新GRE数学真题(OG+机经).pdf

1 y 2x2 7x 3 x y 2 The figure above shows the graph of a function f defined by f x 2x 4 for all numbers x For which of the following functions g defined for all numbers x does the graph of g intersect the graph of f A g x x 2 B g x x 3 C g x 2x 2 D g x 2x 3 E g x 3x 2 3 Each employee of a certain company is in either Department X or Department Y and there are more than twice as many employees in Department X as in Department Y The average arithmetic mean salary is 25 000 for the employees in Department X and is 35 000 for the employees in Department Y Which of the following amounts could be the average salary for all of the employees in the company Indicate all such amounts A 26 000 B 28 000 C 29 000 D 30 000 E 31 000 F 32 000 G 34 000 4 Working alone at its constant rate machine A produces k car parts in 10 minutes Working alone at its constant rate machine B produces k car parts in 15 minutes How many minutes does it take machines A and B working simultaneously at their respective constant rates to produce k car parts minutes 5 1 If the dollar amount of sales at Store P was 800 000 for 2006 what was the dollar amount of sales at that store for 2008 A 727 200 B 792 000 C 800 000 D 880 000 E 968 000 2 At Store T the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008 Give your answer to the nearest 0 1 percent 3 Which of the following statements must be true Indicate all such statements A For 2008 the dollar amount of sales at Store R was greater than that at each of the other four stores B The dollar amount of sales at Store S for 2008 was 22 percent less than that for 2006 C The dollar amount of sales at Store R for 2008 was more than 17 percent greater than that for 2006 6 A certain store sells two types of pens one type for 2 per pen and the other type for 3 per pen If a customer can spend up to 25 to buy pens at the store and there is no sales tax what is the greatest number of pens the customer can buy A 9 B 10 C 11 D 12 E 20 7 A list of numbers has a mean of 8 and a standard deviation of 2 5 If x is a number in the list that is 2 standard deviations above the mean what is the value of x x 8 Frequency Distribution for List X Number 1 2 3 5 Frequency 10 20 18 12 Frequency Distribution for List Y Number 6 7 8 9 Frequency 24 17 10 9 List X and list Y each contain 60 numbers Frequency distributions for each list are given above The average arithmetic mean of the numbers in list X is 2 7 and the average of the numbers in list Y is 7 1 List Z contains 120 numbers the 60 numbers in list X and the 60 numbers in list Y Quantity A Quantity B The average of the 120numbers in list Z The median of the 120 numbers in list Z 9 The figure above shows the graph of the function f in the xy plane What is the value of f f 1 A 2 B 1 C 0 D 1 E 2 10 By weight liquid A makes up 8 percent of solution R and 18 percent of solution S If 3 grams of solution R are mixed with 7 grams of solution S then liquid A accounts for what percent of the weight of the resulting solution A 10 B 13 C 15 D 19 E 26 11 Of the 700 members of a certain organization 120 are lawyers Two members of the organization will be selected at random Which of the following is closest to the probability that neither of the members selected will be a lawyer A 0 5 B 0 6 C 0 7 D 0 8 E 0 9 12 Line k lies in the xy plane The x intercept of line k is 4 and line k passes through the midpoint of the line segment whose endpoints are 2 9 and 2 0 What is the slope of line k Give your answer as a fraction 13 In the course of an experiment 95 measurements were recorded and all of the measurements were integers The 95 measurements were then grouped into 7 measurement intervals The graph above shows the frequency distribution of the 95 measurements by measurement interval Quantity A Quantity B The average arithmetic The median of the 95 mean of the 95 measurements Measurements 14 The random variable X is normally distributed The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X respectively Quantity A Quantity B The value at the 75th 750 percentile of the distribution of X 15 If 1 x x2 x3 60 then the average arithmetic mean of x x2 x3 and x4 is equal to which of the following A 12x B 15x C 20 x D 30 x E 60 x 16 Parallelogram OPQR lies in the xy plane as shown in the figure above The coordinates of point P are 2 4 and the coordinates of