gre数学机经600题

合集下载

【GRE真题机经】必做考场最新高频GRE真题机经2021年2月、3月

填空部分1._____ is valuable in science, even when a scientific idea is true, it can be misused through grandiosity.A.humilityB.experimentationC.patienceD.cooperationE.exposure2.Behavior dubbed reprehensible by the residents of the region is considered conventional, even ______ by those of the neighboring region; fortunately, people traveling between the two are resigned to this disparity.A.eccentricpulsoryC.innovativeD.unconscionableE.transparent3.In its literature and its political discourse, the nation has created various narratives about itself that tend to ______ intractable social divisions in the interest of perpetuating a dubious myth of unity.A.denounceB.obscureC.corroborateD.anatomizeE.explicate4.One of the peculiarities of humans is that we irrationally gravitate to the predictable and avoid risk, whatever the reasons for this _____, it is hardly a sound basis for dealing with complex, long-term problems.A.eccentricityB.predilectionC.vacillationD.proclivityE.waveringF.cowardice5.While normal floods resulting from usual monsoon rainfall are _____ the growth of crops, recently there has been an increase in the frequency of high-intensity floods that do not have such welcome effects.A.conducive toB.hindered byC.devastating forD.deleterious forE.essential forF.indispensable to6.In their quest for kinder cutting, physicians increasingly rely on endoscopic surgery, replacing large scalpels and clamps with cameras and _____ tools that snake into the body through tiny holes.A.flexibilityB.rigidityC.magnitudeD.supplenessE.enormityF.precision7.The university’s once _____ department of economic history has lost prestige and transmogrified into a department of management and marketing.A.respectedB.slightedC.pretentiousD.giganticE.venerableF.snubbed8.Despite their cultural and social significance, rapid growth, and widespread appearin China, video games—unlike traditional media—have received _____ attentionfrom international communication researches.A.undueB.scantC.excessiveD.focusedE.limitedF.dwindling9. Although trains may use energy more (i)_____ than do automobiles, the latter move only when they contain at least one occupant, whereas railway carriages spend a considerable amount of time running up and down the tracks (ii)_____, or nearly so.A. lavishlyB. efficientlyC. routinelyD. vacantE. unimpededF. overlooked10. Britain’s deteriorating economy after 1945 was (i)_____ by politicians who favored the manufacturing sector over the service sector: rather than attempting to (ii)_____ the decline of manufacturing, they should have promoted service industries.A. mishandledB. bolsteredC. forestalledD. augmentE. arrestF. escalate11. People frequently attempt to relieve their workplace frustrations via surreptitious comments around the water cooler but would be better able to resolve their resentment if they were less (i)_____ about their problem and imitated a more (ii)_____ dialogue.A. vexatiousB. clandestineC. opportunisticD. equitableE. sincereF. open12. The description of humans as having an internal clock is not a (i)_____. Or rather, it is—you do not have a tiny watch in your cerebellum—but it also refers to (ii)_____, a specialized bundle of cells that regulates cyclical processes.13. It can be (i)_____ to read Margaret Fuller’s travel writing, as she produced accounts of her travel that (ii)_____ conventions of bourgeois travel narrative, often capitulating to the most well-worn clichés of the genre at precisely the moments when she sought most energetically to cast them off in favor of some new, more passionate mode of14. Scientists said that cosmology was the field where the ratio of theory to data was(i)_____: there was an abundance of theories, but almost no data. Recently, however, that ratio has flipped. A huge and ever-increasing amount of data has (ii)_____ all theories15. The Chavez Pass archaeological site was initially interpreted as indicative of _____ society, since it was thought to have been at the center of a cluster of smaller,16. So (i)_____ is the reputation of the city’s police force for (ii)_____ that whenever a17. Traditional Vietnamese culture has long promoted the idea of gender equality. Founding myths (i)_____ the equal division of labor in child care for mothers and fathers. As is often the case, however, theoretical commitments are (ii)_____ actual processes. In reality, gender-based (iii)_____ persists.18. To the avid reader of E.O. Wilson, much of his most recent book Consilience: The Unity of Knowledge will be (i)_____, as the book represents the culmination of a life spent thinking about everything from the social lives of ants to the social lives of people. Nonetheless, new thoughts have been mixed in with the old to produce a book remarkable for its (ii)_____ and ambition.19. Sometimes the criteria that are used to categorize nation-states are purely factual: for example, the denotation of a state as a coastal state or an inland state. But most state labels have a predominantly (i)_____ character. Labels such as failed state or democratic state tend to be accepted only by those who (ii)_____ the assumptions that (iii)_____ such a marker.20.阅读部分Passage 1David Belasco’s 1912 Broadway production of The Governors Lady created a sensation with a scene set in a Childs cafeteria, a chain restaurant that was an innovator in food standardization and emblematic of modern everyday life. While Belasco’s meticulously detailed reproduction of an immediately recognizable setting impressed the public, it was derided by progressive theater critics who championed the New Stagecraft theories of European artists like Max Reinhardt. The New Stagecraft rejected theatrical literalism; it drew inspiration from the subjectivity and minimalism of modern painters, advocating simplified sets designed to express a dramatic texts central ideas. Such critics considered Belasco a craftsman who merely captured surface realities: a true artist eliminated the inessential to create more meaningful, expressive stage images.1. The author of the passage implies which of the following about Belasco’s production of The Governors Lady?A. It was dismissed by certain theater critics who misunders tood Belasco’s conception of modernity.B. It was intended to marshal elements of the New Stagecraft to serve Belasco’s predilection for realistic staging.C. It demonstrated that theatrical literalism could be used effectively to express a dramatic texts central ideas.D. It elicited responses that reflected a discrepancy between popular tastes in entertainment and the tastes of progressive theater critics.E. It relied on the appeal of an impressively realistic stage set to compensate for weaknesses in other aspects of the production.2. It can be inferred that the theater critics would be most likely to agree with which of the following statements about the theatrical productions?A. Theatrical productions that seek to eliminate the inessential also often eliminate theatrical elements that enhance the expressiveness of a play.B. Theatrical productions that faithfully recreate the visual details of everyday life are unlikely to do justice to a good play’s central ideas.C. Theatrical productions that employ the minimalism characteristic of modern paintings may have greater appeal to modern audiences than productions that rely on theatrical literalism.D. Theatrical productions that aim to represent truths about modern life should not attempt to employ elements of the New Stagecraft.E. Theatrical productions that attempt to produce authentic-looking scenes of everyday reality are likely to fail in that goal because of the theaters inherent limitations.Archaeologists studying Bonito phase (ca. A.D. 900-1140) Native American ceramics from Chaco Canyon, New Mexico, observed that many pots had been altered after firing to revise their decorative designs--usually, intricate geometric patterns painted in black on white slipped surfaces. In some cases, a new design was imposed over an earlier one; less often, the original design was simply covered with white slip. Crown and Wills doubt that the alterations were made to correct design errors. Many Chaco pots with design errors were left unaltered. Furthermore, when errors were corrected, revisions were made prior to firing—either by painting directly over the error or by scraping off designs and applying new slip and paint, which is a less time-consuming method than repainting and refiring flawed pots.1. The author of the passage mentions Crown and Wills primarily in order toA. Distinguish among different factors that might have caused Chaco potters to alter their pots’ decorative designs.B. Introduce new evidence related to the question o f why Chaco potters altered their pots’ decorative designs.C. Show how one potential explanation for the alteration of Chaco pots has been discounted.D. Present a hypothesis about why Chaco pots were altered to revise their decorative designs.E. Explain how archaeologists discerned the method by which Chaco pots were originally decorated.2. According to the passage, which of the following is true of Bonito phase Chaco pots?A. Relatively few of them have original designs concealed beneath white surfaces.B. Relatively few of them were altered after firing.C. Many of their alterations increased the intricacy of their painted designs.D. Many of them have some flaw in their shape or structure.E. Many of them were altered more than once.The physicist Wallace Sabine pioneered the scientific study of architectural acoustics when he was asked in 1895 to fix a university lecture hall in which the echo of a speaker’s words rendered them unintelligible. He found that the length of time it takes a sound’s echo to decay is determined by the absorption of the sound’s original energy by surrounding material. By hanging panels of sound-absorbing felt on the walls, Sabine reduced the echo enough to make the hall usable. And the data he compiled yielded a mathematical formula for the relationship between a room’s echo duration, its quantity and quality of sound-absorbing materials, and its spatial volume.1. Which of the following can be inferred about the ‘university lecture hall’ mentioned in the passage?A. It was not originally designed to be used for lecture.B. It was more suitable for listening to music than for listening to the spoken word.C. Its walls had surfaces made of material with very poor sound-absorbing properties.D. Its poor acoustics resulted from its being designed to accommodate a large audience.E. It was constructed at a time when sound-absorbing building materials were not readily available.2. The passage suggests that Sabine’s work made which of the following possible for the first time?A. to make a room soundproofB. to build an auditorium out of sound-absorbing materialsC. to construct an enclosed space in which sound would not echoD. to design a building to meet predetermined specifications with regard to echo durationE. to render any large room usable for public lectures and performancesIn recent decades, scholars of American literature have skillfully revealed authors’ simultaneous accommodation and resistance to an increasingly commercialized, capitalized environment during the early nineteenth century. Historians of the period have not, however, fully exploited literary criticism, due to the disciplinary boundaries that mark contemporary academic research. Few historians have extensive training in critical theory and its specialized languages, and the sheer volume of work in early American history and literature challenges anyone who would master either field, much less both. Moreover, historians study people across the nation, but much literary scholarship called “American” actually examines works produced in northeastern states. And historians usually study the operations of capitalism in its details, while literary critics produce a generalized picture of literary commodification.1. As discussed in the passage, the literary scholars and the historians differ in which of the following ways?A. the amount of scholarship that they produceB. the nature of their geographic focusC. the extent to which they are critical of early capitalismD. the extent to which they are interested in interdisciplinary studyE. The extent to which they restrict their focus to a particular time period2. The passage cites which of the following as a reason for historians’ failure to fully exploit literary criticism?A. historians’ overly thematic approach to literatureB. historians’ conservative notion of what constitutes literatureC. historian’s lack of interest in critical theoryD. the distinctive nature of much literary criticismE. the ahistorical quality of much literary criticism3. The passage cites which of the following as reasons for historians’ failure to fully exploit literary criticism?A. The amount of scholarship involvedB. The distinctive nature of literary criticismC. The ahistorical quality of much literary criticism数学部分1.A market analyst estimated that 1.9 million smart watches were sold in 2013 and 6.8 million smart watches were sold in 2014. In 2015 the analyst predicted that the percent increase in the number sold from 2014 to 2015 would be half of the percent increase in the number sold from 2013 to 2014. Approximately how many smart watches were predicted by the analyst to be sold in 2015?A.9.3 millionB.12.2 millionC.15.6 millionD.19.0 millionE.24.3 million2.—3<x<0Quantity A Quantity B-3A.Quantity A is greater.B.Quantity B is greater.C.The two quantities are equal.D.The relationship cannot be determined from the information given.3.1<x<2Quantity A Quantity BA.Quantity A is greater.B.Quantity B is greater.C.The two quantities are equal.D.The relationship cannot be determined from the information given.4.AB=ACQuantity A Quantity BThe measure of angle ABC 70°A.Quantity A is greater.B.Quantity B is greater.C.The two quantities are equal.D.The relationship cannot be determined from the information given.5.The figure above shows the standard normal distribution, with mean 0 and standard deviation 1, including approximate probabilities corresponding to the six intervals shown. The random variable W is normally distributed with mean 14.5 and standard deviation 0.2.Quantity A Quantity BP(14.4<W<14.6) 2P(W>14.7)A.Quantity A is greater.B.Quantity B is greater.C.The two quantities are equal.D.The relationship cannot be determined from the information given.6.The 1,200 seniors at a certain college, one-quarter live on campus and the rest live off campus. Three-quarters of the seniors at college own a car. Which of the following statements must be true?A.No seniors live on campus and own a car.B.At least 300 seniors live on campus and own a car.C.At most 600 seniors live off campus and own a car.D.At least 600 seniors live off campus and own a car.E.At least 300 seniors live off campus and do not own a car.7.0 < n < 107The integer n above is the square of an integer and the cube of an integer. If the ones digit of n is 5, what is the value of n?8.9.10.。

