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1.Ifa2=12,thena4=

A.144

B.72

C.36

D.24

E.16

2.Ifniseven,whichofthefollowingcannotbeodd?

In+3

II3n

IIIn2-1

A.Ionly

B.IIonly

C.IIIonly

D.IandIIonly

E.I,IIandIII

3.Onesideofatrianglehaslength8andasecondsidehaslength5.Whichofthefollowingcouldbetheareaofthetriangle?

I24

II20

III5

A.Ionly

B.IIonly

C.IIIonly

D.IIandIIIonly

E.I,IIandIII

4.Acertainanimalinthezoohasconsumed39poundsoffoodinsixdays.Ifitcontinuestoeatatthesamerate,inhowmanymoredayswillitstotalconsumptionbe91pounds?

A.12

B.11

C.10

D.9

E.8

5.Aperfectcubeisanintegerwhosecuberootisaninteger.Forexample,27,64and125areperfectcubes.Ifpandqareperfectcubes,whichofthefollowingwillnotnecessarilybeaperfectcube?

A.8p

B.pq

C.pq+27

D.-p

E.(p-q)6

6.Whatisthelengthofthelinesegmentinthex-yplanewithendpointsat(-2,-2)and(2,3)?

A.3

B.√31

C.√41

D.7

E.9

7.nisanintegerchosenatrandomfromtheset

{5,7,9,11}

pischosenatrandomfromtheset

{2,6,10,14,18}

Whatistheprobabilitythatn+p=23?

A.0.1

B.0.2

C.0.25

D.0.3

E.0.4

8.Adressonsaleinashopismarkedat$D.Duringthediscountsaleitspriceisreducedby15%.Staffareallowedafurther10%reductiononthediscountedprice.IfastaffmemberbuysthedresswhatwillshehavetopayintermsofD?

A.0.75D

B.0.76D

C.0.765D

D.0.775D

E.0.805D

9.Allthedotsinthearrayare2unitsapartverticallyandhorizontally.Whatisthelengthofthelongestlinesegmentthatcanbedrawnjoininganytwopointsinthearraywithoutpassingthroughanyotherpoint?

A.2

B.2√2

C.3

D.√10

E.√20

10.IftheradiusofthecirclewithcentreOis7andthemeasureofangleAOBis100,whatisthebestapproximationtothelengthofarcAB?

A.9

B.10

C.11

D.12

E.13

1.CorrectAnswer:A

Explanation:

a4=a2xa2=12x12=144

2.CorrectAnswer:B

Explanation:

IncaseI,evenplusoddwillgiveodd

IncaseII,oddtimesevenwillgiveeven

IncaseIIIevensquarediseven,andevenminusoddisodd.

(Youcancheckthisbyusinganeasyevennumberlike2inplaceofn)

OnlycaseIIcannotbeodd.

3.CorrectAnswer:D

Explanation:

Themaximumareaofthetrianglewillcomewhenthegivensidesareplacedatrightangles.Ifwetake8asthebaseand5astheheightthearea=x8x5=20

Wecanaltertheanglebetweenthesidestomakeitlessormorethan90,butthiswillonlyreducethearea.(Drawitoutforyourself).Hencetheareacanbeanythinglessthanorequalto20.

4.CorrectAnswer:E

Explanation:

Foodconsumedperday=39/6.

Intheremainingdaysitwillconsume91-39pounds=52pounds

Nowdividethefoodbythedailyconsumptiontofindthenumberofdays

52/(39/6)=52x(6/39)=8

5.CorrectAnswer:C

Explanation:

Aperfectcubewillhaveprimefactorsthatareingroupsof3;forexample125hastheprimefactors5x5x5,and64x125willalsobeacubebecauseitsfactorswillbe4x4x4x5x5x5

Considertheanswerchoicesinturn.

8isthecubeof2,andpisacube,andsotheproductwillalsobeacube.

pqwillalsobeacubeasshownabove.

pqisacubeandsois27,buttheirsumneednotbeacube.Considerthecasewherep=1andq=8,thesumofpqand27willbe35whichhasfactors5x7andisnotacube.

-pwillbeacube.

Sincethedifferencebetweenpandqisraisedtothepowerof6,thisexpressionwillbeacube(withcuberoot=differencesquared).

6.CorrectAnswer:C

Explanation:

Sketchadiagramandcalculatethedistance(hypotenuseofarighttriangle)usingPythagorastheorem.

Verticalheightoftriangle=5;horizontalside=4;hypotenuse=√(25+16)=√41

7.CorrectAnswer:A

Explanation:

Eachoftheintegersinthefirstsetcouldbecombinedwithanyfromthesecondset,givingatotalof4x5=20possiblepairs.

Ofthesethecombinationsthatcouldgiveasumof23are(5+18),and(9+14)

Thismeansthattheprobabilityofgettingasumof23is2/20=1/10

8.CorrectAnswer:C

Explanation:

Ifthepriceisreducedby15%,thenthenewpricewillbe0.85D

Ifthisnewpriceisfurtherreducedby10%,thediscountedpricewillbe0.9x0.85D=0.765D

9.CorrectAnswer:E

Explanation:

Thelongestlinesegmentthatcanbedrawnwithoutpassingthroughanydotsotherthanthoseatthebeginningandendofthesegment,suchalinecouldgofromthemiddledotinthetoprowtoeitherthebottomleftorrightdot.Inanycasethesegmentwillbethehypotenuseofarighttrianglewithsides2and4.UsingPythagorastheoremthehypotenusewillbe√(22+42)=√20

10.CorrectAnswer:D

Explanation:

Iftheradiusis7,thecircumference=14π

Thelengthofthearcis100/360ofthecircumference

Takingπas22/7weget

(100x14x22)/(360x7)whichreducesto440/36=12.22(i.e.approx.12)

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