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gmat数学
第一部分数学基础知识
一、代数Algebra
例1比较大小:
.
Thenumberofdistinctpositivefactorsofn14比较大小
例2:
252因子的个数是多少?
例3比较大小:
Aprinternumberedconsecutivelythepagesofabook,beginningwith1onthefirstpage.Innumberingthepage,heprintedatotalof204digits.
Thenumberofpagesinthebook105
例4比较大小:
Inacertaintwo-digitnumber,
theunits'digitistwicethetens'digit.5
Thetens'digit
例5比较大小:
二、描述统计descriptivestatistics
例6比较大小:
某长方形的周长为40,该长方形的最大面积100
例7比较大小:
空间5个点能够构成的直线数目10
例8:
求3,13,17的标准方差。
三、排列组合combination、概率probability
排列组合排列计算公式:
,组合计算公式:
。
概率
例9:
假如世界杯比赛共有32支球队,分成8个组,每组4个队,每组前两名出线,然后成对进行淘汰赛,直至决赛决出冠军,并且淘汰队不参加比赛,从中间任选出一场比赛观看是半决赛的机会有多大?
例10:
有4对男女,每对中有1男1女,从每对中选出1人,选出2男2女的概率是多少?
例11:
有3个打字员为4家公司服务,如果4家公司各有1份文件要录入,他们只能找到这3个打字员录入,且各公司对打字员的要求是随机的。
问每个打字员都收到文件的概率是多少?
例12:
两个骰子,六面的值分别为1,2,3,4,5,6,投掷这两个骰子,问其中一个骰子的值比另一个的值大2的概率为多大?
四、几何(Geometry)
例13比较大小:
RisapointintherectangularcoordinatesystemandOR=5.
Thex-coordinateofpointR54.9
例14比较大小:
(RS)2+(ST)2(RT)2
例15:
Accordingtothegraphabove,whenx=3,yismostnearly:
(A)-1(B)-1/2(C)0(D)1/2(E)1
五、文字题(WordProblem)
1、利息问题(interest)
单利simpleinterest复利compoundinterest
例16:
If$8000isinvestedat6percentsimpleannualinterest,howmuchinterestisearnedafter3months?
例17:
If$10,000isinvestedat10percentsimpleannualinterest,compoundsemiannually,whatisthebalanceafter1year?
2、折扣问题(discount)
例18:
Thepriceofanitemisdiscountedby20percentandthenthisreducedpriceisdiscountedbyanadditional30percent.Thesetwodiscountsareequaltoanoveralldiscountofwhatpercent?
3、英美常识问题
GRE难题解析
例1:
Onacertainnumberline,if-7isadistanceof4fromnand7isadistanceof18fromn,thenn=?
(A)25(B)11(C)-3(D)11(E)-11
例2:
Thediagramrepresentsarectangulargarden.Theshadedregionsareplantedinflowers,andtheunshadedregionisawalk2feetwide.Allanglesarerightangles.
Thesumoftheareasofthe2,800squarefeet
shadedregions
例3:
Themapshowstheonlyroadsthatconnectthefourtownsandshowsthedistancealongeachroad.
TheroaddistancebetweenAustenandSeburg
TheroaddistancebetweenCoaltownandWoodland
例4:
Howmanypositiveintegerslessthan20areequaltothesumofapositivemultipleof3andapositivemultipleof4?
(A)Two(B)Five(C)Seven(D)Ten(E)Nineteen
例5:
Whichofthefollowingsymbolsshouldbesubstitutedfor
tomakebothofthestatementstrueforallintegersnsuchthat-2(A)≤(B)<(C)=(D)>(E)≥
4-n
6
4-n
5
例6:
Inasoccerleague,Iftherewere10teamsandeachteamplayedeachoftheotherteams16times,howmanygamesdideachteamplay?
(A)144(B)140(C)134(D)125(E)106
例7:
(NOTE:
DRAWNTOSCALE)
POPULATIONOFTHEU.S.AGE55ANDOVER
1984ANDPROJECTIONSFOR1995
INCOMEDISTRIBUTIONFORPOPULATION
OFTHEU.S.AGE55ANDOVER,1984
In1984medianincomeforapersoninthe55~64agecategorywasinwhichofthefollowingintervals?