gre考试数学考试题及答案

gre考试数学考试题及答案1.The number of different prime factors of 48The number of different prime factors of 72答案：C2.The number of different positive divisors of 12The number of different positive divisors of 50答案：C3.The number that is as much greater than 63 as it is less than 10184答案：B4. A K-number is a positive integer with the special property that 3 times its units' digit is equal to 2 times its tens' digit.The number of K-numbers between 10 and 993答案：C5.Of the following which is greatest?A.1/2B.7/15C.49/100D.126/250E.1999/4000答案：D6.If n=pqr, where p,q, and r are three different positive prime numbers, how many different positive divisors does n have, including 1 and n?B.5C.6D.7E.8答案：E7.A decrease of 1 in which of the factors above would result in the greatest decrease in the product?A.11B.13C.17D.19E.23答案：A8.Which of the following numbers is not the sum of three consecutive odd integers?A.15B.75C.123D.297E.313答案：E9.A dresser drawer contains 15 garments. If 40 percent of those garments are blouses, how many are not blouses?A.6C.9D.10E.12答案：C10.If a certain company purchased its computer terminals for a total of $540,400 and each of the terminals was purchased for $350, how many terminals did the company purchase?A.1,624B.1,544C.1,434D.1,384E.1,264答案：B。

考前必看的新GRE有代表性的数学题

大蚂蚱美国留学社区-我们战斗在美国！1.y=2x2+7x – 3 x y2. 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)x3 C g(x)2x – 2 D g(x)2x3 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 大蚂蚱美国留学社区-我们战斗在美国！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? ____________minutes5. 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? A9 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=______ 大蚂蚱美国留学社区-我们战斗在美国！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 C0 D1 E2 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._______ 大蚂蚱美国留学社区-我们战斗在美国！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 th 750 The value at the 75 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 20x D 30x E 60x 大蚂蚱美国留学社区-我们战斗在美国！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 大蚂蚱美国留学社区-我们战斗在美国！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 大蚂蚱美国留学社区-我们战斗在美国！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? 大蚂蚱美国留学社区-我们战斗在美国！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： 8月 5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。

