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GMAT数学高频考点:集合讲解+例题!

锦鲤哥 2020-11-23 17:27:30
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集合作为GMAT数学里面常见的考点,是大家一定要掌握到的,今天雷哥GMAT就给大家盘点一下,关于GMAT数学集合的知识点盘点,例题解析,一起掏出小本本记下来!



集合Sets


集合是指具有某种特定性质的具体的或抽象的对象汇总而成的集体。其中,构成集合的这些对象则称为该集合的元素。


☉ 并集(union):给定两个集合A,B,把他们所有的元素合并在一起组成的集合,叫做集合A与集合B的并集,记作A∪B,读作A并B。


☉ 交集(intersection):两个集合和的交集是含有所有既属于又属于的元素,而没有其他元素的集合,记作A∩B,读作A交B。


☉ 补集(complementary):一般地,设S是一个集合,A是S的一个子集,由S中所有不属于A的元素组成的集合,叫做子集A在S中的绝对补集(简称补集或余集)。



集合的计算公式:

A∪B=A+B-A∩B

A∪B∪C=A+B+C-A∩B-B∩C-A∩C+A∩B∩C



韦恩图Venndiagram:


01.png





例题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.


【解析】C

条件1:X∩Y=20%X,不充分

条件2:X∩Y=30%Y,不充分

结合:20%X=30%Y,X>Y,充分



例题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?

A.52   B.67   C.71   D.73   E.79


【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



例题3:


640.png

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?”

A.312   B.336   C.360   D.384   E.420


【解析】A

设“user-friendly”为A集合,“bargain prices”为B集合,“fast response time”为C集合

A∩C=30%,A∪C=56%+48%-30%=74%

A∪B∪C≤100%

只属于B集合≤26%→1200*26%=312



例题4:


02.png


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

题干: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


文作者:雷哥GMAT数学名师Helen


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