point Q are 8 6 What are the coordinates of point R A 3 2 B 3 3 C 4 4 D 5 2 E 6 2 17 Let S be the set of all positive integers n such that n2 is a multiple of both 24 and 108 Which of the following integers are divisors of every integer n in S Indicate all such integers A 12 B 24 C 36 D 72 18 The range of the heights of the female students in a certain class is 13 2 inches and the range of the heights of the male students in the class is 15 4inches Which of the following statements individually provide s sufficient additional information to determine the range of the heights of all the students in the class Indicate all such statements A The tallest male student in the class is 5 8 inches taller than the tallest female student in the class B The median height of the male students in the class is 1 1 inches greater than the median height of the female students in the class C The average arithmetic mean height of the male students in the class is 4 6 inches greater than the average height of the female students in the class 19 A random variable Y is normally distributed with a mean of 200 and a standard deviation of 10 Quantity A Quantity B The probability of the event 1 6 that the value of Y is greater than 220 20 In a graduating class of 236 students 142 took algebra and 121 took chemistry What is the greatest possible number of students that could have taken both algebra and chemistry students 21 The total amount that Mary paid for a book was equal to the price of the book plus a sales tax that was 4 percent of the price of the book Mary paid for the book with a 10 bill and received the correct change which was less than 3 00 Which of the following statements must be true Indicate all such statements A The price of the book was less than 9 50 B The price of the book was greater than 6 90 C The sales tax was less than 0 45 22 Which of the following statements individually provide s sufficient additional information to determine the area of triangle ABC above Indicate all such statements A DBC is an equilateral triangle B ABD is an isosceles triangle C The length of BC is equal to the length of AD D The length of BC is 10 E The length of AD is 10 23 The fabric needed to make 3 curtains sells for 8 00 per yard and can be purchased only by the full yard If the length of fabric required for each curtain is 1 6 yards and all of the fabric is purchased as a single length what is the total cost of the fabric that needs to be purchased for the 3 curtains A 40 00 B 38 40 C 24 00 D 16 00 E 12 80 24 The fabric needed to make 3 curtains sells for 8 00 per yard and can be purchased only by the full yard If the length of fabric required for each curtain is 1 6 yards and all of the fabric is purchased as a single length what is the total cost of the fabric that needs to be purchased for the 3 curtains A 40 00 B 38 40 C 24 00 D 16 00 E 12 80 25 In the xy plane the point with coordinates 6 7 is the center of circle C The point with coordinates 6 5 lies inside C and the point with coordinates 8 7 lies outside C If m is the radius of C and m is an integer what is the value of m m 26 What is the least positive integer that is not a factor of 25 and is not a prime number A 26 B 28 C 36 D 56 E 58 27If 1 is expressed as a terminating decimal how many nonzero digits 1 211 517 will the decimal have A One B Two C Four D Six E Eleven 28 Eight hundred insects were weighed and the resulting measurements in milligrams are summarized in the boxplot below a What are the range the three quartiles and the interquartile range of the measurements b If the 80th percentile of the measurements is 130 milligrams about how many measurements are between 126 milligrams and 130 milligrams 29 The figure shows a normal distribution with mean m and standard deviation d including approximate percents of the distribution corresponding to the six regions shown Suppose the heights of a population of 3 000 adult penguins are approximately normally distributed with a mean of 65 centimeters and a standard deviation of 5 centimeters a Approximately how many of the adult penguins are between 65 centimeters and 75 centimeters tall b If an adult penguin is chosen at random from the population approximately what is the probability that the penguin s height will be less than 60 centimeters Give your answer to the nearest 0 05 机经题 机经题 8 月 5 选选 1 1 3 个数的平均数是 