(A)lessthan$10,000(B)$10,000~$19,999(C)$20,000~$24,999(D)$25,000~$34,999(E)$35,000~$49,999
例8:
Asampleofemployeesweretestedondata-entryskillsforonehour,andthenumberoferrors(x)theymadeandthepercentofemployees(p)makingxerrorswererecordedasfollows.
Numberoferrorx
0
1
2
3
4
5
6ormore
PercentofemployeesP
2%
5%
10%
24%
14%
20%
22%
whatwasthemediannumberoferrorsinthesample?
(A)3(B)3.5(C)4(D)4.5
(E)Itcannotbedeterminedfromtheinformationgiven.
例9:
d=7.56872andDisthedecimalexpressionfordroundedtothenearestthousandth.
ThenumberofdecimalplacewheredandDdiffer
4
例10:
Inacertaincountry,apersonisbornevery3secondsandapersondiesevery10seconds.Therefore,thebirthanddeathratesaccountforapopulationgrowthrateofonepersonevery
例11:
Ofthepositiveintegersthataremultiplesof30andarelessthanorequalto360,whatfractionaremultiplesof12?
(A)1/6(B)1/5(C)1/3(D)2/5(E)1/2
8inches
例12:
ThefigureshowsalargesquareformedbyfittingthreeL-shapedtilesandonesmallsquaretiletogether.Ifarectangularfloor10feetby12feetistobetiledinlargesquaresofthisdesign,howmanyL-shapedtileswillbeneeded?
(A)810(B)405(C)270(D)135(E)45
8inches
例13:
Thedailyrateforahotelroomthatsleeps4peopleis$39foronepersonandxdollarsforeachadditionalperson.If3peopletaketheroomforonedayandeachpays$21fortheroom,whatisthevalueofx?
(A)6(B)8(C)12(D)13(E)24
例14:
Apositiveintegerwithexactlytwodifferentdivisorsgreaterthan1mustbe
(A)aprime(B)aneveninteger(C)amultipleof3
(D)thesquareofaprime(E)thesquareofanoddinteger
例15:
x>z,y>zx+yz
例16:
x>yandxy≠0(x+y)/x(x+y)/y
例17:
2AF=AB=BD=DE=AE
ThesumoftheareaoftriangularregionABFandareaoftriangularregionCDE
TheareaofrectangularregionBCEF
例19:
Thereare1200representstoapoll,eachfavoringtheirpreferenceforcandidatesA,B,andC.54%favoredA,48%favoredB,and42%favoredC,andthereis30%favoredbothAandB.What’sthelargestpossiblenumberofrepresentsfavoringc,butnotC&B,norC&A?
(A)25%(B)30%(C)28%(D)38%(E)40%
例20:
Outof100ladiesattendingthechurchfete,85hadawhitehandbag;75hadblackshoes;60carriedanumbrella;90worearing,Howmanyladiesmusthavehadallfouritems?
(A)15(B)35(C)5(D)10(E)25
例21:
Inaninsurancecompany,eachpolicyhasapaperrecordandanelectricrecord.Forthosepolicieshavingincorrectpaperrecord,60%alsohavingincorrectelectricrecord;Forthosepolicieshavingincorrectelectricrecord,75%alsohavingincorrectpaperrecord.3%ofallpolicieshavebothincorrectpaperandincorrectelectricrecord.Ifwerandomlypickoutonepolicy,what’stheprobabilitythattheonehavingbothcorrectpaperandcorrectelectricrecord?
(A)0.80(B)0.94(C)0.75(D)0.88(E)0.92
ak
100
200
300
400
500
pk
0.10
0.25
0.20
0.25
0.20
例22:
Ifinanexperimenttheprobabilitiesofobtainingthevaluesa1,a2,a3,a4,a5arep1,p2,p3,p4,p5,respectively,thentheexpectedvalueisdefinedasa1p1+a2p2+a3p3+a4p4+a5p5.Forthevaluesandtheircorrespondingprobabilitiesinthetableabove,whatistheexpectedvalue?
