GRE数学经典全解析.pdf

1 DS 工作室工作室 为您倾情整理 GRE 数学数学 第一部分第一部分 数学基础知识数学基础知识 一 代数一 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 2 三 排列组合三 排列组合 combination 概率 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 文字题五 文字题 Word Problem 3 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 4 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 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 follows Number of error x 0 1 2 3 4 5 6 or more Percent of employees P 2 5 10 24 14 20 22 what was the median number of errors in the sample 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 4 5 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 6 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 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 record 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 If in an experiment the probabilities of obtaining the values a1 a2 a3 a4 a5 are 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