数量关系解题技巧数学运算.docx

数量关系解题技巧数学运算.docx

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数量关系解题技巧数学运算

数量关系解题技巧—数学运算（Mathematicalskillsforsolvingquantitativerelations）

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Mathematicalskillsforsolvingquantitativerelations

Thesecondtypeofquestioninquantityrelationismathematicaloperation

Thesequestionsareusuallyshort

Itsknowledgecontentandprinciplesaregenerallyrelativelysimple

Butbecauseofthetimelimit

Soit'squickandaccurate

Weshouldpayattentiontothefollowing4aspects:

first,mastersomecommonlyusedmathematicalskills,methodsandlaws

Usesimplealgorithmsasmanyaspossible

Twoistoaccuratelyunderstandandanalyzethetext

Correctlygraspthemeaningofthequestions

Threeisfamiliarwithacertaintypeofquestionsandproblem-solvingmethods

Fouristostrengthentraining

Increasesensitivitytonumbers

Andmemorizesomebasicnumbers

Herearesomeofthemoretypicalquestions

It'sveryhelpfultoimprovetheperformance

First,thequestiontypeissolvedbyusingthemethodof"roundingandrounding"

Example:

thevalueof5.2+13.6+3.8+6.4is

A.29B.28C.30D.29.2

TheanswerisA

"Roundingmethod"isthemostcommonlyusedmethodinsimplecalculation

Themethodisbasedonthecommutativelawandtheassociativelaw

Makenumbersintointegers

Calculateagain

It'smucheasier

Two.Usingthemantissaestimationmethodtosolvethequestiontype

Example:

thevalueof425+683+544+828is

A.2488B.2486C.2484D.2480

TheanswerisD

Ifthenumbersarelarger

Thereseemstobenolawtofollow

Youcanfirstexaminewhetherthemantissaofanumberofanswersisunique

Ifitis

Thenyoucanusethenumberofdigitstocalculatethemantissa

Andthenfindtheonlycorrespondingitem

Theabovequestions

Addingthenumberofeachbit=5348=20

Themantissais0

SoyoucanquicklypicktherightanswerforD

Three,usingthe"benchmarknumber"methodtosolvetheproblemtype

Example:

1997+1998+1999+2000+2001

A.9993B.9994C.9995D.9996

TheanswerisC

Whenmorethantwonumbersareaddedtogether

Andwhentheirvaluesareclose

Youcanfindanintermediatenumberasabenchmark

Thenaddeachaddendandbenchmarkdifference

Soastogettheirsums

Inthisquestion

Select2000asthebasenumber

Othernumbersare3lessthan2000

2less

1less

Andmorethan1

Therefore,thesumoffivenumbersis9995

Thismethodcanalsobeusedtofindthearithmeticmeanofseveralsimilarnumbers

1.proportionaldistributionproblem

Example:

thetotalnumberofstudentsingradeoneortwoandgradethreeinaschoolis450

Theproportionofstudentsinthreegradesis2:

3:

4

Howmanystudentsarethereinthemostnumberofclasses?

A.100B.150C.200D.250

TheanswerisC

Answerthisquestion

Youcancountthetotalas234=9

Thelargestnumberofthemisdefinitelythethreegradeof4/9

Sotheansweris200people

2.mileproblem

Example:

someonewalkingfromoneplacetoanother

Afterthewholejourneyof2/5

It's2.5kilometersfromthemidpoint

HowmanykilometersisthedistancebetweenaandB?

A.15B.25C.35D.45

TheanswerisB

Themidpointofthewholejourneyis2.5/5ofthewholecourse

Thedistancefrom2/5is0.5/5

Thisroadis2.5kilometers

Soyoucanquicklycalculatetheentirelengthof25kilometers

3.engineeringproblems

Example:

aproject

Ateamdoitalone

15daystofinish;Bteamdoitalone

10daystocomplete

Twoteamscooperation

Howmanydaysisitgoingtobedone?

A.5days,B.6days,C.7.5days,D.8days

TheanswerisB

Thisquestionisanengineeringproblem

Thegeneralquantitativerelationandstructureofengineeringproblemsare:

Totalwork

________=workingtime

Workefficiency

Wecanthinkofthewholeprojectas"1""

Worktocompletetheworkefficiencyfor1/nnthatday,thetwogroupstogethertocompletetheworkefficiencyfor1/n11/n2,accordingtothisformulacanquicklygettheanswerfor6days

inaddition

Therearemanyvariationsinengineeringproblems

Suchaspondirrigationproblemsandsoon

Youcanusethiskindofthinkingtosolveproblems

4.plantingtrees

Example:

ifyouplantatreeatadistanceofonemeter

Howmanytreesareplantedonthe345meterroad?

A.343B.344C.345D.346

TheanswerisD

Thistopicshouldpayattentiontomoreanalysisoftheactualsituation

Asthestartingpointandendpointtoconsidertwotoplanttrees

Sotheansweris346

1,8754896x48933=（D）

A.428303315966B.428403225876C.428430329557D.428403325968

Solvingproblem:

multiplyingtwoproductfactorsintoonedigitnumber

Thenumberofdigitsshouldbe8

ExcludingA,B,C

2,3543278x2221515=（D）

A.7871445226160B.7861445226180C.7571445226150D.7871445226170

Solvingproblem:

multiplyingthetennumbersoftwoproductfactors

Theproductshouldbe70

ExcludingA,B,C

3,36542x42312=（D）

A.1309623104B.1409623104C.1809623104D.