(A)350(B)320(C)300(D)270(E)250
例23:
Thestandarddeviationofthesamplemeasurements0,2,4,6,and8
Thestandarddeviationofthesamplemeasurements1,3,5,7,and9
例24:
Whatisthetotalnumberofdifferent5-digitnumbersthatcontainallofthedigits2,3,4,7and9andinwhichnoneoftheevendigitsoccurnexttoeachother?
(A)72(B)100(C)120(D)60(E)48
例25:
Wateristobepouredatarateof2.5gallonsperminuteintoa500-gallontankthatinitiallycontains50gallonsofwater.
Thepercentofthetank'scapacitythatwillbe
filled1hourafterwaterbeginstobepouredin
60percent
例26:
Inthefigure,ifx,y,andzareintegerssuchthatx(A)59and91(B)69and135(C)91and178(D)120and135(E)120and178
例27:
Thefigureshowsthedimensionsofrectangularboxthatistobecompletelywrappedwithpaper.Ifasinglesheetofpaperistobeusedwithoutpatching,thenthedimensionsofthepapercouldbe
(A)17inby25in(B)21inby24in(C)24inby12in
(D)24inby14in(E)26inby14in
例28:
Inthetable,whatistheleastnumberoftableentriesthatareneededtoshowthemileagebetweeneachcityandeachoftheotherfivecities?
(A)15(B)21(C)25(D)30(E)36
例29:
Astorecurrentlychargesthesamepriceforeachtowelthatitsells.Ifthecurrentpriceofeachtowelwastobeincreasedby$1,10fewerofthetowelscouldbeboughtfor$120,excludingsalestax.Whatisthecurrentpriceofeachtowel?
(A)$1(B)$2(C)$3(D)$4(E)$12
注:
1. a only if b 表示a==>b
2. a if only b 表示b==>a
3. 2/3 as many A as B 是:
A为B的2/3
4. twice as many A as B 是:
A为B的2倍
GRE数学常用符号及术语
一.数学中常用符号
+:
plus X:
multiply
-:
subtract ÷:
divide
V~:
square root |...|:
absolute value
=:
is equal to =/=:
is not equal to
>:
is greater than <:
is less than
//:
is parallel to _|_:
is perpendicular to
>=:
is greater than or equal to (或 no less than)
<=:
is less than or equal to (或no more than)
二.表达相应数目的前缀
1:
uni-,mono- 2:
bi-,du-,di- 3:
tri-,ter-, 4:
tetra-,quad-, 5:
penta-,quint,
6:
hex-,sex-, 7:
sept-,hapta-, 8:
oct, 9:
enn-, 10:
dec-,deka-,
三.数学中常用单词术语
abscissa
横坐标
absolutevalue
绝对值
acuteangle
锐角
adjacentangle
邻角
addition
加
algebra
代数
altitude
高
anglebisector
角平分线
arc
弧
area
面积
arithmeticmean
算术平均值(总和除以总数)
arithmeticprogression
等差数列(等差级数)
arm
直角三角形的股
at
总计(乘法)
average
平均值
base
底
becontainedin
位于...上
bisect
平分
center
圆心
chord
弦
circle
圆形
circumference
圆周长
circumscribe
外切,外接
clockwise
顺时针方向
closestapproximation
最相近似的
combination
组合
commondivisor
公约数,公因子
commonfactor
公因子
complementaryangles
余角(二角和为90度)
Compositenumber
合数(可被除1及本身以外其它的数整除)
concentriccircle
同心圆
cone
圆锥(体积=1/3*∏*r*r*h)
congruent
全等的
consecutiveinteger
连续的整数
coordinate
坐标的
cost
成本
counterclockwise
逆时针方向
cube
1.立方数
2.立方体(体积=a*a*a 表面积=6*a*a)
cylinder
圆柱体
decagon
十边形
decimal
小数
decimalpoint
小数点
decreased
减少
decreaseto
减少到
decreaseby
减少了
degree
角度
define
1.定义2.化简
denominator
分母
denote
代表,表示
depreciation
折旧
distance
距离
distinct
不同的
dividend
1.被除数2.红利
dividedevenly
被