【VIP专享】GRE数学经典全解析

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GRE数学

第一部分数学基础知识

一、代数Algebra

例1 比较大小：.

The number of distinct positive factors of n 14比较大小

例2：252因子的个数是多少？

例3 比较大小：A printer numbered consecutively the pages of a book, beginning with 1 on the first page. In numbering the page, he printed a total of 204 digits.

The number of pages in the book 105

例4 比较大小：In a certain two-digit number,

the units' digit is twice the tens' digit. 5

The tens' digit

例5比较大小：

二、描述统计descriptive statistics

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

1．排列组合排列计算公式：，组合计算公式：。

2．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：R is a point in the rectangular

coordinate system and OR=5.

The x-coordinate of point R 5 4.9

例14 比较大小： (RS)2+(ST)2 (RT)2

例15： According to the graph above, when

x=3, y is most nearly:

(A) -1 (B) -1/2 (C) 0 (D) 1/2 (E) 1 五、文字题(Word Problem)

1.利息问题(interest)

单利simple interest 复利compound interest

例16：If $ 8000 is invested at 6 percent simple annual interest, how much interest is earned after 3 months?

例17：If $ 10,000 is invested at 10 percent simple annual interest, compound semiannually, what is the balance after 1 year?

2.折扣问题(discount)

例18：The price of an item is discounted by 20 percent and then this reduced price is discounted by an additional 30 percent. These two discounts are equal to an overall discount of what percent? 3. 英美常识问题

GRE难题解析

例1：On a certain number line, if -7 is a distance of 4 from n and 7 is a distance of 18 from n ,then n=?

(A) 25 (B) 11 (C)- 3 (D) 11 (E)-11

例2：The diagram represents a rectangular garden.

The shaded regions are planted in flowers, and the

unshaded region is a walk 2 feet wide. All angles are

right angles.

The sum of the areas of the 2,800 square feet

shaded regions

例3：The map shows the only roads that connect the

four towns and shows the distance along each road.

The road distance between Austen and Seburg The road distance between Coaltown and Woodland

例4：How many positive integers less than 20 are equal to the sum of a positive multiple of 3 and a positive multiple of 4?

(A) Two (B) Five (C) Seven (D) Ten (E) Nineteen

例5：Which of the following symbols should be substituted for to make both of the statements true for all integers n such that -2< n ≤3?

(A) ≤ (B) < (C) = (D) > (E) ≥

4-n 6

4-n 5

例6：In a soccer league, If there were 10 teams and each team played each of the other teams 16 times, how many games did each team play?

(A) 144 (B) 140 (C) 134 (D) 125 (E) 106

例7：(NOTE: DRAWN TO SCALE)

POPULATION OF THE U.S. AGE 55 AND OVER

1984 AND PROJECTIONS FOR 1995 INCOME DISTRIBUTION FOR POPULATION

OF THE U.S. AGE 55 AND OVER,1984

In 1984 median income for a person in the 55~64 age category was in which of the following intervals?

(A) less than ＄10,000 (B) ＄10,000~＄19,999 (C) ＄20,000~＄24,999 (D) ＄25,000~＄34,999 (E) ＄35,000~＄49,999

例8：A sample of employees were tasted on data-entry skills for one hour , and the number of errors (x) they made and the percent of employees (p) making x errors were recorded as

(A) 3 (B) 3.5 (C) 4 (D) 4.5

(E) It cannot be determined from the information given.

例9：d=7.56872 and D is the decimal expression for d rounded to the nearest thousandth. The number of decimal place where d and D differ

例10：In a certain country, a person is born every 3 seconds and a person dies every 10 seconds. Therefore, the birth and death rates account for a population growth rate of one person every

例11：Of the positive integers that are multiples of 30 and are less than or equal to 360, what fraction are multiples of 12?

(A) 1/6 (B) 1/5 (C) 1/3 (D) 2/5 (E) 1/2

例12：The figure shows a large square formed by fitting

three L-shaped tiles and one small square tile together . If a

rectangular floor 10 feet by 12 feet is to be tiled in large

squares of this design, how many L-shaped tiles will be

needed?

(A) 810 (B) 405 (C) 270 (D) 135 (E) 45

例13：The daily rate for a hotel room that sleeps 4 people is $39 for one person and x dollars for each additional person. If 3 people take the room for one day and each pays $21 for the room, what is the value of x?

(A) 6 (B) 8 (C) 12 (D) 13 (E) 24

例14：A positive integer with exactly two different divisors greater than 1 must be

(A) a prime (B) an even integer (C) a multiple of 3

(D) the square of a prime (E) the square of an odd integer

例15：x>z, y>z x + y z

例16：x>y and xy ≠0 (x + y)/x (x + y)/y

例17：2AF=AB=BD=DE=AE

The sum of the area of triangular

region ABF and area of triangular region CDE

The area of rectangular region BCEF

例18：Each of the following numbers has two digits blotted out. Which of the numbers could be the number of hours in x days, where x is an integer?

8inches 8inches

(A)25,06 (B)50,26 (C)56,02 (D)62,50 (E)65,20

例19：There are 1200 represents to a poll, each favoring their preference for candidates A, B, and C. 54% favored A, 48% favored B, and 42% favored C, and there is 30% favored both A and B. What’s the largest possible number of represents favoring c, but not C&B, nor C&A?

(A)25% (B)30% (C)28% (D)38% (E)40%

例20：Out of 100 ladies attending the church fete, 85 had a white handbag; 75 had black shoes;

60 carried an umbrella; 90 wore a ring, How many ladies must have had all four items?

(A)15 (B)35 (C)5 (D)10 (E)25

例21：In an insurance company, each policy has a paper record and an electric record. For those

policies having incorrect paper record, 60% also having incorrect electric record; For those policies having incorrect electric record, 75% also having incorrect paper record. 3% of all policies have both incorrect paper and incorrect electric record. If we randomly pick out one policy, what’s the probability that the one having both correct paper and correct electric rec ord?

(A)0.80 (B)0.94 (C)0.75 (D)0.88 (E)0.92

例2212345are p1,p2,p3,p4,p5 , respectively, then the expected value is defined as a1 p1+ a2 p2+a3 p3+ a4 p4+ a5p5.For the values and their corresponding probabilities in the table above, what is the expected value?

(A)350 (B)320 (C)300 (D)270 (E)250

例23：The standard deviation of the sample measurements 0, 2, 4, 6, and 8 The standard deviation of the sample measurements 1, 3, 5, 7, and 9

例24：What is the total number of different 5-digit numbers that contain all of the digits 2, 3,4,7

and 9 and in which none of the even digits occur next to each other?

(A)72 (B)100 (C)120 (D)60 (E)48

例25：Water is to be poured at a rate of 2.5 gallons per minute into a 500-gallon tank that initially contains 50 gallons of water.

The percent of the tank's capacity that will be

filled 1 hour after water begins to be poured in

60 percent