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》由会员分享,可在线阅读,更多相关《数量关系解题技巧数学运算.docx(19页珍藏版)》请在冰豆网上搜索。
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)
Icarefullycollateddocuments,documentsfromthenetwork
Ionlycollectandsortout
Ifthereisanymistake
Pleasecheckityourself!
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