe5throotoftheproduct.

Addingthe5numbers,doublingthesum,andthenmovingthedecimalpointoneplacetotheleft.

Orderingthe5numbersnumericallyandthenselectingthemiddlenumber.

None

Ionly

IIonly

IIIonly

IandIII

Onarecenttrip,Cindydrovehercar290miles,roundedtothenearest10miles,andused12gallonsofgasoline,roundedtothenearestgallon.TheactualnumberofmilespergallonthatCindy'scargotonthistripmusthavebeenbetween

(A)

(B)

(C)

(D)

(E)

290and

12.5

295and

12

285and

12

285and

12.5

295and

12.5

290

11.5

285

11.5

295

12

295

11.5

285

11.5

【解方程】

Whichofthefollowingisequivalenttoexpressionsaredefined?

2x4

2x28x8

forallvaluesofxforwhichboth

(A)

(B)

1

2x26

1

9x2

(C)

(D)

(E)

2

x6

1

x4

1

x2

Atacertaindiner,ahamburgerandcoleslawcost$3.95,andahamburgerandfrenchfriescost

$4.40.Iffrenchfriescosttwiceasmuchascoleslaw,howmuchdofrenchfriescost?

$0.30

$0.45

$0.60

$0.75

$0.90

Ifx≠0andx ,then,intermsofy,x

2y

y

y

2

4y2

12y

–2y

If2x+5y=8and3x=2y,whatisthevalueof2x+y?

4

70

19

64

19

56

19

40

19

Ifxandyarepositiveintegersand1+x+y+xy=15,whatisthevalueofx+y?

(A)3

(B)5

(C)6

(D)8

(E)9

Acertainused-bookdealersellspaperbackbooksat3timesdealer'scostandhardbackbooksat4timesdealer'scost.Lastweekthedealersoldatotalof120books,eachofwhichhadcostthedealer$1.Ifthegrossprofit(salesrevenueminusdealer'scost)onthesaleofallofthesebookswas$300,howmanyofthebookssoldwerepaperbacks?

40

60

75

90

100

Ifbandcarepositivenumbersand1bc,thenb+c=

b c 8

(A)4

(B)6

(C)7

(D)8

(E)9

Acertainstoresellsallmapsatonepriceandallbooksatanotherprice.OnMondaythestoresold12mapsand10booksforatotalof$38.00,andonTuesdaythestoresold20mapsand15booksforatotalof$60.00.Atthisstore,howmuchlessdoesamapsellforthanabook?

$0.25

$0.50

$0.75

$1.00

$l.25

Ifg(x)=x+4forallxandf(x)=followingvaluesofx?

–5

2x25

x

forallnonzerox,thenf(x)=g(x)forwhichofthe

–3

1

3

5

Ifx=y+4andx=20–y,thenx2y2

16

80

144

256

384

If(x26x9)6(x3)90,thenx=

-6

-3

0

3

6

Aplanewasoriginallyflyingatanaltitudeofxfeetwhenitascended2,000feetandthendescended5,000feet.Iftheplane'saltitudeafterthesetwochangeswas 1itsoriginal

3

altitude,thenthesolutionofwhichofthefollowingequationsgivestheplane'soriginalaltitude,infeet?

x2,0001(x3,000)

3

1(x3,000)x

3

x3,0001x

3

x7,0001x

3

x3,0001x

3

Al,Lew,andKarenpooledtheirfundstobuyagiftforafriend.Alcontributed$2less

than1

3

ofthecostofthegiftandLewcontributed$2morethan1

4

ofthecost.IfKaren

contributedtheremaining$15,whatwasthecostofthegift?

$24

$33

$36

$43

$45

Ifz3z12,thenz=

z1 z3

2

1

-1

-2

–3

Ifxy≠0andx2y2–xy=6,whichofthefollowingcouldbeyintermsofx?

1/(2x)

–2/x

3/x

Ionly

IIonly

IandII

IandIII

IIandIII

Ifthesumoftwopositiveintegersis24andthedifferenceoftheirsquaresis48,whatistheproductofthetwointegers?

108

119

128

135

143

【不等式】

Ifq,randsarethenumbersshownabove,whichofthefollowingshowstheirorderfromgreatesttoleast?

q,r,s

q,s,r

r,q,s

s,q,r

s,r,q

Ifx+5>2and,x–3<7,thevalueofxmustbebetweenwhichofhefollowingpairsofnumbers?

