MATH23.docx

MATH23.docx

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MATH23

Math:

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Q1:

Acertaincompany’sprofitin1996was15percentgreaterthanitsprofitin1995,anditsprofitin1997was20percentgreaterthanitsprofitin1996.Thecompany’sprofitin1997waswhatpercentgreaterthanitsprofitin1995?

A.5%

B.18%

C.33%

D.35%

E.38%

Answer:

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Q2:

Thefunctionfisdefinedforeachpositivethree-digitintegernbyf（n）=2x3y5z,wherex,y,andzarethehundreds,tens,andunitsdigitsofn,respectively.Ifmandvarethree-digitpositiveintegerssuchthatf（m）=9f（v）,thenm-v=

A.8

B.9

C.18

D.20

E.80

Answer:

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Q3:

Alexdepositedxdollarsintoanewaccountthatearned8percentannualinterest,compoundedannually.OneyearlaterAlexdepositedanadditionalxdollarsintotheaccount.Iftherewerenoothertransactionsandiftheaccountcontainedwdollarsattheendoftwoyears,whichofthefollowingexpressesxintermsofw?

A.

B.

C.

D.

E.

Answer:

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Q4:

All48seniorsinacertainhighschooltakeoneoftwoEnglishclasses.Whatistheaverage（arithmeticmean）heightoftheseniorsinthisschool?

（1）Intheschool,theaverageheightoftheseniorsintheEnglishclasswiththelargernumberofstudentsis70inches.

（2）Intheschool,theaverageheightoftheseniorsintheEnglishclasswiththesmallernumberofstudentsis

oftheaverageheightoftheseniorsintheotherEnglishclass.

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:

60°

Theparallelogramshownhasfoursidesofequallength.Whatistheratioofthelengthoftheshorterdiagonaltothelengthofthelongerdiagonal?

A.

B.

C.

D.

E.

Answer:

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Q6:

TheoperationΘisdefinedbyxΘy=

+

forallnonzeronumbersxandy.Ifzisanumbergreaterthan1,whichofthefollowingmustbetrue?

I.xΘ（-z）=0

II.zΘ

=1

III.

Θ

=z

A.Ionly

B.IandIIonly

C.IandIIIonly

D.IIandIIIonly

E.I,II,andIII

Answer:

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Q7:

Iftheaverage（arithmeticmean）of5differentnumbersis12,whatisthemedianofthe5numbers?

（1）Themedianofthe5numbersisequalto

ofthesumofthe4numbersotherthanthemedian.

（2）Thesumofthe4numbersotherthanthemedianisequalto45.

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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Q8:

ThechargeforasingleroomatHotelPis25percentlessthanthechargeforasingleroomatHotelRand10percentlessthanthechargeforasingleroomatHotelG.ThechargeforasingleroomatHotelRiswhatpercentgreaterthanthechargeforasingleroomatHotelG?

A.15%

B.20%

C.40%

D.50%

E.150%

Answer:

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Q9:

IfSisthesumofalltheintegersfrom1to30,inclusive,whatisthegreatestprimefactorofS?

A.3

B.5

C.29

D.31

E.37

Answer:

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Q10:

Isx

（1）Theratioofxtoyis

.

（2）xy>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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Q11:

Lastyear,ifArturospentatotalof$12,000onhismortgagepayments,realestatetaxes,andhomeinsurance,howmuchdidhespendonhisrealestatetaxes?

（1）Lastyear,thetotalamountthatArturospentonhisrealestatetaxesandhomeinsurancewas33

percentoftheamountthathespentonhismortgagepayments.

（2）Lastyear,theamountthatArturospentonhisrealestatetaxeswas20percentofthetotalamountthathespentonhismortgagepaymentsandhomeinsurance.

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:

Thetotalcostofanofficedinnerwassharedequallybykofthenemployeeswhoattendedthedinner.Whatwasthetotalcostofthedinner?

（1）Eachofthekemployeeswhosharedthecostofthedinnerpaid$19.

（2）Ifthetotalcostofthedinnerhadbeensharedequallybyk+1ofthenemployeeswhoattendedthedinner,eachofthek+1employeeswouldhavepaid$18.

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:

Ismbetween35and75?

（1）misbetween40and80.

（2）misbetween50and90.

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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Q14:

Theaverage（arithmeticmean）costperbookforthe12booksonacertaintableiskdollars.Ifabookthatcosts18dollarsisremovedfromthetableandreplacedbyabookthatcosts42dollars,thenintermsofk,whatwillbetheaveragecostperbook,indollars,forthebooksonthetable?

A.k+2

B.k–2

C.12+

D.12–

E.12k–6

Answer:

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Q15:

Thesequencea1,a2,…,an,…issuchthatan=4an–1–3forallintegersn>1.Ifa3=x,thena1=

A.4x–3

B.16x–15

C.

D.

E.

Answer:

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Q16:

Ifkisapositiveinteger,whatistheremainderwhen2kisdividedby10?

（1）kisdivisibleby10.

（2）kisdivisibleby4.

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:

TobeeligibleforretirementbenefitsattheOmegaCorporation,thesumofanemployee’sage,inyears,andthenumberofyearsofemploymentmustbeatleast70.Ifx,wherex<70,isacertainemployee’sagewhenhiredandyistheminimumnumberofyearsofemploymentrequiredfortheemployeetobeeligibleforretirementbenefits,whichofthefollowingequationsrepresentstherelationshipbetweenxandy?

A.xy=70

B.x+y=70

C.2x+y=70

D.x+2y=70

E.2x+2y=70

Answer:

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Q18:

10,000100isequivalenttowhichofthefollowing?

I.（1002）（100100）

II.100200

III.10400

A.None

B.Ionly

C.IIIonly

D.IIandIIIonly

E.I,II,andIII

Answer:

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Q19:

Foreachpositiveintegern,theintegern*isdefinedbyn*=n2+1.Whatisthevalueofthepositiveintegerk?

（1）Whenkisdividedby4,theremainderis1.

（2）18≤k*≤36

A.Statement

（1）ALONEissufficient,butstatement

（2）aloneisnotsufficient.

B.Statement