(完整word版)gre数学难题集锦

数学无忧之最终幻想版1.正整数n有奇数个因子,则n为完全平方数2.因子个数求解公式:将整数n分解为质因子乘积形式,然后将每个质因子的幂分别加一相乘.n=a*a*a*b*b*c 则因子个数=(3+1)(2+1)(1+1)eg. 200=2*2*2 * 5*5 因子个数=(3+1)(2+1)=12个3.能被8整除的数后三位的和能被8整除;能被9整除的数各位数的和能被9整除.能被3整除的数,各位的和能被3整除.4.多边形内角和=(n-2)x1805.菱形面积=1/2 x 对角线乘积6.欧拉公式：边数=面数+顶点数-28.三角形余玄定理C2=A2+B2-2ABCOSβ,β为AB两条线间的夹角9.正弦定理:A/SinA=B/SinB=C/SinC=2R(A,B,C是各边及所对应的角,R是三角形外接圆的半径)10.Y=k1X+B1,Y=k2X+B2，两线垂直的条件为K1K2=-111.N的阶乘公式:N!=1*2*3*....(N-2)*(N-1)*N 且规定0!=11!=1Eg:8!=1*2*3*4*5*6*7*812. 熟悉一下根号2、3、5的值sqrt(2)=1.414 sqrt(3)=1.732 sqrt(5)=2.23613. ...2/3 as many A as B: A=2/3*B...twice as many... A as B: A=2*B14. 华氏温度与摄氏温度的换算换算公式:(F-32)*5/9=CPS.常用计量单位的换算:（自己查查牛津大字典的附录吧）练习题:1：还有数列题：a1=2，a2=6，a n=a n-1/a n-2，求a150.解答: a n=a n-1/a n-2,所以a n-1=a n-2/a n-3,带入前式得a n=1/a n-3,然后再拆一遍得到a n=a n-6,也就是说,这个数列是以6为周期的,则a150=a144=...=a6,利用a1,a2可以计算出a6=1/3.如果实在想不到这个方法,可以写几项看看很快就会发现a150=a144,大胆推测该数列是以6为周期得,然后写出a1-a13(也就是写到你能看出来规律),不难发现a6=a12,a7=a13,然后那,稍微数数,就可以知道a150=a6了,同样计算得1/3.2：问摄氏升高30度华氏升高的度数与62比大小. key:F=30*9/5=54<623：那道费波拉契数列的题:已知,a1=1 a2=1a n=a n-1+a n-2，问a1,a2,a3,a6四项的平均数和a1,a3,a4,a5四项的平均数大小比较.解答:费波契那数列就是第三项是前两项的和,依此类推得到a1-a6为:1 123 5 8 13 21 a1+a2+a3+a6=12, a1+a3+a4+a5=11,所以为大于.4：满足x^2+y^2<=100的整数对（x,y）有多少？key: 按照X的可能情况顺序写出:X= Y=11-921-931-941-951-861-871-781-691-4 ＝>Myanswer:加起来=695：24，36，90，100四个数中,该数除以它的所有的质因子，最后的结果是质数的是那个：Key:906:0.123456789101112….，这个小数无限不循环地把所有整数都列出来.请问小数点后第100位的数字是多少？Key:位数0 1 2 3 4 5 6 7 8 9 1010 11 12 ………………………19 2020 21……………………………29 20 30……………………………… 39 20 40……………………………… 49 2050 51 52 53 54 55 56 ――――――第101位＝5？？7：2904x=y2（y的平方），x、y都是正整数，求x的最小值.因为：X^2×Y^2×Z^2=(X×Y×Z)^2所以把2904除呀除＝2×2×2×3×11×11＝2^2×11^2×6再乘一个6就OK了2^2×11^2×6×6＝（2×11×6）^2=132^2Key：最小的x＝68:序列A n=1/n-1/(n+1),n>=1,问前100项和.解答：An ＝1/n-1/(n+1)A n-1=1/(n-1)-1/nA n-2=1/(n-2)-/(n-1)………………………………………………A1＝1－1/2把左边加起来就是A n+A n-1+……+A1=1-1/(n+1) ...消掉了好多好多项之后的结果Key:把n＝100带入得前100项之和为100/1019:等腰三角形，腰为6.底边上的高为x,底边为y,问4x2+y2和144谁大解答:勾股定理得(y/2)2+x2=62,所以4x2+y2=144 10:-1<r<t <0(有一数轴) question:r+r*t*t与-1的关系Key:我想的办法只能是尝试:原式=r(1+t*t)恒小于零1)r －1， t 0 则原式－12)r －1， t －1则原式－23)r 0 ， t 0 则原式 0例如：r＝-0.9 t=-1/3 时,原式=-1,若此时-0.9<t<-1/3 原式<-1 反之>-1.11:有长方形4feet*8feet,长宽各截去x inch,长宽比2：5，解答:列出方程:(4*12-x)/(8*12-x)=2/5=> x=161.排列(permutation):从N个东东(有区别)中不重复(即取完后不再取)取出M 个并作排列,共有几种方法：P(M,N)=N!/(N-M)!例如:从1-5中取出3个数不重复,问能组成几个三位数？解答：P(3,5)=5!/(5-3)!=5!/2!=5*4*3*2*1/(2*1)=5*4*3=60也可以这样想从五个数中取出三个放三个固定位置那么第一个位置可以放五个数中任一一个,所以有5种可能选法，那么第二个位置余下四个数中任一个,....4.....，那么第三个位置……3……所以总共的排列为5*4*3=60同理可知如果可以重复选(即取完后可再取),总共的排列是5*5*5=1252．组合(combination):从N个东东(可以无区别)中不重复(即取完后不再取)取出M个(不作排列,即不管取得次序先后),共有几种方法C(M,N)=P(M,N)/P(M,M)=N!/(M-N)!/M!C(3,5)=P(3,5)/P(3,3)=5!/2!/3!=5*4*3/(1*2*3)=10可以这样理解：组合与排列的区别就在于取出的M个作不作排列-即M的全排列P(M,M)=M!，那末他们之间关系就有先做组合再作M的全排列就得到了排列所以C(M,N)*P(M,M)=P(M,N),由此可得组合公式性质:C(M,N)=C( (N-M), N )即C(3,5)=C( (5-2), 5 )=C(2,5) = 5!/3!/2!=103．概率概率的定义：P=满足某个条件的所有可能情况数量/所有可能情况数量概率的性质：0<=P<=11)不相容事件的概率：a,b为两两不相容的事件（即发生了a，就不会发生b)P(a或b)=P(a)+P(b)P(a且b)=P(a)+P(b)=0 (A,B不能同时发生)2）对立事件的概率:对立事件就是a+b就是全部情况,所以不是发生a,就是b发生,但是,有一点a,b不能同时发生.例如:a:一件事不发生b:一件事发生,则A,B是对立事件显然：P（一件事发生的概率或一件事不发生的概率）=1（必然事件的概率为1）则一件事发生的概率=1 - 一件事不发生的概率...........公式1理解抽象的概率最好用集合的概念来讲，否则结合具体体好理解写a,b不是不相容事件(也就是说a,b有公共部分)分别用集合A和集合B来表示即集合A与集合B有交集，表示为A*B （a发生且b发生）集合A与集合B的并集，表示为A U B （a发生或b发生）则:P（A U B）= P(A)+P(B)-P(A*B).................公式23）条件概率：考虑的是事件A已发生的条件下事件B发生的概率定义：设A，B是两个事件，且P（A）>0,称P（B|A）=P（A*B）/P（A）....................公式3为事件A已发生的条件下事件B发生的概率理解：就是P（A与B的交集）/P（A集合）理解: “事件A已发生的条件下事件B发生的概率”，很明显，说这句话的时候，A，B都发生了，求的是A，B同时发生的情况占A发生时的比例，就是A与B同时发生与A发生的概率比.4）独立事件与概率两个事件独立也就是说，A，B的发生与否互不影响，A 是A，B是B，用公式表示就是P（A|B）=P(A)所以说两个事件同时发生的概率就是：P（A U B）＝P（A）×P（B）................公式4练习题:1：A, B独立事件，一个发生的概率是0.6 ，一个是0.8，问：两个中发生一个或都发生的概率？解答：P＝P(A且!B)+P(B且!A)+P(A且B)=0.6*(1-0.8)+0.8*(1-0.6)+0.6*0.8=0.92另一个角度,所求概率P=1-P(A,B都不发生)=1-(1-0.8)*(1-0.6)=0.922：一道概率题：就是100以内取两个数是6的整倍数的概率.解答:100以内的倍数有6,12,18,...96共计16个所以从中取出两个共有16*15种方法,从1-100中取出两个数的方法有99*100种,所以P=(16*15)/(99*100)=12/505=0.0243：1-350 inclusive 中，在100-299inclusive之间以3,4,5,6,7,8,9结尾的数的概率.因为100-299中以3,4,5,6,7,8,9结尾的数各有20个,所以Key:（2*10*7）/350=0.44.在1-350中（inclusive），337-350之间整数占的百分比Key:(359-337+1)/350=4%5.在E发生的情况下，F发生的概率为0.45，问E不发生的情况下，F发生的概率与0.55比大小解答:看了原来的答案,我差点要不考G了.无论柳大侠的推理还是那个哥哥的图,都太过分了吧?其实用全概率公式是很好解决这个问题的,还是先用白话文说一遍吧:某一个事件A的发生总是在一定的其它条件下如B,C,D发生的,也就是说A的概率其实就是在,B,C,D发生的条件下A发生的概率之和.A在B发生时有一个条件概率,在C发生时有一个条件概率,在D发生时有一个条件概率,如果B,C,D包括了A发生的所有的条件.那么,A 的概率不就是这几个条件概率之和么.P(A)=P(A|B)+P(A|C)+P(A|D)好了,看看这个题目就明白了.F发生时,E要么发生,要么不发生,OK?所以,P(F)=P(F|E)+P(F|!E) 感觉上也没错吧? 给了P(F|E)=0.45,所以P(F|!E)= P(F)-P(F|E)= P(F)-0.45如果P(F)=1,那么P(F|!E)=0.55如果0.45=<P(F)<1,那么0=<P(F|!E)<0.55如果…………，唉，我就不说你什么了…………sigh1.mode（众数）一堆数中出现频率最高的一个或几个数e.g. mode of 1,1,1,2,3,0,0,0,5 is 1 and 02.range（值域）一堆数中最大和最小数之差 ,所以统计学上又称之为极差.(两极的差)e.g. range of 1,1,2,3,5 is 5-1=43.mean（平均数）arithmatic mean（算术平均数）: n个数之和再除以ngeometric mean （几何平均数）: n个数之积的n次方根4.median（中数）将一堆数排序之后，正中间的一个数（奇数个数字），或者中间两个数的平均数（偶数个数字）e.g. median of 1,7,4,9,2,2,2,2,2,5,8 is 2 median of 1,7,4,9,2,5 is (5+7)/2=65.standard error（标准偏差）一堆数中，每个数与平均数的差的绝对值之和，除以这堆数的个数(n)e.g. standard error of 0,2,5,7,6 is:(|0-4|+|2-4|+|5-4|+|7-4|+|6-4|)/5=2.46.standard variation一堆数中，每个数与平均数之差的平方之和，再除以n标准方差的公式：d2=[(a1-a)2+(a2-a)2+....+(an-a)2 ]/ne.g. standard variation of 0,2,5,7,6 is: average=4((0-4)2 +(2-4)2+(5-4)2+(7-4)2+(6-4)2)/5=6.87.standard deviation就是standard variation的平方根 d8.the calculation of quartile(四分位数的计算)Quartile（四分位数）：第0个Quartile实际为通常所说的最小值（MINimum）；第1个Quartile（En：1st Quartile）；第2个Quartile实际为通常所说的中分位数（中数、二分位分、中位数：Median）；第3个Quartile（En：3rd Quartile）；第4个Quartile实际为通常所说的最大值（MAXimum）；我想大家除了对1st、3rd Quartile不了解外，对其他几个统计值的求法都是比较熟悉的了，而求1st、3rd是比较麻烦的.下面以求1rd为例：设样本数为n（即共有n个数），可以按下列步骤求1st Quartile：1．n个数从小到大排列，求(n-1)/4，设商为i，余数为j2．则可求得1st Quartile为：(第i+1个数)*(4-j)/4+(第i+2个数)*j/4例（已经排过序啦！）：1）.设序列为{5}，只有一个样本则：(1-1)/4 商0，余数01st=第1个数*4/4+第2个数*0/4=52）.设序列为{1,4}，有两个样本则：(2-1)/4 商0，余数11st=第1个数*3/4+第2个数*1/4=1.753）.设序列为{1,5,7}，有三个样本则：(3-1)/4 商0，余数2 1st=第1个数*2/4+第2个数*2/4=34）.设序列为{1,3,6,10}，四个样本：(4-1)/4 商0，余数21st=第1个数*1/4+第2个数*3/4=2.55）.其他类推！因为3rd与1rd的位置对称，这是可以将序列从大到小排（即倒过来排），再用1rd的公式即可求得：例（各序列同上各列，只是逆排）：1.序列{5}，3rd=52.{4,1}，3rd=4*3/4+1*1/4=3.253.{7,5,1}，3rd=7*2/4+5*2/4=64.{10,6,3,1}，3rd=10*1/4+6*3/4=79．The calculation of Percentile设一个序列供有n个数，要求（k%）的Percentile：（1）从小到大排序，求(n-1)*k%，记整数部分为i，小数部分为j可以如此记忆：n个数中间有n-1个间隔，n-1/4就是处于前四分之一处，（2）所求结果＝（1－j）*第(i＋1)个数＋j*第(i+2)个数特别注意以下两种最可能考的情况：（1）j为0，即(n-1)*k%恰为整数，则结果恰为第(i+1)个数（2）第(i+1)个数与第(i+2)个数相等，不用算也知道正是这两个数.注意：前面提到的Quartile也可用这种方法计算，其中1st Quartile的k%=25%2nd Quartile的k%=50%3rd Quartile的k%=75%计算结果一样.例：（注意一定要先从小到大排序的，这里已经排过序啦！）