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                      【盤點】GMAT數學必須掌握的知識點 | 申友GMAT

                      瀏覽次數:351 日期:2019-05-29 17:41:45
                      GMAT數學有很多需要大家掌握的知識點,比如集合。集合是指具有某種特定性質的具體的或抽象的對象匯總而成的集體。其中,構成集合的這些對象則稱為該集合的元素。

                      今天,由申友GMAT的Helen老師來為大家帶來GMAT數學知識盤點。


                      一、集合Sets


                      集合是指具有某種特定性質的具體的或抽象的對象匯總而成的集體。其中,構成集合的這些對象則稱為該集合的元素。

                      并集(union):給定兩個集合A,B,把他們所有的元素合并在一起組成的集合,叫做集合A與集合B的并集,記作A∪B,讀作A并B。

                      交集(intersection):兩個集合和的交集是含有所有既屬于又屬于的元素,而沒有其他元素的集合,記作A∩B,讀作A交B。

                      補集(complementary):一般地,設S是一個集合,A是S的一個子集,由S中所有不屬于A的元素組成的集合,叫做子集A在S中的絕對補集(簡稱補集或余集)。

                      集合的計算公式:

                      A∪B=A+B-A∩B

                      A∪B∪C=A+B+C-A∩B-B∩C-A∩C+A∩B∩C

                      韋恩圖Venn diagram:


                       

                       

                      例題1:

                      Is the number of members of Club X greater than the number of members of Club Y ?

                      (1) Of the members of Club X, 20 percent are also members of Club Y.

                      (2) Of the members of Club Y, 30 percent are also members of Club X.

                      A.Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

                      B.Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

                      C.BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

                      D.EACH statement ALONE is sufficient.

                      E.Statements (1) and (2) TOGETHER are NOT sufficient.


                      【解析】C

                      條件1:X∩Y=20%X,不充分

                      條件2:X∩Y=30%Y,不充分

                      結合:20%X=30%Y,X>Y,充分

                       

                      例題2:


                      Last year 26 members of a certain club traveled to England, 26 members traveled to France, and 32 members traveled to Italy. Last year no members of the club traveled to both England and France, 6 members traveled to both England and Italy, and 11 members traveled to both France and Italy. How many members of the club traveled to at least one of these three countries last year?

                      A52

                      B67

                      C71

                      D73

                      E79


                      【解析】B

                      E=26,F=26,I=32

                      E∩F=0,E∩I=6,F∩I=11

                      E∪F∪I=26+26+32-6-11=67

                       

                      例題3:



                      The table gives three factors to be considered when choosing an Internet service provider and the percent of the 1,200 respondents to a survey who cited that factor as important. If 30 percent of the respondents cited both “user-friendly” and “fast response time,” what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time?”

                      A312

                      B336

                      C360

                      D384

                      E420


                      【解析】A

                      設“user-friendly”為A集合,“bargain prices”為B集合,“fast response time”為C集合

                      A∩C=30%,A∪C=56%+48%-30%=74%

                      A∪B∪C≤100%

                      只屬于B集合≤26%→1200*26%=312

                       

                      例題4:


                      Club

                      number of students

                      Chess

                      40

                      Drama

                      30

                      Math

                      25

                       

                      The table above shows the number of students in three clubs at McAuliffe School. Although no student is in all three clubs, 10 students are in both Chess and Drama, 5 students are in both Chess and Math, and 6 students are in both Drama and Math. How many different students are in the three clubs?
                      A.68
                      B.69
                      C.74
                      D.79
                      E.84


                      【解析】C

                      題干:C∩D=10,C∩M=5,D∩M=6,C∩D∩M=0

                      C∪D∪M=C+D+M-C∩D-C∩M-D∩M+C∩D∩M

                      C∪D∪M=40+30+25-10-5-6=74

                       

                      二、函數Function


                      函數的定義:給定一個數集A,假設其中的元素為x?,F對A中的元素x施加對應法則f,記作f(x),得到另一數集B。假設B中的元素為y。則y與x之間的等量關系可以用y=f(x)表示。我們把這個關系式就叫函數關系式,簡稱函數。函數概念含有三個要素:定義域A、值域C和對應法則f。其中核心是對應法則f,它是函數關系的本質特征。

                       

                      例題1:

                      An operation θ is defined by the equation a θ b =(a-b)/(a+b) , for all numbers a and b such that a ≠ –b. If a ≠ –c and a θ c = 0, then c =

                      A.–a

                      B.–1/a

                      C.0

                      D.1/a

                      E.a

                      【解析】E

                      a θ c=(a-c)/(a+c)=0

                      a=c

                       

                      例題2:

                      If [x] is the greatest integer less than or equal to x, what is the value of [–1.6] + [3.4] + [2.7] ?

                      A.3

                      B.4

                      C.5

                      D.6

                      E.7

                      【解析】A

                      [–1.6] + [3.4] + [2.7]=-2+3+2=3

                       

                      例題3:

                      For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(5, 2) = 2 and max(5, 2) = 5. For the integer w, what is the value of min(10, w) ?

                      (1) w = max(20, z) for some integer z.

                      (2) w = max(10, w)

                      A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

                      B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

                      C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

                      D. EACH statement ALONE is sufficient.

                      E. Statements (1) and (2) TOGETHER are NOT sufficient.


                      【解析】D

                      條件1:如果z>20,w=z>20;若z<20,w=20,所以min(10, w)=10,充分

                      條件2:w = max(10, w)可知w>10,所以min(10, w)=10,充分


                      更多詳細的GMAT備考資料請關注申友GMAT公眾號【申友GMAT與商科留學】:Thinku-GMAT


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