GMAT数学讲义

GMAT数学教学提纲曹文龙1课程内容和安排1.LectureOneGMAT数学考试介绍2.LectureTwoDataSufficiency题型3.LectureThree基本数论4.LectureFour代数计算5.LectureFive初等几何6.LectureSix文字应用题2LectureOneGMAT数学考试介绍•LectureOneGMAT数学考试介绍•本节课授课要点：••考试特点••参考材料••GMAT数学考分换算••GMAT高分换算3考试特点75min答完37道题满分51分错3个以内---51分错5个以内---50分错7个以内---49分（不准确）4参考资料•OG（官方指南）（易）•陈向东GMAT数学高分突破•PREP模考软件——破解版（难）•机经5数学51+语文31~33分=700分6LectureTwoGMAT数学考试题型本节课授课要点：•PS题型——ProblemSolving•DS题型——DataSufficiency1.PS题型——ProblemSolving机考，5选1单选题2.DS题型——DataSufficiency72.1形式-DS例题TomandJackareinalinetopurchasetickets.（题干）Howmanypeopleareintheline?（问题）（1）Thereare20peoplebehindTomand20peopleinfrontofJack.（2）Thereare5peoplebetweenTomandJack.（条件）8-DS选项（固定选项）(A)Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.(B)Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.(C)BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.(D)EACHstatementALONEissufficient.(E)Statement(1)and(2)TOGETHERareNOTsufficient.92.2DS答题步骤从问句切入问句类型：•数值计算——特殊疑问句（吃的啥）答案：确定唯一实数解•判断是非——一般疑问句（吃了吗）答案：“YES”或者“NO”10例题1.1：Whatisthevalueofx?3x=15唯一解充分5x30不唯一解不充分11例题1.2：TomandJackareinalinetopurchasetickets.Howmanypeopleareintheline?(1)Thereare20peoplebehindTomand20peopleinfrontofJack.(2)Thereare5peoplebetweenTomandJack.122.2.2一般疑问句答案：明确回答”YES”或者”NO”.充分：完全符合或者完全不符合Question提出的内容，即能理直气壮回答”YES”或者”NO”，不留任何余地的Statement.不充分：不完全符合Question提出的内容，即只能心虚回答”Yes,but…”或者”No,but…”，及其它一切无法判断结果的Statement.13例题1.3：Isxequalto1?(1)x2=1(2)x2=414例题1.4：体会下列两个Question的区别.Thereareeightballsinthepocket.Question1:Arealltheballsinthepocketred?充分：”YES”:所有的球都是红色的”NO”:有任何一球是其他颜色Question2:Arethereanyredballsinthepocket?充分：”YES”:有任何一球是红色的”NO”:所有的球都不是红色的15Question1:Arealltheballsinthepocketred?Question2:Arethereanyredballsinthepocket?Statement1:Threeballsareremoved;whosecolorsarebrown,green,andred,respectively.Statement2:Threeballsareremoved;whosecolorsarebrown,green,andyellow,respectively.Statement3:Threeballsareremoved;whosecolorsarered,red,andred,respectively.16牢记：当分析Statement(1)时，不要预测Statement(2)；当分析Statement(2)时，确信忘记Statement(1)；17例1.5：Eachpersononacommitteewith40membersvotedforexactlyoneof3candidates,F,G,orH.DidCandidateFreceivethemostvotesfromthe40votescast?(1)candidateFreceived11ofthevotes.(2)candidateHreceived14ofthevotes18LectureThree基本数论本节课授课要点：•奇偶数•因数与质因数•最大公约数与最小公倍数•余数•小数、分数与科学计数法•比率与比例191.奇数与偶数(OddandEvenNumbers)注意：零也是个普通的偶数奇数+奇数=偶数奇数×奇数=奇数偶数+偶数=偶数奇数×偶数=偶数奇数+偶数=奇数偶数×偶数=偶数两数同奇或同偶相加减等于偶数两数奇偶不同相加减等于奇数两数相乘为奇数则都为奇数两数相乘为偶数则至少有一个为偶数202.