Nosolutionisgiven:

multiplyingthefirsttwodigitsoftwoproductfactors（36x42）

Theproductshouldbe1512

Thereisno"15"inthefirsttwodigitsofeachoption

therefore

There'snorightanswer

4,50x62x70x82=（D）

A.12722410B.12822340C.17892520D.17794000

SolutionThinking:

from50x70toknowthatthemantissahastwozeros

ExcludingA,B,C

D

5,125x618x32x25=（D）

A.61708000B.61680000C.63670000D.61800000

Solutions:

125x618x32x25=（125x8）x（4x25）x618=61800000

6,86x84=（D）

A.7134B.7214C.7304D.7224

SolutionThinking:

86x84=（8+1）800+（4x6）=7224

7,99x101=（D）

A.9099B.9089C.9189D.9999

SolutionThinking:

99x101=（100-1）（100+1）=1002-1=9999

8,twotruckstotalloadof500tons

Thefirstoneis50tonsmorethansecondvehicles

ThefirstandthesecondareDtonsrespectively

A.（265

235）B.（245）

295）C.（285）

215）D.（275）

225）

Solution:

don'tuse（500+50）,2forthefirstcarloadingalgorithm

Accordingtotheproblemandquicklyfindoutaslongasconsistentwiththedifferenceofthenumberofpersons

9,thestoresoldtwogoodsfor3000yuaneach

Theprofitandlosswereboth20%

Thentheshopshouldbe（D）

A.earn500yuan,B.deficit300yuan,C.flat,D.deficit250yuan

SolutionThinking:

quicklycalculatethecostofmaking20%ofgoodsshouldbe2500yuan

And20%ofthecostofgoodsiscertainlynotmorethan2500yuan

AandCwereexcludedimmediately

Andthenconvertedfromthelossoftwo,thecostis3750yuan

thus

750yuan-500yuanis250yuan

10,todayisTuesday

55x50dayslater（A）

A.Monday,,Tuesday,C.,Wednesday,D.,Thursday,B.

Problemsolving:

from55to7multiples,minus1,50is7multiplesplus1

Quicklaunchforlessthan1days

Ifyouuse55x50/7=3966

Theanswerisalsoavailable

Butittakesmoretime

11,20bakersbake200loavesofbreadin2hours

Atthisrate

2bakerscanbake100loavesofbreadinDhours

A.20B.15C.12D.10

Problemsolving:

first,ask20masterstobake100loavesofbreadin1hours

10timesfrom20masters,10timesof2masters,and10timesof1hours,thatis,twohours

12,theexaminationpaperonthejudgmenttodo1points

Wrongdeduction1points

Zhanggot6pointsonthejudgmentquestion

HeshouldhavedoneBin10subjects

A.1B.2C.3D.4

Problemsolvingthinking:

10questionsanswered10points

Notonlydidnotscorewrongpoints,butdeducted1points

Twoquestionsshouldbedonewrong

13,48and108ofthegreatestcommondivisoris（D）

A.6B.8C.24D.12

Solution:

dreams48=2x2x3x4

108=2x2x3x3x3

*（48,

108）=2x2x3=12

14,if[5,7]=74

[4,6]=52

[3,5]=34

Then[0,4]=（D）

A.53B.51C.26D.16

Thesolutionoftheproblemisthatthenumberoftheinnersolitarynumbersdecreasessuccessively

Andviceversa

A,BandCcanbeexcludedimmediately

inaddition

Canbetheanswer（and）thatthebracketstwonumbersaresquare

15,theprovisionsofacompany

Wherethepurchaseofmorethan1000yuanofgoods

Youcanenjoy30percentoffprivileges

Thereare4200yuantopurchase

Canbuytheoriginalpriceof（B）yuanofgoods

A.7000B.6000C.5500D.5400

Problemsolvingidea:

thedecompositionof4200yuaninto6700yuancanbelaunched6000yuan

16.Dividethe10applesintothreepiles

Eachheapcontainsatleast1

Proper（A）seedclassification

A.8B.9C.10D.11

Solvingproblems:

listbyenumerationmethod

Quicklyremoveduplicates

17,theannualinterestrateofbankdepositsis2.5%

Interesttaxpayable20%

Original10thousandyuan1yearsperiod

Theactualinterestisnolonger250yuan

Inordertomaintainthisinterestincome

Thesameperioddepositsshouldbeincreasedto（C）yuan

A.15000B.20000C.12500D.30000

18,theannualinterestrateofbankdepositsis2.5%

Interesttaxpayable20%

Original10thousandyuan1yearsperiod

Theactualinterestisnolonger250yuan

Inordertomaintainthisinterestincome

Thesameperioddepositsshouldbeincreasedto（C）yuan

A.15000B.20000C.12500D.30000

SolutionThinking:

compensationof20%ofinteresttaxshouldincrease25%deposit

Soitshouldbeaddedto:

10000+2500=12500（element）

19,thereare80documents

A,B,C3peopleparticipatedinthetreatment

Bthan8copies

Butit'sjusta3/5ofthenumberofcopies

Theratioofthenumberofdocumentstheydealtwithwas（D）

A.2:

4:

6B.2:

4:

5C.2:

5:

8D.2:

3:

5

Solution:

sincethefilesareprocessedindividually,theyareintegers

Then,ifthesumofthethreeratioscannotbedividedinto80,thefractionwillbeeliminated

Itshouldberuledout

20,someonewitha15%offdiscounttobuyabicycle,save60yuan

Hepaid（D）yuan

A.350B.380C.400D.340

Thinking:

toobtaintheoriginalpriceby60,15/100

Deduct60yuanagain

ItcanalsobeworkedoutquicklyfromC-D=60

21,the