-3and10

-3and4

2and7

3and4

3and10

Whichofthefollowinginequalitiesisequivalentto–2<x<4?

|x–2|<4

|x–1|<3

|x+1|<3

|x+2|<4

Noneoftheabove

Whichofthefollowingisequivalenttothestatementthat0.5isbetween

1<n<6

2<n<3

2<n<5

4<n<6

n>10

Ify+|y|=0,whichofthefollowingmustbetrue?

y>0

y≥0

2and3？

n n

y<0

y≤0

y=0

Onthenumberline,thenumberpistwiceasmanyunitsfrom-2as-2isfrom6.Ifpislessthan–2,whatisthevalueofp?

–18

–10

–6

10

14

Ifx2<x.thenxmustbe

lessthan0

equalto0

between0and1

equalto1

greaterthan1

If

(A)

p1,andpandqarepositiveintegers,whichofthefollowingmustbegreaterthan1?

q

(B) p

q2

(C) p

2q

(D) q

p2

(E)q

p

Whichofthefollowinginequalitiesisanalgebraicexpressionfortheshadedpartofthenumberlineabove?

|x|≤3

|x|≤5

|x–2|≤3

|x–1|≤4

|x+1|≤4

Ifx<12,thenitmustbetruethat

-x<-12

-x-2<14

-x+2<-10

x+2<10

x-2<11

【函數(shù)】

Ifr☉s=rs+r+s,thenforwhatvalueofsisr☉sequaltorforallvaluesofr?

–1

0

1

r

1

r1

TheoperationΘisdefinedbyxΘy=1+

x

1forallnonzeronumbersxandy.Ifzisa

y

numbergreaterthan1,whichofthefollowingmustbetrue?

xΘ(-z)=0

zΘ z =1

z1

2Θ2=z

z z

Ionly

IandIIonly

IandIIIonly

IIandIIIonly

I,II,andIII

Iftheoperation⊙isdefinedbyx⊙y= forallpositivenumbersxandy,then(5⊙45)⊙60=

30

60

90

30

60

Forallrealnumbersv,theoperationv*isdefinedbytheequationv*=v-thenv=

15

18

21

24

27

Iffisthefunctiondefinedbyf(x)=x2(1-x)2forallx,thenf(1-x)=

f(x)

[f(x)]2

1-f(x)

(1-x)f(x)

f(1)-f(x)

【數(shù)列】

v.If(v*)*=8,

3

Inthesequence1,2,4,8,16,32,…,eachtermafterthefirstistwicethepreviousterm.Whatisthesumofthe16th,17th,and18thtermsinthesequence?

218

3(217)

7(216)

3(216)

7(215)

Ifasequenceof8consecutiveoddintegerswithincreasingvalueshas9asits7thterm,whatisthesumofthetermsofthesequence?

22

32

36

40

44

Thesequencea1,a2,…,an,…issuchthatan=2an-1-xforallpositiveintegersn≥2andforcertainnumberx.Ifa5=99anda3=27,whatisthevalueofx?

3

9

18

36

45

Ifa1

(A)

(B)

(C)

(D)

(E)

=1anda

3

8

5

8

8

5

5

3

8

3

n+1

=1+ 1 foralln≥1,whatisthevalueofa?

5

an

Thesumofalltheintegersksuchthat–26<k<24is

0

-2

-25

-49

-51

Whatisthedifferencebetweenthesixthandthefifthtermsofthesequence2,4,7, whose

nthtermisn2n1?

2

3

6

16

17

Thepagesofareportarenumberedconsecutivelyfrom1to10.Ifthesumofthepagenumbersuptoandincludingpagenumberxofthereportisequaltoonemorethanthesumofthepagenumbersfollowingpagenumberx,thenx=

(A)4

(B)5

(C)6

(D)7

(E)8

Inacertainsequence,thefirsttermis1,andeachsuccessivetermis1morethanthereciprocalofthetermthatimmediatelyprecedesit.Whatisthefifthtermofthesequence?