多个整数之和为奇数——其中包含奇数个奇数多个整数之和为偶数——其中包含偶数个奇数多个整数之积为奇数——全部都是奇数多个整数之积为偶数——其中包含至少一个偶数211.Ifxandyareintegersandxy2isapositiveoddinteger,whichofthefollowingmustbetrue?Ⅰ.xyispositive.Ⅱ.xyisodd.Ⅲ.x+yiseven.(A)Ⅰonly(B)Ⅱonly(C)Ⅲonly(D)ⅠandⅡonly(E)ⅡandⅢonly22例题2.1：Isxaneveninteger?(1)xisthesquareofaninteger.(2)xisthecubeofaninteger.23例2.2：Ifaandbarepositiveintegerssuchthata－banda/barebothevenintegers,whichofthefollowingmustbeanoddintegers?(A)a/2(B)b/2(C)(a+b)/2(D)(a+2)/2(E)(b+2)/224【因数与质因数(FactorsandPrimeFactors)】要特别记住：1不是质数，也不是合数。2是唯一一个偶质数251.If,andifx=–1,andnisthesumofthefirst404primenumbers,theny=(A)–2(B)–1(C)0(D)1(E)226例题2.3：Ifyisthesmallestpositiveintegersuchthat3,150multipliedbyyisthesquareofaninteger,thenymustbe(A)2(B)5(C)6(D)7(E)1427例题2.4：Howmanydifferentprimenumbersarefactorsofthepositiveintegern?(1)Fourdifferentprimenumbersarefactorsof2n.(2)Fourdifferentprimenumbersarefactorsofn2.28例题2.5：Howmanyfactorsdoes360have?(A)24(B)36(C)48(D)120(E)36029303.最大公约数与最小公倍数(GreatestCommonDivisorsandLeastCommonMultiples)31两个数的最大公约数与最小公倍数的求解方法：(1)将两个数分别各自分解质因数(2)每一个质数，取较小的指数，相乘得到最大公约数每一个质数，取较大的指数，相乘得到最小公倍数323334例2.8：IfMistheleastcommonmultipleof90,196,and300,whichofthefollowingisNOTafactorofM?(A)600(B)700(C)900(D)2,100(E)4,9003536例题2.9：Ifpositiveintegerxisamultipleof6andpositiveintegeryisamultipleof14,isxyamultipleof105?(1)xisamultipleof9.(2)yisamultipleof25.37例题2.10：Threesortsofjuicesareservedataparty.Every2guestsshareabottleofapplejuice,every3guestsshareabottleoflemonevery4guestsshareabottleoforangejuice.If65bottlesofjuicesaredrunkofffinally,howmanyguestsareatthisparty?(A)12(B)24(C)36(D)48(E)60384.余数(Remainders)注意：余数可以是零3除以6商为0余3涉及余数的运算多使用枚举，即代数字39例题2.11：Whatistheremainderwhenthepositivexisdividedby8?(1)Whenxisdividedby12,theremainderis5.(2)Whenxisdividedby18,theremainderis11.40例2.12：Whatisthesumoftheremainderswhenthefirst40positiveintegersaredividedby6?(A)96(B)100(C)120(D)132(E)13641例:2.13：Ifnisapositiveinteger,whatistheremainderwhen38n+3+2isdividedby5?(A)0(B)1(C)2(D)3(E)442常见底数幂运算个位数总结：底数为2的幂运算的个位数以2，4，8，6循环底数为3的幂运算的个位数以3，9，7，1循环底数为4的幂运算的个位数以4，6循环底数为7的幂运算的个位数以7，9，3，1循环底数为8的幂运算的个位数以8，4，2，6循环底数为9的幂运算的个位数以9，1循环43【连续数(ConsecutiveNumbers)】任何连续N个整数的乘积必然是N的倍数2个连续整数之积至少是2的倍数.3个连续整数之积至少是6的倍数.4个连续整数之积至少是24的倍数.44例题2.14：Ifnisanintegergreaterthan6,whichofthefollowingmustbedivisibleby3(A)n(n+1)(n–4)n(n+1)(n-1-3)=n(n+1)(n-1)–3n(n+1)(B)n(n+2)(n–1)n(n+2)(n+1-2)=n(n+1)(n+2)-2n(n+2)(C)n(n+3)(n–5)(D)n(n+4)(n–2)(E)n(n+5)(n–6)45例题2.15：TheproductoftwoconsecutivepositiveintegersCANNOTbe(A)aprimenumber1*2(B)divisibleby1111*12(C)amultiple