MATH12.docx
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MATH12
MathSection
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Q1:
ThepopulationofCityXis50percentofthepopulationofCityY.ThepopulationofCityXiswhatpercentofthetotalpopulationofCityXandCityY?
A.25%
B.(331/3)%
C.40%
D.50%
E.(662/3)%
Answer:
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Q2:
Whatisthegreatestprimefactorof2100-296?
A.2
B.3
C.5
D.7
E.11
Answer:
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Q3:
Howmanylitersofapplejuicewereaddedtothecranberryjuiceinacertaincontainer?
(1)Theamountofapplejuicethatwasaddedwas3/2theamountofcranberryjuiceinthecontainer.
(2)Therewere5litersofcranberryjuiceinthecontainer.
A.Statement
(1)ALONEissufficient,butstatement
(2)aloneisnotsufficient.
B.Statement
(2)ALONEissufficient,butstatement
(1)aloneisnotsufficient.
C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.
D.EACHstatementALONEissufficient.
E.Statements
(1)and
(2)TOGETHERareNOTsufficient.
Answer:
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Q4:
Inademographicstudy,thepopulationandtotalincomeofacertainregionwereestimatedfromotherdata,andbothestimateshadlowerandupperlimits.Atthetimeoftheestimates,wasthepercapitaincomefortheregiongreaterthan$16,500?
(1)Thelowerlimitfortheestimateofthepopulationwas330,000people.
(2)Thelowerlimitfortheestimateofthetotalincomewas$5,500,000,000.
A.Statement
(1)ALONEissufficient,butstatement
(2)aloneisnotsufficient.
B.Statement
(2)ALONEissufficient,butstatement
(1)aloneisnotsufficient.
C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.
D.EACHstatementALONEissufficient.
E.Statements
(1)and
(2)TOGETHERareNOTsufficient.
Answer:
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Q5:
Isx<1?
(1)x+1=2x-1
(2)x-3≠0
A.Statement
(1)ALONEissufficient,butstatement
(2)aloneisnotsufficient.
B.Statement
(2)ALONEissufficient,butstatement
(1)aloneisnotsufficient.
C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.
D.EACHstatementALONEissufficient.
E.Statements
(1)and
(2)TOGETHERareNOTsufficient.
Answer:
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Q6:
Aboxcontains10lightbulbs,fewerthanhalfofwhicharedefective.Twobulbsaretobedrawnsimultaneouslyfromthebox.Ifnofthebulbsinboxaredefective,whatisthevalueofn?
(1)Theprobabilitythatthetwobulbstobedrawnwillbedefectiveis1/15.
(2)Theprobabilitythatoneofthebulbstobedrawnwillbedefectiveandtheotherwillnotbedefectiveis7/15.
A.Statement
(1)ALONEissufficient,butstatement
(2)aloneisnotsufficient.
B.Statement
(2)ALONEissufficient,butstatement
(1)aloneisnotsufficient.
C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.
D.EACHstatementALONEissufficient.
E.Statements
(1)and
(2)TOGETHERareNOTsufficient.
Answer:
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Q7:
Thereare11womenand9meninacertainclub.Iftheclubistoselectacommitteeof2womenand2men,howmanydifferentsuchcommitteesarepossible?
A.120
B.720
C.1,060
D.1,520
E.1,980
Answer:
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Q8:
B
AC
Inthefigureshown,thetriangleisinscribedinthesemicircle.IfthelengthoflinesegmentABis8andthelengthoflinesegmentBCis6,whatisthelengthofarcABC?
A.15
B.12
C.10
D.7
E.5
Answer:
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Q9:
If5x=2yandxy≠0,theniswhatpercentofy?
A.2%
B.4%
C.10%
D.40%
E.50%
Answer:
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Q10:
Inthefigureshown,twoidenticalsquaresareinscribedintherectangle.Iftheperimeteroftherectangleis18√2,thenwhatistheperimeterofeachsquare?
A.8√2
B.12
C.12√2
D.16
E.18
Answer:
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Q11:
Theproductoftheunitsdigit,thetensdigit,andthehundredsdigitofthepositiveintegermis96.Whatistheunitsdigitofm?