｛1，3，4，5，6，7，8，9，19，29，39，49，59，69，79，80｝共16个样本要求:percentile＝30%：则(16-1)*30%=4.5=4+0.5 i＝4，j＝0.5(1-0.5)*第5个数＋0.5*第6个数=0.5*6+0.5*7=6.510.To find median using Stem-and-Leaf (茎叶法计算中位数)Stem-and-Leaf method 其实并不是很适用于GRE考试,除非有大量数据时可以用这种方法比较迅速的将数据有序化.一般GRE给出的数据在10个左右,茎叶法有点大材小用.Stem-and-Leaf 其实就是一种分级将数据分类的方法.Stem就是大的划分,如可以划分为1～10，11～20，21～30…，而Leaf就是把划分到Stem一类中的数据再排一下序.看了例子就明白了.Example for Stem-and-Leaf method:Data：23，51，1，24，18，2，2，27，59，4，12，23，15，200| 1 2 2 41| 12 15 182| 20 23 23 24 275| 51 59Stem (unit) = 10Leaf (unit) = 1分析如下：最左边的一竖行 0, 1, 2, 5叫做Stem, 而右边剩下的就是Leaf(leaves). 上面的Stem-and-Leaf 共包含了14个data, 根据Stem及leaf的unit, 分别是： 1, 2, 2, 4 (first row), 12, 15, 18 (second row), 20, 23, 23, 24, 27(third row), 51, 59 (last row). Stem and Leaf其实就是把各个unit，比如个位，十位等归类了而已，一般是从小到大有序排列，所以在找Stem-and Leaf 找median的时候，一般不需要你自己把所有的数写出来从新排序.所以只要找到中间的那个数 (如果data个数是偶，则取中间两数的平均数), 就是median 了.这道题的median是18和20的平均值 =19. 大家在碰到这种题的时候都可以用上面的方法做，只要注意unit也就是分类的数量级就行了.为什么用Stem-and-Leaf 方法？可能你觉得这样做太麻烦了，其实Stem-and-Leaf 方法好处就是：你不必从一大堆数里去按大小挑数了，按照data给出的顺序填到表里就可以了.但是，GRE考试这样做是否值自己斟酌.我的方法，不就是找十来个数么？排序！在先浏一眼数据看看大致范围，然后在答题纸上按个的写，觉得小的写前面，大的写后面，写了几个数之后，就是把剩下的数儿们，一个个的插到已写的数中间么！注意尽可能的把数之间的距离留大一些，否则，如果某些数比较密集，呵呵，你会死的很惨的.11．To find the median of data given by percentage(按比例求中位数)给了不同年龄range, 和各个range的percentage, 问median 落在哪个range里. 把percentage加到50%就是median的range了.担小心一点，range首先要保证是有序排列.Example for this:Given: 10～20 = 20%, 30～50 = 30%, 0～10 = 40%, 20～30 = 10%, 问median在哪个range里.分析：千万不要上来就加，要先排序，切记！！重新排序为： 0～10 = 40%, 10～20 = 20%, 20～30 = 10%, 30～50 = 40%. 然后从小开始加， median（50％）落在 10～20这个range里.如果觉得比较玄乎，我的方法，GRE大部分的题都可以这么搞.0～10岁 40匹ETS猪，10～20岁 20匹ETS 猪，20～30岁匹ETS猪，30～50岁匹ETS猪，这100匹ETS猪按着年龄排下来，你说第五十匹ETS猪的年龄落在那个范围.(原题: 说一堆人0-10岁占 10%,11-20岁占12%,21-30岁占 23%,31-40岁占 20%,〉40岁占 35%,问median 在什么范围?)12：比较,当n<1时，n，1，2 和1，2,3的标准方差谁大standard error 和 standard variation (作用=standard deviation)都是用来衡量一组数据的离散程度的统计数值,只不过由于standard error中涉及绝对值,在数学上是很难处里的所以,都用标准方差,实际上standard error更合理一些,它代表了数据和平均值的平均距离.很明显题目中如果n=0的话,0,1,2的离散程度应该和1,2,3的离散程度相同.如果n<0,则n,1,2,的离散程度大于后者,而0<n<1的话,则后者大于前者,但是n为整数,这种情况不成立.故而Key:n是整数，前〉=后(n=0,等；n=-1,-2,……大于)13.算数平均值和加权平均值三组数据的频数分布FREQUENCY DISTRIBUTION：1（6），2（4），3（1），4（4），5（6）1（1），2（4），3（6），4（4），5（1）1（1），2（2），3（3），4（4），5（5）其中括号里的是出现的频率，问MEAN和AVERAGE相等的有那些.答案：只有第二个.mean-arithmetic mean 1+2+3+4+5）/ 5 = 3average-weighted average 加权平均值:(1*1+2*4+...5*1)/(1+4+6+4+1)=48/16=314.正态分布题.一列数从0到28，给出正态分布曲线.75%的percentile 是20，85%的percentile是r,95%的percentile是26,问r与23的大小.Key:r<23下面是来自柳大侠的七种武器中的正态分布15．正态分布高斯分布（Gaussian）（正态分布）的概率密度函数为一钟型曲线，即222)(221)(σπσaxexp--=a为均值，σ为标准方差，曲线关于x=a的虚线对称，σ决定了曲线的“胖瘦”，形状为：如果把曲线的片段放大就比较清楚了.O为AB的中点. A(20, 75%)B(26, 95%)O(23, 85%)C(r, 85%)由于曲线上凸，显然C的横坐标小于O，所以r<23. 只要画一下图就很easy了.2) 正态分布题好象是：有一组数平均值9，标准方差2，另一组数平均值3，标准方差1，问分别在（5，11）和（1，4）中个数(概率)谁大，应该是相等.解：令图1中的曲线a=0, 1=σ, 就得到了标准正态分布，曲线如图3.此时问分布在区间（x1, x2）的概率，就是图中的阴影ABOCax1 x2图3面积.注意此时的曲线关于x=0对称.（★）对于一般的正态分布，可以通过变换，归一化到标准的正态分布，算法为：设原正态分布的期望为a ，标准方差为σ,欲求分布在区间（y1, y2）的概率，可以变换为求图3中分布在（x1, x2）间的概率.其中σay x -=.比如题目中a=9，2=σ, 区间为（5, 11），则区间归一化为(－2，1)，即22951-=-=x 129112=-=x同理，a=3，1=σ, 区间为（1, 4），则区间归一化后也为(－2，1).所以两者的分布概率相等.估计最难的题也就是利用钟型曲线的对称性，比如归一化后的区间并不相同，而是(-2,1)和（-1,2），但根据对称性，仍然可以比较概率的大小.代数部分 1. 有关数学运算add ，plus subtract difference multiply, times product divide divisible 可被整除 divided evenly 被整除dividend divisor 因子，除数 quotient 商 remainder factorial power radical sign, root sign 根号round toto the nearest 四舍五入 2. 有关集合 unionproper subsetsolution set3.algebraic term 代数项 like terms, similar termsnumerical coefficientliteral coefficientinequality 不等triangle inequality range值 original equationequivalent equationlinear equation 线性方程(e.g. 5x +6=22)4.proper fraction improper fraction 假分数mixed number vulgar fraction ，common fraction simple fraction complex fraction numerator denominator(least) common denominatorquarter decimalfraction infinite decimal 无穷小recurring decimal tenths unit 十分位5.arithmetic mean weighted average 加geometric meanexponent base 乘幂的底数, cubesquare root cube root common logarithm digit constant variable inverse function complementary functionlinear factorizationabsolute value 绝对值， e.g.｜-32｜=32round off 四舍五入 6.natural number positive numbernegative number odd integer, odd number 奇even integer, even number integer, whole number positive whole number 正整数 negative whole number consecutivenumber real number, rational number 实数, irrational （number ） inverse composite number 合数 prime number 质数reciprocal common divisor 公multiple (least)common multiple (最小) (prime) factor (质) common factor ordinary scale, decimal scale nonnegative tens 十位 units mode median common ratio7.arithmetic progression(sequence) geometric progression(sequence)8.approximate (anti)clockwise (逆) 顺时针cardinal ordinal direct proportion distinct estimationparentheses proportion 比例permutation combination tabletrigonometric function unit 单位, 几何部分 1. 所有的角alternate angle corresponding angle 同vertical angle central angle 圆 interior angle exterior angle 外角 supplementary angles complementary angle adjacent angle acute angleobtuse angle right angle round anglestraight angleincluded angle 2.equilateral triangle scalene triangle isosceles triangle 等腰right triangle oblique 斜 inscribed triangle3.semicircle concentric circles quadrilateral pentagon hexagon heptagon octagon 八边nonagon decagon polygonparallelogram equilateral plane squarerectangle regular polygon 正多边 rhombus trapezoid 4.arcline, straight line line segment parallel lines segment of acircle5.cuberectangular solidregular solid/regular polyhedron circular cylinder cone sphere 球solid6.altitude depth side circumference, perimeter radian surface area volume arm 直角三角cross section center of acircle chord radius angle bisector diagonal diameteredge face of a solid hypotenuse included side leg 三角median of a trianglebase 底边，底数（e.g. 2的5次方，2 opposite midpoint endpoint vertex (复数形式vertices) tangent transversalintercept7.coordinate system rectangularcoordinate origin abscissaordinate number linequadrant slope complex plane 复平面8.plane geometry trigonometrybisect circumscribe inscribe 内切 intersectperpendicular pythagorean theorem congruent 全等的 multilateral1.cent penny 一美分硬币 nickel 5美分硬币 dime dozen 打（12 score 廿(20个) Centigrade Fahrenheit quart gallon 加仑(1 gallon = 4 quart) yard 码 meter micron inch foot 英 minute 分(角度的度量单位，60分=1度)square measure cubic meterpint 品脱(干量或液量的单位)2.intercalary year(leap year) 闰年(366天) common year 平年(365天) depreciation down payment discount margin 利润 profit interest simple interest compounded interest dividend 红利 decrease to decrease byincrease to increase by denote list price markup per capita ratio retail pricetie 打平救命三招1.代数法往变量里分别代三个数（最大，最小，中间值）看看满足不满足2.穷举法分别举几个特例，不妨从最简单的举起，然后总结一下规律3.圆整法对付计算复杂的图表题，不妨四舍五入舍去零头，算完后看跟那个答案最接近即可无论你赞同何种观点，形成一套自己的解题思路是尤为重要的。