3

5

5

8

8

5

5

3

9

2

Ifthesumof7consecutiveintegersis434,thenthegreatestofthe7integersis

71

69

67

65

62

Ifs1,s2,s3,isthesequencesuchthatsn

nn1

forallpositiveintegersn,thenthe

productofthefirst10termsofthissequenceis

(A)

(B)

(C)

(D)

(E)

1

(10)(11)

1

11

1

10

9

10

10

11

IfthesumofthefirstnpositiveintegersisS,whatisthesumofthefirstnpositiveevenintegers,intermsofS?

S

2

S

2S

2S+2

4S

【三角形四邊形】

OnamapTownGis10centimetersdueeastofTownHand8centimetersduesouthofTown

J.Whichofthefollowingisclosesttothestraight-linedistance,incentimeters,betweenTown

HandTownJonthemap?

6

13

18

20

24

Inthefigureabove,iftheareaoftherectangularregionPQRSis40,andifPT=TS,whatistheareaofthepentagonalregionPQRST?

15

20

25

30

Itcannotbedeterminedfromtheinformationgiven.

Whatistheareaoftheshadedregioninthefigureabove?

72

57

55

541

2

491

2

Acirclegraphshowshowthebudgetofacertaincompanywasspent:63percentforsalaries,12percentforresearchanddevelopment,6percentforutilities,5percentforequipment,4percentforsupplies,andtheremainderfortransportation.Iftheareaofeachsectorofthegraphisproportionaltothepercentofthebudgetitrepresents,howmanydegreesofthecircleareusedtorepresenttransportation?

10°

18°

36°

90°

324°

Thesumoftheinterioranglesofanypolygonwithnsidesis180(n–2)degrees.IfthesumoftheinterioranglesofpolygonPisthreetimesthesumoftheinterioranglesofquadrilateralQ,howmanysidesdoesPhave?

6

8

10

12

14

Thefigureaboveshowstheshapeofatunnelentrance.Ifthecurvedportionis 3ofacircle

4

andthebaseoftheentranceis12feetacross,whatistheperimeter,infeet,ofthecurvedportionoftheentrance?

9π

12π

9

18π

9

Ifasquaremirrorhasa20-inchdiagonal,whatistheapproximateperimeterofthemirror,ininches?

40

60

80

100

l20

Thefigureaboveshowsthedimensionsofanisoscelestriangleintermsofx.Whatistheareaofthetriangle?

24

30

48

60

96

【圓】

Thefigureaboverepresentsarectangularparkinglotthatis30metersby40metersandanattachedsemicirculardrivewaythathasanouterradiusof20metersandaninnerradiusof10meters.Iftheshadedregionisnotincluded,whatisthearea,insquaremeters,ofthelotanddriveway?

1,350π

1,200+400π

1,200+300π

1,200+200π

1,200+150π

Ifthecircumferenceofacircularregionisc,whichofthefollowingrepresentstheareaofthatcircularregion?

c2

(A)

(B)

(C)

(D)

(E)

2

c2

4

c2

2

c2

4

c2

42

Whatisthediameterofacircularregionthathasarea10π?

5

10

20

10

2

ThepointsR,T,andUlieonacirclethathasradius4.IfthelengthofarcRTUis4/3,whatisthelengthoflinesegmentRU?

4/3

8/3

3

4

6

Apointontheedgeofafanbladethatisrotatinginaplaneis10centimetersfromthecenterofthefan.Whatisthedistancetraveled,incentimeters,bythispointin15secondswhenthefanrunsattherateof300revolutionsperminute?

750π

1,500π

1,875π

3,000π

7,500π

Phobus,oneofthesatellitesofMars,revolvesaboutMarsatadistanceofapproximately5,800milesfromthecenterofMarsandapproximately3,700milesfromthesurfaceofMars.IfitisassumedthatMarsissphericalandtheorbitofPhobusiscircular,whatistheapproximatecircumference,inmiles,ofMarsatitsequator?

2,100π

4,200π

7,400π

9,500π

190,000π

IfOisthecenterofthecircleaboveandthelengthofarcRSPistwicethelengthofarcPQR,thenxequals

60

100

120

150

240

IfthenumberofsquareunitsintheareaofcircleCistwicethenumberoflinearunitsinthecircumferenceofC,whatisthenumberofsquareunitsinthearea?

