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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: . 14 比较大小

The number of distinct positive factors of n 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 例 4 比较大小: In a certain two-digit number, the units' digit is twice the tens' digit. The tens' digit 5 105

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 例 7 比较大小:空间 5 个点能够构成的直线数目 例 8:求 3,13,17 的标准方差. 三,排列组合 combination,概率 probability , 10 100




, 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) 几何 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) +(ST)
2 2

例 15: According to the graph above, when x=3, y is most nearly: (RT)

(A) -1

(B) -1/2

(C) 0

(D) 1/2

(E) 1

五,文字题(Word Problem) 文字题 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

4-n 4-n

6 5

both of the statements true for all integers n such that -2< n≤3? (A) ≤ (B) < (C) = (D) > (E) ≥

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



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

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 Percent of employees P 0 2% 1 5% 2 10% 3 24% 4 14% 5 20% 6 or more 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

例 10: a certain country, a person is born every 3 seconds and a person dies every 10 seconds. In 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 8inches

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 例 16:x>y and xy≠0 例 17:2AF=AB=BD=DE=AE The sum of the area of triangular region ABF and area of triangular region CDE 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? (A)25 , 06 (B)50 , 26 (C)56 , 02 (D)62 , 50 (E)65 , 20 The area of rectangular region BCEF x+y (x + y)/x z (x + y)/y

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




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 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 例 26:In the figure, if x, y, and z are integers such that x<y<z, then the least and the greatest possible values of x+z are (A)59 and 91 (D)120 and 135 (B)69 and 135 (C)91 and 178

60 percent

(E)120 and 178

例 27:The figure shows the dimensions of rectangular box that is to be completely wrapped with paper. If a single sheet of paper is to be used without patching, then the dimensions of the paper could be (A)17 in by 25 in (B)21 in by 24 in (D)24 in by 14 in (E)26 in by 14 in (C)24 in by 12 in

例 28: In the table, what is the least number of table entries that are needed to show the mileage between each city and each of the other five cities? (A)15 (B)21 (C)25 (D)30 (E)36


例 29:A store currently charges the same price for each towel that it sells. If the current price of each towel was to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel? (A)$ 1 (B)$ 2 (C)$3 (D)$ 4 (E)$ 12

GRE 数学常用符号及术语 一.数学中常用符号 +: plus X: multiply -: subtract ÷: divide V~: square root |...|: absolute value =: is equal to =/=: is not equal to >: is greater than <: is less than //: is parallel to _|_: is perpendicular to >=: is greater than or equal to (或 no less than) <=: is less than or equal to (或 no more than) 二.表达相应数目的前缀 1:uni-,mono2:bi-,du-,di3:tri-,ter-, 4:tetra-,quad-, 5:penta-,quint, 6:hex-,sex-, 7:sept-,hapta-, 8:oct, 9:enn-, 10:dec-,deka-, 三.数学中常用单词术语

abscissa absolute value acute angle adjacent angle addition algebra altitude angle bisector arc area arithmetic mean

arithmetic progression arm at average base

横坐标 绝对值 锐角 邻角 加 代数 高 角平分线 弧 面积 算术平均值 (总和除 以总数) 等差数列(等差级 数) 直角三角形的股 总计(乘法) 平均值 底

be contained in bisect center chord circle circumference circumscribe clockwise closest approximation combination common divisor common factor complementary angles Composite number

平分 圆心 弦 圆形 圆周长 外切,外接 顺时针方向 最相近似的 组合 公约数,公因子 公因子 余角(二角和为 90 度) 合数 (可被除 1 及本 身以外其它的数整 除) 同心圆

concentric circle

cone congruent consecutive integer coordinate cost counterclockwise cube

cylinder decagon decimal decimal point decreased decrease to decrease by degree define denominator denote depreciation distance distinct dividend divided evenly divisible division divisor down payment equation equilateral triangle even number expression exterior angle face factor fraction geometric mean

geometric progression have left height

圆 锥 ( 体 积 = 1/3*∏*r*r*h) 全等的 连续的整数 坐标的 成本 逆时针方向 1.立方数 2. 立 方 体 ( 体 积 = a*a*a 表面积= 6*a*a) 圆柱体 十边形 小数 小数点 减少 减少到 减少了 角度 1.定义 2.化简 分母 代表,表示 折旧 距离 不同的 1.被除数 2.红利 被除数 可整除的 1.除 2.部分 除数 预付款,定金 方程 等边三角形 偶数 表达 外角 (立体图形的)某一 面 因子 1.分数 2.比例 几何平均值 (N 个数 的乘积再开 N 次方) 等比数列(等比级 数) 剩余 高

hexagon hypotenuse improper fraction increase increase by increase to inscribe intercept integer interest rate in terms of... interior angle intersect irrational isosceles triangle least common multiple least possible value leg length list price margin mark up mark down maximum median, medium

六边形 斜边 假分数 增加 增加了 增加到 内切,内接 截距 整数 利率 用...表达 内角 相交 无理数 等腰三角形 最小公倍数 最小可能的值 直角三角形的股 长 标价 利润 涨价 降价 最大值 中数 (把数字按大小 排列,若为奇数项, 则中间那项就为中 则 数, 若为偶数项, 中间两项的算术平 均值为中数. (1, 例: 3,8)其中数为 3; (1,3,8,9)其中数为 (3+8)/2=5) 三角形的中线 中点 最小值 减 乘法 倍数 乘 自然数 负数 非零 数线 分子 钝角

median of a triangle mid point minimum minus multiplication multiple multiply natural number negative number nonzero number lines numerator obtuse angle

octagon odd number ordinate overlap parallel lines parallelogram pentagon per capita perimeter permutation perpendicular lines pyramid plane plus polygon positive number power prime factor prime number product profit proper fraction proportion purchasing price quadrant quadrihedrogon quadrilateral quotient ratio rational radius radian real number reciprocal rectangle rectangular prism reduced regular polygon remainder retail value rhombus right angle right triangle round

八边形 奇数 纵坐标 重叠 平行线 平行四边形 五边形 每人 周长 排列 垂直线 三角锥 平面 加 多边形 正数 次方(2 的 5 次方= the fifth power of 2) 质因子 质数 乘积 利润 真分数 比例 买价 象限 四角锥 四边形 商 比例 有理数 半径(复数为 radii) 弧度 实数 倒数 长方形 长方体 减少 正多边形 余数 零售价 菱形 直角 直角三角形 四舍五入

sale price segment set sequence scalene triangle side simple interest slope solution speed sphere

square square root straight angle subtract subtraction sum surface area supplementary tangent tenths' digit tenth tie times total


to the nearest trapezoid triangle two digits units' digit veiocity vertex angle vertical angle volume whole number width 3-digit number

卖价 线段 集合 数列 不等边三角形 边长 单利 斜率 (方程的)解 过度 球体(表面积= 4*∏*r*r,体积= 4/3*∏*r*r*r) 1.平方数,平方 2.正方形 平方根 平角 减 减法 和 表面积 补角 相切 十分位 十分位 并列,打平 倍 1.总数(用于加法 中,相当于+) 2.总计(用于减法 中,相当于-) 最接近的 梯形 三角形 2位 个位 速度 顶角 对顶角 体积 整数 宽 三位数




1. a only if b 表示 a==>b 2. a if only b 表示 b==>a 3. 2/3 as many A as B 是: A 为 B 的 2/3 4. twice as many A as B 是: A 为 B 的 2 倍



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