GRE数学真题机经-2018年6月新增部分

2. If the areas of the 4 squares are 50, 32, 18 and 12, what is the ratio of the small shaded portion to the area of the large shaded portion?(Note: Figure not drawn to scale)
Column A：Number of boys who are left-handed
Column B：8
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
Quantity B: y
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
GRE数学真题机经-2018年年6月月新增部分
题目目
1. AB is the diameter of the circle. If AF=BF= 3√2，and AC=5, what is the area of square BCDE?
答案：11
解析：题干干求正方方形BCDE的面面积，根据AF=BF=3 ，三⻆角形ABF为直⻆角三⻆角形，得出AB=6。根据AC=5，三⻆角形ABC为直⻆角三⻆角形，得出BC²=AB²AC²=6²-5²=11。正方方形BCDE的面面积=BC²=11

gre数学机经600题

gre数学机经600题
如果一个等腰三角形的两边长分别为5和8，那么这个等腰三角形的周长是多少？
A. 13
B. 16
C. 18
D. 21
一个正方形的面积是64，它的边长是多少？
A. 4
B. 8
C. 16
D. 32
一个数的5倍减去它的3倍等于10，这个数是多少？
A. 2
B. 5
C. 10
D. 15
一个圆的半径是6，它的面积是多少？
A. 12π
B. 36π
C. 72π
D. 144π
如果一个长方形的长是12，宽是8，那么它的面积是多少？
A. 16
B. 20
C. 96
D. 192
一个三角形的三边长分别为3，4，5，它的面积是多少？
A. 3
B. 6
C. 10
D. 12
一个数的平方是64，这个数是多少？
A. 4
B. 8
C. -4
D. ±8
一个圆的周长是20π，它的半径是多少？
A. 5
B. 10
C. 20
D. 40
请注意，这些题目只是模拟题，不代表真实的GRE数学考试题目。

实际考试中的题目可能会有更广泛的范围和难度。

4-13最全GRE机经

2013/4/13大陆GRE最全机经汇总Verbal阅读1、白鲨的捕食对像是海狮（sea lion），科学家认为白鲨的数量增长非但对海豹和海狮有影响，而且对整个食物链有影响，正如水獭（sea otter）影响水草一样。

水獭吃两种水生生物a 和b，a 和b 则吃水草，所以水獭就凭借这点保护了水草。

水獭数量增长后，水草也增长了。

同理，这种逻辑链和之前白鲨增长是能够相互类比的，白鲨可以用来保护一些鱼类。

问题：多选题。

在文中出现的两条食物链中，海豹和海狮和以下哪种动物作用相似？答案：a 和b这是一道高频机经，4.13G有数位G友抽到了该题目！！！2、omega-3和omega-6脂肪酸，好像是在PP2里面的。

问了2道题：（1）有关omega-6脂肪酸说法正确的是。

（2）古人和现代人有什么地方是相似的。

3、其他有说某某文物的Mark可能作为signitrue之类的。

（1）考了文章purpose。

（2）问文章末段提到有15种管被发现的目的。

4、还有考古发现某地的巨大蜗牛和当地人吃这种蜗牛并驯化培育这种蜗牛.大概问了人们是怎么知道培育古人蜗牛了……5、还有一篇说传统观点认为鞭毛没用，P认为这是说法是bad logic，他观察到细菌运动时鞭毛怎样，所以鞭毛是运动器官之类的。