4

8

4π

8π

16π

【立體幾何】

Arightcylindricalcontainerwithradius2metersandheight1meterisfilledtocapacitywith

oil.Howmanyemptyrightcylindricalcans,eachwithradiuscanbefilledtocapacitywiththeoilinthiscontainer?

1

2

4

8

16

1meterandheight4meters,

2

Intherectangularsolidabove,thethreesidesshownhaveareas12,15,and20,respectively.Whatisthevolumeofthesolid?

60

120

450

1,800

3,600

Eachedgeofacubicalblockofwoodmeasures2inches.Whatisthesurfaceareaoftheblockinsquareinches?

4

8

12

16

24

Thevolumeofaboxwithasquarebaseis54cubiccentimeters.Iftheheightoftheboxistwicethewidthofthebase,whatistheheight,incentimeters?

(A)2

(B)3

(C)4

(D)6

(E)9

Acertaincompanyhasrecordsstoredwitharecord-storagefirmin15-inchby12-inchby10-inchboxes.Theboxesoccupy1.08millioncubicinchesofspace.Ifthecompanypays

$0.25perboxpermonthforrecordstorage,whatisthetotalamountthatthecompanypayseachmonthforrecordstorage?

$150

$300

$600

$1,200

$2,400

【坐標(biāo)系】

y=kx+3

Intheequationabove,kisaconstant.Ify=17whenx=2,whatisthevalueofywhenx=4?

34

31

14

11

7

y

l

2

-3

0

x

Thegraphofwhichofthefollowingequationsisastraightlinethatisparalleltolinelinthefigureabove?

3y–2x=0

3y+2x=0

3y+2x=6

2y–3x=6

2y+3x=-6

Inthefigureabove,howmanyofthepointsonlinesegmentPQhavecoordinatesthatarebothintegers?

5

8

10

11

20

【集合】

Inasurvey,2,500executiveswereeachaskedwhethertheyreadNewsletterAorNewsletter

B.Accordingtothesurvey,55percentoftheexecutivesreadNewsletterA,62percentreadNewsletterB,and37percentreadbothNewsletterAandNewsletterB.HowmanyoftheexecutivessurveyedreadneitherNewsletterAnorNewsletterB?

425

500

600

675

750

Ofthezstudentsatacertaincollege,xarestudyingFrenchandyarestudyingGerman.IfwarestudyingbothFrenchandGerman,whichofthefollowingexpressesthenumberofstudentsatthecollegenotstudyingeitherFrenchorGerman?

z+w–x–y

z–w–x–y

z–w–x+y

w+x+y–z

w–x–y–z

Accordingtoasurvey,93percentofteenagershaveusedacomputertoplaygames,89percenthaveusedacomputertowritereports,and5percenthavenotusedacomputerforeitherofthesepurposes.Whatpercentoftheteenagersinthesurveyhaveusedacomputerbothtoplaygamesandtowritereports?

82%

87%

89%

92%

95%

Onenight18percentofthefemaleofficersonapoliceforcewereonduty.If180officerswereondutythatnightandhalfofthesewerefemaleofficers,howmanyfemaleofficerswereonthepoliceforce?

90

180

270

500

1,000

Outofatotalof1,000employeesatacertaincorporation,52percentarefemaleand40percentofthesefemalesworkinresearch.If60percentofthetotalnumberofemployeesworkinresearch,howmanymaleemployeesdoNOTworkinresearch?

520

480

392

208

88

Atamonthlymeeting,2/5oftheattendeesweremalesand7/8ofthemaleattendeesarrivedontime.If9/10ofthefemaleattendeesarrivedontime,whatfractionoftheattendeesatthemonthlymeetingdidnotarriveontime?

11/100

3/25

7/50

3/20

4/25

Ineachproductionlotforacertaintoy,25percentofthetoysareredand75percentofthetoysareblue.HalfthetoysaresizeAandhalfaresizeB.If10outofalotof100toysareredandsizeA,howmanyofthetoysareblueandsizeB?

15

25

30

35

40

Ofagroupofpeoplesurveyedinapoliticalpoll,60percentsaidthattheywouldvoteforcandidateR.OfthosewhosaidtheywouldvoteforR.90percentactuallyvotedforR.andofthosewhodidnotsaythattheywouldvoteforR.5percentactuallyvotedforR.WhatpercentofthegroupvotedforR?