30 把这 3 个数翻倍之后也加在这个 list 中 问加进去后 6 个数的平均数是多少 2 一个矩形里有个圆 圆外的面积涂阴影 圆面积是阴影面积的一半 求矩形 面积与圆面积的比例 补充 好像还有个答案是 0 50 3 哪个选项满足 f x f x 然后给了一些函数表达式 爆简单吧 4 本金是 a 给了具体数的 忘了 单利 年利率 r 一个月一个月后利息是 a 100 求 r 5 1 9 这 9 个整数中选 2 个 选中的都是 3 的倍数的概率 6 x 0 0 yB B B A C A B D 大小关系不确定 1 17 除以某个数余 2 这个数叫 A B 是 4 我选 D A 可以是 3 或 5 2 y 方开根号 8 A 3 2y B 3 2y 选 D y 可以是正负 8 3 数列首项 a1 是 1 1 2 2 an 1 1 n 1 2 前一项 算下来就是 a1 3 4 a2 8 9 3 4 A 是 a5 B 是 1 2 选 A a5 7 12 4 5 n k 3 7 Column A Column B n k k n 1 A line passes 4 6 6 5 Column A Column B 6 7 8 9 10 The slope of the line A 1 2 u v w z and u v w z are odd consecutive integers Column A Column B The median of 5 integers The range of 5 integers F x 2x 4y 6 and G x 4x 2y 10 F x and G x intersect at a point a b Column A Column B A b When 15 is divided by z remainder is 2 Column A Column B z 3 In the figure above This is regular hexagon Column A Column B The length of AB The length of CD 11 12 13 14 15 16 有一射击队 人数 600 人 对其射击结果打分 结果服从正态分布 得到算 数平均分为 84 分 标准方差为 5 假定分数大于 90 分的概率为 k 另一射击 Column A Column B The sum of a b c 180 0 x 1 Column A Column B n x N The mean of 600 females is 80 and standard deviation is 5 86 is kth percentile The mean of 400 males is 75 and standard deviation is 3 81 is nth percentile Column A Column B k n In the figure above the line passes 0 0 4 4 Column A Column B lal lbl x y 2 Column A Column B y x 2 1 25y Column A Column B 5n 3 3 5n 1 2 队 人数 400 人 对其射击结果打分 结果服从正态分布 得到算数平均分为 80 分 标准方差为 3 假定分数大于 86 分的概率为 n 问 k 和 n 谁大 具体 数据记不清了 但就是这样的题目 17 已知 P1 3 4 Pn 1 1 n 1 2 Pn 1 n 2 问 P8 和 1 2 的大小 数值填空数值填空 1 3 个不同的整数相加是 76 x 是 3 数中最大的 求 x 的最小值 我填的是 27 2 原题不是这么说的 而是给了一个图再描述 信息提取出来是这样滴 x y 两个角 相加 180 度 x 是 y 的 2 5 倍 12 求 x 3 7 个队伍比赛 第一轮中 每个队跟其余 6 个队都各赛 3 场 求第一轮中总的 比赛场数 4 一个比赛有七个人参与 规定每两个人组队完成一个游戏 如果在一轮比赛 中 每个人都要和另外一个人组队 每个队要进行三个游戏 那么问最终这一轮 比赛后 一共进行了多少个游戏 不确定题型不确定题型 1 A 衣服买了 100 件 B 衣服买了 150 件 A 衣服的单价比 B 衣服便宜 30 美元 总共花了 10500 块 问 A 衣服的单价是多少 2 x y 6 这个方程式在坐标上所围成的图形宽是多少 3 7 In 1981 Ms Jones paid 20 percent less in federal taxes than in 1980 and in 1982 she paid 30 percent more in 1981 In 1982 Ms Jones paid what percent less or more in federal taxes than in 1980 4 ABC is right triangle and angle B D are right angles BAC 30 AC 4 what is the length of BD 5 Y 6 The average of set A consisting 30 integers is 30 If the value of each components of set A is twice and appended to the original set A what is the average of new set consisting 60 integers 7 From 6 boys and 3 girls 2 people are selected What is the probability that two selected are girls 8 变化率最大的是 1990 2000 A 84 90 B 82 88 C 87 80 D 100 90 E 46 50 Questions 9 11 A 4 B 7 C 8 D 12 E 23 F 46 Total 30 billion 1 billion 109 9 What is the central angle of the potion 12 10 What amount of total is difference between B and D in billion 11 What fraction of the others is E 12 Which of followings is f x f x A x3 x2 1 B x4 x2 C x2 x x2 D x3 x2 x 13 If the value of a solution of 8x2 2x k is 1 2 what is the other solution 14 What is the median of 10 10 8 8 8 12 12 15 连续扔硬币六次 同一面不连续出现的概率有多少 16 把圆形蛋糕分成 8 份时 把 sector shape cake 的 central angle 设为 x 分成 12 份时 sector shape cake 的 central angle 设为 Y 时 x y 17 The three vertexes of a rectangle are 0 4 0 3 7 3 what is the perimeter of the rectangle 18 If the average score of 20 cards is 2 what is the value of x 19 If x y 11 what is the greatest value of x y x and y are positive integers 20 In a rectangle of which width and height is 10 and 12 each a circle is located If the diameter of the circle is 8 what is the area of the rectangle except the circle 21 x and y are positive integers greater than 1 If 4x 12y 100 and x y what is the value of x 22 one fifth of 1 of x In terms of x 9 月 1 六个连续的奇数 整数 相加 不可能得到以下哪个结果 2 一个等腰直角三角形里面镶嵌一个正方形 图画的不好 差不多是这样 正 方形的底边是个三角形的斜边是重合 并且是斜边的 1 3 已知三角形面积是 r 求 1 这个小三角面积 3 V1 一个数把它的三角形向右移六次 得到的数是原来这个数的倒数的九倍 Number 1 2 5 7 1 4 Score x 1 2 1 3 2 求这个数 好像是这个 记得不太清楚了 V2 一个数的小数点向右移动六位后得到的数与原数的倒数的 3 倍还是多少 相等 求这个数 最后结果是 0 003 中间的关系是怎么着我也忘了 看清题 认识倒数 reciprocal 就能做对 4 x 的平方 36 让我们比较 x 的最大值跟最小值的差与 12 的大小 应该是等 于 5 给了一个表格 表示一二三四年级的人数 一个教授要建一个小组 从二三 四年级中各选相应的人数 用乘法计算就对了 6 一道图表题给的一个大学的藏书的来源 好像是四个书店 第二个图是某一 个书店卖给这个大学的书中不同种类书的数量 需要注意的是 图中列出的并 不是所有图书的种类而是部分图书种类 因此给出的这些书的总数小于这个书店 卖给大学的书 要用第一个表中的数据 题目中有一个好像用到了 但是即使没 注意到这个问题也不一定做错 7 比较25的九次方的倒数 与 625的4次方还是几次方的 最后两个结果是相 等的 8 有个等腰直角三角形内嵌正方形的题 开始还没想到 后来才想起来 问一 个三角形的面积占总面积的比例 9 还有一个是正方形绕一点旋转 对着那点绕成的圆面积 10 一道图表分析题 提供了一个柱面图 显示了几年间某公司在欧洲分部和美 国分部的年收入情况 出了三道题