（1）P怎样怎样by citing。

（2）P和P的反对者都会同意什么观点。

6、研究对比了辐射和没受辐射的人群发现受辐射的人群比较容易骨折,因此辐射容易使人的骨质变脆弱。

问base on which assumption？7、一个短阅读是什么iriduim什么65万年前恐龙的那个，是说250万年前也有个什么meteolize还是什么的impact地球，但是not enough让生物灭绝还是什么的，和65做了下对比。

这个地方有个题问的是infer一下250万年的那个事件的特征还是什么的，我选的是caused by a modest-size meteolize，这个原文中出现了的应该没错。

gre考试例题

gre考试例题GRE考试的全称为Graduate Record Examination，是一项针对研究生和商学院申请者的标准化考试，主要测试英语语言能力、数学推理能力和批判性思维能力。

以下是GRE数学考试的一些经典例题：1.如果一组数据包含3个数：2，4，9，那么这组数据的第40百分位数是：A. 2B. 4C. 5D. 9E. 202.函数y = f(x)在x = c处的导数f'(c)表示函数在c点的切线斜率。

如果f'(c) = 0，则c可能是函数的拐点。

已知函数y = x^3在x = c处的导数为1，则c等于：A. -1B. 0C. 1D. 2E. -2/33.在等差数列{a_n} 中，a_3 + a_8 > 0，则一定有：A. a_1 + a_10 > 0B. a_6 > -a_7C. a_6 > a_5D. a_1 + a_11 > 0E. a_2 + a_9 > 04.一个箱子中有大小相同的红球、白球和黄球，已知红球10个，白球8个，黄球若干个。

某人闭着眼睛从中随机取出8个球，取出红球和白球的个数刚好和取出黄球的个数相等，则箱子里黄球的个数为：A. 8B. 10C. 12D. 14E. 165.一个正整数N的所有因数中，只有两个是素数，则称N为“半素数”。

例如，28的所有因数是1、2、4、7、14和28，其中素数有2和7，因此28是一个“半素数”。

小于30的所有“半素数”之和为：A. 206B. 273C. 359D. 431E. 453。

新GRE数学真题(OG+机经)

1.y=2x2+7x – 3x y2.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–2B g(x) x 3C g(x) 2x – 2D g(x) 2x 3E g(x) 3x – 23.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) salaryis $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 $26,000B $28,000C $29,000D $30,000E $31,000F $32,000G $34,0004.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 partsin 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce k car parts?____________minutes5.1)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 $727,200B $792,000C $800,000D $880,000E $968,0002)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 lessthan 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 9B 10C 11D 12E 207.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 XNumber 1 2 3 5Frequency 10 20 18 12Frequency Distribution for List YNumber 6 7 8 9Frequency 24 17 10 9List 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 BThe 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 isthe value of f ( f (–1)) ?A –2B –1C 0D 1E 210.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 0.5B 0.6C 0.7D 0.8E 0.912.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 BThe average (arithmetic The median of the 95mean) of the 95 measurementsMeasurements14.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 BThe value at the 75th750percentile of thedistribution of X15.If 1+x+x2+x3=60, then the average (arithmetic mean) of x, x2, x3, andx4 is equal to which of the following?A 12xB 15xC 20xD 30xE 60x16.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 both24 and 108. Which of the following integers are divisors of every integer nin S ?Indicate all such integers.A 12B 24C 36D 7218.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 standarddeviation of 10.Quantity A Quantity BThe probability of the event 1/6that the value of Y isgreater than 22020.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 bothalgebra and chemistry?__________students21.The total amount that Mary paid for a book was equal to the price of the book plusa 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 1023.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 eachcurtain 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 3curtains?A $40.00B $38.40C $24.00D $16.00E $12.8024.The fabric needed to make 3 curtains sells for $8.00 per yard and can bepurchased 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 $40.00B $38.40C $24.00D $16.00E $12.8025.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 26B 28C 36D 56E 5827If 1 is expressed as a terminating decimal, how many nonzero digits1/[(211)(517)]will the decimal have?A OneB TwoC FourD SixE Eleven28.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：8月5选11. 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。

新Gre易错数学题即相关机经汇总

新Gre易错数学题即相关机经汇总易错题与机经汇总1. n个数从⼩到⼤排列，求（n-1）/4，设商为i，余数为j ，则可求得1st Quartile为：（第i+1个数）*（4-j）/4+（第i+2个数）*j/42. 4个*，2个·的排列⽅式15（=）3 .5双袜⼦，同时去2只，刚好配对的概率。

1/94. 40⼈说French，60⼈说Russian，80⼈说Italy，说两种语⾔的有50⼈，说三种语⾔的有10⼈。

共有125⼈，问不说这些语⾔的有⼏⼈。

Key:125-（40+60+80-50-10*2）=155 。

等腰直⾓三⾓形边长2加2倍根号2，求⾯积。

6. 某种溶液浓度为125gram per liter，转换成ounce per gallon，求表达式。

已知 1 ounce=28.xxx gram and 1 gallon=3.875 liter7. x，y，z 均⽅差为d，求x+10，y+10，z+10的均⽅差（d）8. 1的概率是0.8，2的概率是0，6，问是1或是2或是both的概率，1-0.6*0.8（数字瞎编）=0.92.9. 还有⼀组测量数据中，12.1⽐mean低1.5个标准差，17.5⽐mean⾼3.0个标准⽅差。

问mean是多少.13.9（设标准差为X12.1+1.5X=M，17.5-3X=M）10. 图表题，1992年总和是50，96年是60，每年⾄少增长1，问最⼤的年增长：7.011 .x+y=5&2x+2y=8之间最短距离与1⽐较《112. 以40miles/hour速度经过⼀1.5miles的路，若超速则罚款fine=50+（速度-40）*10，现⼀⼈⽤108秒通过此路，问她的fine=？key 15013. xyz togather finish the task for 9 hour，xy togather need 12 hour，z alone needs ？hour. key 3614. 直线l.在X轴截距是3，在Y轴截距是4。

GRE数学经典几何练习题

GRE数学经典几何练习题GRE数学经典几何练习题导语：小编从不同的方面和大家一起来探讨GRE数学几何题型案例，希望能对大家的GRE数学考试带来益处。

1.两条直线比斜率:一条x轴intercede 3,y轴intercede 4, 和一条x轴intercede 4,一个y轴intercede 3.解：slope1=(4-0)/(0-3)=-4/3 slop2=(3-0)/(0-4)=-3/4注意由于两条直线的斜率是负数, 后者斜率大一些.2.直线y+x=4, 与x^2+y=4交点的距离?解：meykey:根号2。

4-x=4-x23.有一个题目觉得很有意思，就是问y=x*x+1和y=x-1的图是下列哪一个?比较简单。

选的是D。

(very sure)4.一直线在X轴截距为a，Y轴上截距为b，问斜率是多少。

(-b/a)解：两点式：列出两点(a,0)(0,b),k=(b-0)/(0-a)=-b/a5.圆里头最长的线段是哪条?就是直径6.图中一三角形,X,,Z分别为两个角的外角,Y为第三个内角,问X+Z 与180+Y的大小?解： Y+(180-X)+(180-Z)=180 (内角和为180)可退出Y+180= X+Z 所以相等7.钝角三角形，两短边为6，8，问其面积与24的大小。

解： (小)8.三角形三边为8,5,6,问5,6 夹角于90谁大?mykey:前者大.9.三角形三条边6，8，10.5，问6和8所对的.两个角相加与90度比解：小于。

(因为由勾股定律知其一定是钝角三角形)10.45度的直角三角形，面积是16，问斜边。

解：答案是8(简单)以上便是小编收集的GRE数学经典几何考题，希望考生能多加练习，通过多做题来准确把握出题者的出题思路，了解题目难易程度，更加了解考试的题型，做到熟能生巧。