56%

59%

62%

65%

74%

InCompanyX,30percentoftheemployeesliveovertenmilesfromworkand60percentoftheemployeeswholiveovertenmilesfromworkareincarpools.If40percentoftheemployeesofCompanyXareincarpools,whatpercentoftheemployeesofCompanyXlivetenmilesorlessfromworkandareincarpools?

12%

20%

22%

28%

32%

【排列組合】

If10personsmeetatareunionandeachpersonshakeshandsexactlyoncewitheachoftheothers,whatisthetotalnumberofhandshakes?

(A)10·9·8·7·6·5·4·3·2·1

10·10

10·9

45

36

Inacertaincontest,Fredmustselectany3of5differentgiftsofferedbythesponsor.Fromhowmanydifferentcombinationsof3giftscanFredmakehisselection?

10

15

20

30

60

12IceCreamFlavors10KindsofCandies8LiquidToppings

5KindsofNuts

WithorWithoutWhippedCream

CREATEYOUROWNSUNDAE

Ifacustomermakesexactlyoneselectionfromeachofthefivecategoriesshowninthetableabove,whatisthegreatestpossiblenumberofdifferenticecreamsundaesthatacustomercancreate?

9,600

4,800

2,400

800

400

Inhowmanydifferentwayscan3peoplebeassignedtofill3differentpositionssothateachpersonisassignedtoexactlyoneposition?

Twelve

Nine

Six

Three

One

Ifacodewordisdefinedtobeasequenceofdifferentletterschosenfromthe10lettersA,B,C,D,E,F,G,H,I,andJ,whatistheratioofthenumberof5-lettercodewordstothenumberof4-lettercodewords?

5to4

3to2

2to1

5to1

6to1

BenandAnnareamong7contestantsfromwhich4semifinalistsaretobeselected.Ofthedifferentpossibleselections,howmanycontainneitherBennorAnn?

5

6

7

14

21

Ifallofthetelephoneextensionsinacertaincompanymustbeevennumbers,andifeachoftheextensionsusesallfourofthedigits1,2,3,and6,whatisthegreatestnumberof

four-digitextensionsthatthecompanycanhave?

4

6

12

16

24

Thereare11womenand9meninacertainclub.Iftheclubistoselectacommitteeof2womenand2men,howmanydifferentsuchcommitteesarepossible?

(A)

120

(B)

720

(C)

1,060

(D)

1,520

(E)

1,980

【概率】

Ifapersonpurchases15ofthe3,000ticketssoldinarafflethatawardsoneprize,whatistheprobabilitythatthispersonwillnotwin?

(A)0

(B) 1

200

(C)

(D)

(E)1

1

2

199

200

Ifa3-digitintegerisselectedatrandomfromtheintegers100through199,inclusive,whatistheprobabilitythatthefirstdigitandthelastdigitoftheintegerareeachequaltoonemorethanthemiddledigit?

(A)

(B)

(C)

(D)

(E)

2

225

1

111

1

110

1

100

1

50

Xavier,Yvonne,andZeldaeachtryindependentlytosolveaproblem.Iftheirindividual

probabilitiesforsuccessare1,

4

1,and

2

5,respectively,whatistheprobabilitythatXavier

8

andYvonne,butnotZelda,willsolvetheproblem?

11

8

7

8

9

64

5

64

3

64

Sixtypercentofthemembersofastudygrouparewomen,and45percentofthosewomenarelawyers.Ifonememberofthestudygroupistobeselectedatrandom,whatistheprobabilitythatthememberselectedisawomanlawyer?

0.10

0.15

0.27

0.33

0.45

Thereisatotalof120marblesinabox,eachofwhichisred,green,blue,orwhite.Ifonemarbleisdrawnfromtheboxatrandom,theprobabilitythatitwillbewhiteis 1andthe

4

probabilitythatitwillbegreenis1.Whatistheprobabilitythatthemarblewillbeeitherred

3

orblue?

(A)1

6

(B)1

4

(C)2

7

(D)1

3

(E)5

12

Acointhatistossedwilllandheadsortails,andeachoutcomehasequalprobability.Whatistheprobabilitythatthecoinwilllandheadsatleastonceontwotosses?

1/4

1/3

1/2

2/3

3/4

Ifacertaincoinis