(1)misodd.
(2)Thehundredsdigitofmis8.
A.Statement
(1)ALONEissufficient,butstatement
(2)aloneisnotsufficient.
B.Statement
(2)ALONEissufficient,butstatement
(1)aloneisnotsufficient.
C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.
D.EACHstatementALONEissufficient.
E.Statements
(1)and
(2)TOGETHERareNOTsufficient.
Answer:
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Q12:
DivisionRofCompanyQhas1,000employees.Whatistheaverage(arithmeticmean)annualsalaryoftheemployeesatCompanyQ?
(1)TheaverageannualsalaryoftheemployeesinDivisionRis$30,000.
(2)TheaverageannualsalaryoftheemployeesatCompanyQwhoarenotinDivisionRis$35,000.
A.Statement
(1)ALONEissufficient,butstatement
(2)aloneisnotsufficient.
B.Statement
(2)ALONEissufficient,butstatement
(1)aloneisnotsufficient.
C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.
D.EACHstatementALONEissufficient.
E.Statements
(1)and
(2)TOGETHERareNOTsufficient.
Answer:
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Q13:
Thesequencea1,a2,…,an,…issuchthatan=2an-1-xforallpositiveintegersn≥2andforcertainnumberx.Ifa5=99anda3=27,whatisthevalueofx?
A.3
B.9
C.18
D.36
E.45
Answer:
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Q14:
BoxWandBoxVeachcontainseveralbluesticksandredsticks,andalloftheredstickshavethesamelength.Thelengthofeachredstickis18incheslessthantheaveragelengthofthesticksinBoxWand6inchesgreaterthantheaveragelengthofthesticksinBoxV.Whatistheaverage(arithmeticmean)length,ininches,ofthesticksinBoxWminustheaveragelength,ininches,ofthesticksinBoxV?
A.3
B.6
C.12
D.18
E.24
Answer:
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Q15:
Ifx≠0,then(x+1/x)2-(x-1/x)2=
A.1/x
B.x
C.1
D.2
E.4
Answer:
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Q16:
Ifm,p,andtarepositiveintegersandm
(1)t–p=p-m
(2)t–m=16
A.Statement
(1)ALONEissufficient,butstatement
(2)aloneisnotsufficient.
B.Statement
(2)ALONEissufficient,butstatement
(1)aloneisnotsufficient.
C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.
D.EACHstatementALONEissufficient.
E.Statements
(1)and
(2)TOGETHERareNOTsufficient.
Answer:
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Q17:
Ifacertaincoinisflipped,theprobabilitythatthecoinwilllandheadsis1/2.Ifthecoinisflipped5times,whatistheprobabilitythatitwilllandheadsuponthefirst3flipsandnotonthelast2flips?
A.3/5
B.1/2
C.1/5
D.1/8
E.1/32
Answer:
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Q18:
Thefunctionfisdefinedbyf(x)=√x–10forallpositivenumbersx.Ifu=f(t)forsomepositivenumberstandu.Whatistintermsofu?
A.√(u+10)
B.(√u+10)2
C.√(u2+10)
D.(u+10)2
E.(u2+10)2
Answer:
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Q19:
y
l
2
-30x
Thegraphofwhichofthefollowingequationsisastraightlinethatisparalleltolinelinthefigureabove?
A.3y–2x=0
B.3y+2x=0
C.3y+2x=6
D.2y–3x=6
E.2y+3x=-6
Answer:
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Q20:
WhatisthetotalnumberofexecutivesatCompanyP?
(1)Thenumberofmaleexecutivesis3/5thenumberoffemaleexecutives.
(2)Thereare4morefemaleexecutivesthanmaleexecutives.
A.Statement
(1)ALONEissufficient,butstatement
(2)aloneisnotsufficient.
B.Statement
(2)ALONEissufficient,butstatement
(1)aloneisnotsufficient.
C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.
D.EACHstatementALONEissufficient.
E.Statements
(1)and
(2)TOGETHERareNOTsufficie