愿大家都能取得好的成绩!。

GRE机经易错题

1.How many such numbers in 1-100 that when divided by 5 the remainder is 3, and divided by 6 the remainder is 2?A：2B：3C：4D：5E：62.n＞2Quantity A Quantity BThe standard deviation of {2,2,2,n} The standard deviation of {2,n,n,n}A：Quantity A is greater.B：Quantity B is greater.C：The two quantities are equal.D：The relationship cannot be determined from the information given.3.What is the 57 digit to the right of the decimal point of ?A：2B：8C：5D：7E：14.CD = 6, point A lies on line CD, point B is not on line CD, where 1 ≤ AB < 2, what’s the range of area of triangle BCD?A：3B：4C：5D：6E：85.Triangle ABC has an acute angle C, AC=3, BC=4,what’s the value range of line AB?A：1B：2C：3D：4E：56.A man walks from point A to pointB on the rectangular grids shown. He could only choose to walk north or east at any corner, what’s the probability of choosing a path via point C? A：B：C：D：E：7.,where a and b are both integers, what is the possible value of a+b ?A：9B：12C：15D：17E：29F：100G：106H：1098.k is an odd integer which is greater than 100, d is a divisor other than k itself Quantity A Quantity BdA：Quantity A is greater.B：Quantity B is greater.C：The two quantities are equal.D：The relationship cannot be determined from the information given.9.There are 30 pencils in 5 different colors, 6 pencils in each color, how many pencils we need to pick to guarantee that every color has at least 2 pencils?A：24B：25C：26D：27E：2810.A 10-day long course, in the analysis of attendance for three students：A attended for 8 days, B attended for 7 days, C attended for 6 days, among which only 1 day all of them attended. How many days at least two students attended?A：6B：7C：8D：9E：1011.S={1,2,3,4,6}, T={1,2,3,6,8}, pick one number from each set separately, how manydifferent possible product of the two selected numbers ?A：10B：11C：12D：13E：1412.Randomly select a number from 1-1000, what is the probability that none of the digit would be 6 in this number?A：B：C：D：E：13.Line l intersected with two parallel lines m and n.Quantity A Quantity BNumber of points which is at equaldistance to three lines 3A：Quantity A is greater.B：Quantity B is greater.C：The two quantities are equal.D：The relationship cannot be determined from the information given.14.m,n are both integers, m is a factor of, how many pairs of (m, n) that ? A：ZeroB：OneC：ThreeD：FourE：Six15.S = {3 5 7 8 8 9 10 11 12}, T = {3 5 7 9 10 11 12}Quantity A Quantity BThe standard deviation of Set S The standard deviation of Set TA：Quantity A is greater.B：Quantity B is greater.C：The two quantities are equal.D：The relationship cannot be determined from the information given.16.A four-digit number 7a6b, a, b are both integers, what’s the probability that this number would be divided by 4? ________17.The probability of A is 60% and the probability of B is 50%, what is the most possible probability that neither A nor B would happen?A：0.80B：0.40C：0.75D：0.55E：0.6818.If Bob can do a job in 20 days and Jane can do the job in 30 days, they work together to do this job and in this period, Bob stop work for 2.5 days and Jane stop work for x days,and the job be finished for 14 days, what is x?A：1.6B：3.2C：1.5D：1.25E：1.1519.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 policies having incorrect electric record, 75% also having incorrect paper record.3% of all policies have both incorrect paper and incorrect electric records. If we randomly pick out one policy, what’s the probability that the one having both correct paper and correct electric records?A：0.80B：0.94C：0.75D：0.88E：0.9220.Two librarians, Robert and Patricia, cataloged a combined total of 180 new books, each of which was cataloged by only one of the two librarians. Although they spent the same amount of time cataloging their books, Robert spent an average of 15 minutes per book whereas Patricia spent an average of 12 minutes per book.Quantity A Quantity BThe number of books cataloged by Robert 60A：Quantity A is greater.B：Quantity B is greater.C：The two quantities are equal.D：The relationship cannot be determined from the information given.21.The unit price of commodity X is $21.94, for every order on commodity X, a tax of $20 would be imposed on the buyer. Some buyer has made n orders on commodity X, with the standard deviation of 5 on number of commodities in every order. What’s the standard deviation of the total price he/she paid for every order?A：5B：21.94C：43.88D：109.7E：2522.There is a 3*3 table, we need to fill it with three different numbers, A, B and C. There should not be two identical numbers in either each row or each column. How many different methods are available?A：6B：8C：10D：12E：1623. Hal has 4 girl friends and 5 boy friends. In how many different ways can Hal invite 2 girls and 2 boys to his birthday party?A.54B.60C.72D.120E.24024. An office has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee?A.10B.12C.15D.24E.3025. Joan has 100 candies to distribute among 10 children. If each child receives at least 1 candy and no two children receive the same number of candies, what is the maximum number of candies that a child can receive?A.10B.34C.39D.45E.5526. From a group of 8 people, it is possible to create exactly 56 different k-person committees. Which of the following could be the value of k ? Indicate all such values.A. 1B. 2C. 3D. 4E. 5F. 6G.727. How many 4-digit numbers begin with an even digit and end with an odd digit ？A 250B 500C 2,000D 2,500E 5,00028. How many positive integers can be expressed as a product of two or more of the prime numbers 5,7,11，and 13 if no one product is to include the same prime factor more than once ？A EightB nineC TenD ElevenE Twelve29. N equals the number of positive 3-digit numbers that contain odd digits only.Quantity ANQuantity B125A. Quantity A is greater.B. Quantity B is greater.C. The two quantities are equal.D. The relationship cannot be determined from the information given.Quantity ANumber of different triangles possible using the given points as vertices.Quantity B42A. Quantity A is greater.B .Quantity B is greater.C. The two quantities are equal.D. The relationship cannot be determined from the information given.31. What percent of the integers between 100 and 999，inclusive，have all three digits thesame ？A 1%B 2%C 3%D 4%E 5%32. Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?Give your answer as a fraction.33. For a certain probability experiment, the probability that event A will occur is 1/2 and the probability that event B will occur is 1/3. Which of the following values could be the probability that the event A∪B (that is, the event A or B, or both) will occur?Indicate all such values.A. 1/3B. 1/2C. 3/434. A and B are independent events, and the probability that both events occur is 1/2. Which of the following could be the probability that event A occurs?Indicate all such probabilities.A. 0B. 1/4C. 1/2D. 3/4E. 135. In a certain state, each license plate consists of either three digits (between 0 and 9, inclusive) followed by two letters or three letters followed by two digits. For example, 055-XY, 123-PP, and AAA-70 are all acceptable plates. How many different license plates can the state issue?36. A positive integer is a palindrome if it reads exactly the same from right to left as it does from left to right. For example, 5 and 66 and 373 are all palindromes. How many palindromes are there between 1 and 1,000, inclusive?37. A box contains 10 balls numbered from 1 to 10 inclusive. If Ann removes a ball at random and replaces it, and then Jane removes a ball at random, what is the probability that both women removed the same ball?A. 1/100B. 1/90C. 1/45D. 1/10E. 41/4538. A: {71,73,79,83,87} B: {57,59,61,67}If one number is selected at random from set A, and one number is selected at random from set B, what is the probability that both numbers are prime?A. 9/20B. 3/5C. 3/4D. 4/5E. 139. A box at a yard sale contains 3 different china dinner sets, each consisting of 5 plates.A customer will randomly select 2 plates to check for defects. What is the probability that the 2 plates selected will be from the same dinner set?A. 2/7B. 2/5C. 2/3D. 5/6E. 3/240. If an integer greater than 100 and less than 1,000 is to be selected at random, what is the probability that the integer selected will be a multiple of 7?142/999142/900142/899128/900128/89941. The greatest of the 21 positive integers in a certain list is 16. The median of the 21 integers is 10. What is the least possible average (arithmetic mean) of the 21 integers?A. 4B. 5C. 6D.7E.842. For a certain distribution, the measurement 12.1 is 1.5 standard deviations below the mean, and the measurement 17.5 is 3.0 standard deviations above the mean. What is the mean of the distribution?A. 13.8B. 13.9C.14.0D. 14.1E. 14.2。

GRE机经

GRE机经一、municipal solid waste城市固体废物的大部分构成和占比。

真题例句：most municipal solid waste comes from paperboard and paper products.二、大多数城市固体废物来自纸板和纸制品。

三、divorce cases越来越多的离婚案件给家庭法院造成了严重的积压。

真题例句：despite concerted efforts by court officials to alleviate the problem.尽管法院官员为缓解这一问题作出了一致努力。

四、England英格兰的罗马遗迹。

真题例句：England's countryside is dotted with Roman ruins.英格兰的乡村已经布满了罗马遗迹。

五、Meteorites证明南极发现的陨石的起源的方法。

真题例句：even though their Martian origin could not be proved until rock can be brought back from the planet itself in order to compare.即使他们的火星起源要到可以从行星本身带回岩石进行比较时才能被证明。

六、Comedy在过去十年中喜剧市场及喜剧演员的发展。

真题例句：it is as necessary for a comedian to study the works of Charlie Chaplin as an engineer's study of mathematics.喜剧演员学习查理·卓别林的作品就像工程师的数学学习课程一样是必要的。

七、heart attacks许多发作了致命心脏病的人在这之前都是没有心脏病或动脉阻塞的健康人。

真题例句：Medical researchers have been puzzled by the fact that many fatal heart attacks occur in apparently healthy people.医学研究人员对许多致命的心脏病发作发生在明显健康的人身上这一事实感到困惑。

GRE数学2016.12.18机经

GRE数学2016.12.18机经12.18号我考了今年的第三次gre考试，这次是在北京大学考的，在临考试前10天左右刷出的考位，目前来看一般都可以在考前刷到考位，不过一定要注意临考试三天左右（具体没查）会不让报名。

来北大考场我并没有提前踩点，早晨提前出门，跟着导航走的，8:30左右进入校门，不到9点就找到了，到达考场（三楼）后考官直接把保密协议发给我，还有钥匙，（6月份考试在广播大学考试，9:30左右才发保密协议），我自动就把包存里面，吃的留了出来，一瓶饮料和一袋能量棒。

果真考完了2个小时四个部分以后会有空腹感，我本人低血糖，所以如果没有东西吃的话估计下午三个部分会扛不住。

本次考试数学加试，第一个部分语言较为复杂，第二个部分语言简明，第三个部分普通，个别题目需要多读几遍，避免掉入陷阱，或者理解错误。

三个部分我剩的时间分别为6分20秒左右；13分钟左右；7分钟左右。

以下为鸡精部分：1. 标准差的题，12 13 15 16 19 20 和12 14 15 16 17 20 两组数比较标准差大小（我在4.16那次考试也遇到了两组数比较标准差大小的题目，目前来看基本不会考运算。

在公众号的“工作”中的“专题”里面有我总结的标准差的专题）2. 一个长方形内切一个圆（inscribed in/inside a circle），然后告诉长和宽分别为w和l，圆的半径为5，表示一下w和l 和另外一个常数（100或者50……）的数量关系3. 有关男生和女生的，比例关系的题，考了两道一道，答案对应的是50%，另外一道对应的应该是13/24。

（去年考过的一道原题：At a certain elementary school, 10 percent of the fifth-grade students aremembers of the school band. If 12 percent of the fifth-grade boys and 8 percent ofthe fifth-grade girls aremembers of the band, what percent of the fifth-gradestudents at the school are boys?A. 10%B. 12%C. 20%D. 30%E. 50%）4. 函数y＝x＋2的图像对应的是哪一个5. 一种20liters的液体浓度起初是12%，加进去多少liters的20%的浓度液体可以使得它调节到15%。

新GRE官方整理机经

10.【比大小】col A :the least 5 integers with 4 different prime factors, each greater than 2. col B:1155. 选D 官方：机经说的是最小的5个整数和1155作比较，因为5个数字里一个等于1155，另外四个比1155大，所以没法比较。如果题干说的是the 5th least integer with blabla（第5小的整数），那么选A。如果题干说the least integer with blabla，选C。如果是题干别的意思，请仔细计算。 11.【算术题】What is the average of four tenths and five thousandths? 选0.2025 官方：(4/10+5/1000)/2 = 0.2025。 12 【算术题】The difference between a five-digit integer and its reflection must be divisible by which of the following? 答案:9 官方:设这个五位数是10000a+1000b+100c+10d+e, 它的reflection就是10000e+1000d+100c+10b+a, 两个数相减，等于9999a+990b-990d-9999e, 所以肯定能被9整除。 13 【算术题】x,y,z,是正数，2（x+y+z）除以7余1,在問（x+y+z)除以7余几答案是4 Twice the sum of three positive integers x,y,z when divided by 7 gives remainder 1 then what is the remainder when x+y+z is divided by 7? 官方：简单的做法代个数进去算算就可以了；标准做法是把括号里的看做一个整体X，穷举X mod 7分别等于 0到6的时候，2X mod 7等于多少，然后把等于1的那些挑出来。mod表示求余函数。 14 【算术题】一个管子半径是2feet，高是8feet，问500个管子的体积是多少？答案是16000pi 官方：圆柱体体积公式：底面积×高＝pi*r^2*h, pi*2^2*8*500=16000pi 15 【算术题】一個压土机的轮子直径是2，長是8；转500圈能压多少面积的土?答案是8000pi 官方：求表面积公式：底面周长×高＝pi*d*h, pi*2*8*500=8000pi A road roller which levels a surface has height as 16 and diameter as 2, then if it revolves for around 500 revolutions. What is the area of the land that it covers in 500 revolutions? 答案：16000pi A road roller makes a surface level flat which has a height of 18 and diameter 6, and it revolves for 300 revolutions. Find the area of the land covered in 300 revolutions? 答案：32400pi 出现多次变体，计算时请注意。 16 【算术题】Courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $1.55 ? 答案选B A 1155 B 1145 C 1040 D 950 E 259 官方:(1.55-0.65)/0.1=900grams, 900+250=1150grams, 因为最多是1150grams,所以选B.如果再少就用不了这么多钱,就是在1150到1050之间才是$1.55. 17 【算术题】五十个算术平均值是x，五十个数中，有一数是18.x，若这个数从18.x变为28.x时，其算术平均值变化多少？答案是0.2 Mean of 50 numbers given to be 19.5, and when a number 18.5 from those numbers is replaced by is replaced by 28.5, then what is the difference between the new mean and the old mean? 官方：一个数从18.x变成28.x，说明这50个数的总数增加了10，那他的算术平均值变化就是10/50=0.2 18 【比大小】xy坐标系从原点（0,0)经过（x,11/10x)的直线的angle与45度比大小答案选 A

GRE机经易错题word文本

gre数学经典难题

gre数学经典难题1. 费马大定理：对于大于2的整数n，不存在正整数解使得a^n + b^n = c^n成立。

其中a、b、c为整数，n>2。

这个问题是在17世纪由法国数学家皮埃尔·德·费马提出并称为“最后的定理”。

这个问题一直困扰着数学界，直到1994年安德鲁·怀尔斯证明了费马大定理。

2. 黎曼猜想：对于所有大于1的自然数n，皆存在复数s，使得ζ(s) = 0。

其中ζ(s)代表黎曼ζ函数。

这个问题是由德国数学家伯纳德·黎曼于1859年提出，并在他的一篇论文中做出了重要的猜想。

该猜想对数论和解析数论有重要影响，但至今仍未被证明。

3. 四色定理：对于任何一张地图，只需要使用四种颜色就能够给地图上的所有区域正确着色，使得相邻的区域不会有相同的颜色。

这个问题源于1852年，被彼得·古斯塔夫·勒谢斯尔·鲁尔夫提出，并被称为“四色猜想”。

经过数十年的努力，直到1976年，该问题被肯尼斯·阿普尔和沃尔夫冈·黑肯证明为正确。

4. 正五边形作园：能否用尺规作出一个面积和一个已知正方形相等的正五边形？这个问题最早由古希腊数学家伊巴泰斯提出，在公元三世纪时成为了热门问题。

直到19世纪初，法国的阿道夫·昆特和瑞士的尔尼斯特·里希特多夫独立证明了无法通过尺规作园解决该问题。

5. 无穷小的比较：对于两个无穷小序列，a_n和b_n，当n趋于无穷时，如何判断它们的相对大小？这个问题涉及到极限和无穷小的概念，是微积分中的一个经典难题。

解决这个问题需要利用数列极限的定义和性质，并进行推理和比较。

这些经典难题代表了数学中一些长期未解决的问题，它们在数学发展中具有重要的影响和意义。

gre数学机经600题

【GRE真题机经】必做考场最新高频GRE真题机经2021年2月、3月

最新GRE数学机经200道.

gre考试数学考试题及答案

考前必看的新GRE有代表性的数学题

(完整word版)gre数学难题集锦

GRE数学真题机经-2018年6月新增部分

gre数学机经600题

4-13最全GRE机经

gre考试例题

新GRE数学真题(OG+机经)

新Gre易错数学题即相关机经汇总

GRE数学经典几何练习题

GRE机经易错题

GRE机经

GRE数学2016.12.18机经

新GRE官方整理机经

GRE机经易错题word文本

gre数学经典难题