1、GRE-练习十五及答案解析(总分：55.00，做题时间：90 分钟)一、单项选择题(总题数：35，分数：36.00)1.The odds in favor of winning a game can be found by computing the ratio of the probability of winning to the probability of not winningIf the probability that Pat will win a game is （分数：1.00）A.B.C.D.E.2.The 4 beads in a bag are identical ex
2、cept that 2 are red and 2 are blueIf 2 beads are to be simultaneously and randomly selected，what is the probability that they will both be blue?（分数：1.00）A.B.C.D.E.3.In a series of races，10 toy cars are raced，2cars at a timeIf each car must race each of the other cars exactly twice，how many races mus
3、t be held?A. 40 B. 90C. 100 D. 180E. 200（分数：1.00）A.B.C.D.E.4. The figure above shows a rectangular play area in which one child stands at B while another child runs back and forth along the entire side ADIf the running child is in a position randomly located along side AD at a given time，what is the
4、 probability that the two children are at most 50 feet apart at that time?（分数：1.00）A.B.C.D.E.5.A certain computer program generates a sequence of numbers P1，P 2，P n，by the rules P1=1，P 2=1，and for n3，P n=Pn+1+pn-2，Which of the following equals P 5?A. 10 B. 11 C. 14D. 15 E. 17（分数：1.00）A.B.C.D.E.6.The
5、 buyer of a certain mechanical toy must choose 2 of 4 optional motions and 4 of 5optional accessoriesHow many different combinations of motions and accessories are available to the buyer?A. 8 B. 11 C. 15D. 20 E. 30（分数：1.00）A.B.C.D.E.7.In a graduating class of 236 students。142took algebra and 121 too
6、k chemistryWhat is the greatest number of students that could have taken both algebra and chemistry?A. 21 B. 27 C. 37D. 121 E. 142（分数：1.00）A.B.C.D.E.8.If one number is chosen at random from the first 1，000 positive integers，what is the probability that the number chosen is multiple of both 2 and 8?（
7、分数：1.00）A.B.C.D.E.9.The odds that a certain event will occur is the ratio of the probability that the event will occur to the probability that it will not occurIf the odds that Pat will win a prize are 4 to 3，what is the probability that Pat will not win the prize?（分数：1.00）A.B.C.D.E.10.For which of
8、the following lists of number is the median equal to the average(arithmetic mean)?A. 3，4，7 B. 1，10，19 C. 7，7，10，12D. 0，1，1，5 E. 0，2，3，4（分数：1.00）A.B.C.D.E.11.kak pk11000.1022000.2533000.2044000.2555000.20If in an experiment the probabilities of obtaining the values a1，a 2，a 3，a 4， and a 5are p1，P 2，P
9、 3，P 4 and P5，respectively，then the expected value is defined as a1p1+a2p2+a3p3+a4p4+a5p5For the values and their corresponding probabilities in the table above，what is the expected value?A. 350 B. 320 C. 300D. 270 E. 250（分数：1.00）A.B.C.D.E.12.What iS the sum of the first 2，003 terms of the sequence
10、0，2，7，1，0，2，7，l，0，2，7，1，if the pattern 0，2，7，1 is repeated throughout the sequence?A. 503 B. 2，010 C. 2，013D. 5，009 E. 20，030（分数：1.00）A.B.C.D.E.13.City Y has installed 30 parking meters at15-foot intervals along a straight streetWhat iS the number of feet between the first meter and the last meter?A
11、. 200 B. 420 C. 435D. 450 E. 465（分数：1.00）A.B.C.D.E.14.If for a given spin，the pointer shown in the figure above is equally likely to stop on any of the numbered sectors，what is the probability that the pointer will stop on an odd-numbered sector?(Assume that the pointer cannot stop on a dividing lin
12、e between sectors)（分数：1.00）A.B.C.D.E.15.If the average(arithmetic mean)of x，y，x，5 and 7 is 8，which of the following must be true?The median of the five numbers cannot be 5At least one of x，y，and z is greater than 9The range of the five numbers is 2 or moreA. only B. onlyC. only D. and E. and （分数：1.0
13、0）A.B.C.D.E.16.Three red marbles and 2 white marbles are placed in an empty boxOne marble at a time is to be selected randomly and removed from the box until all 5 marbles have been removed What is the probability that each of the first 3 marbles removed will be red?（分数：1.00）A.B.C.D.E.A sample of em
14、ployees were tested on dataentry skills for one hour，and the number of errors (x) they made and the percent of employees (p) making x errors were recorded as followsNumberof ErrorsPercent ofEmployeesx p0123456 or more2%5%10%24%17%20%22%（分数：2.00）(1).If those employees who made 6 or more errors were r
15、emoved from the sample and an employee were selected at random from those remaining，what is the probability that the employee selected made no errors?（分数：1.00）A.B.C.D.E.(2).What was the median number of errors in the sample?A. 3B. 3.5C. 4D. 4.5E. It cannot be determined from the information given（分数
16、：1.00）A.B.C.D.E.17.A gardener wishes to plant 5 bushes in a straight rowEach bush has flowers of a different solid color(white，yellow，pink，red，and purple.How many ways can the bushes be arranged so that the middle bush is the one with red flowers?A. 24 B. 30 C. 60D. 96 E. 120（分数：1.00）A.B.C.D.E.18.A
17、square dart board has four dark circular regions of radius 3 inches，as shown in the design aboveEach point on the dart board is equally likely to be hit by a dart that hits the boardWhat is the probability that a dart that hits the board will hit one of the circular regions?（分数：1.00）A.B.C.D.E.19.In
18、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. 134D. 125 E. 106（分数：1.00）A.B.C.D.E.20.If a1，a 2，a 3，a nis a sequence such that a1=-2 and an+1 is the reciprocal of the square of an for all n1，what is the v
19、alue of a 4?（分数：1.00）A.B.C.D.E.21.The integers between 1 and 100，inclusive，are put in list A if they are divisible by 2and in list B if they are divisible by 3How many integers in list A arenot in list B?A. 11B. 16C. 25D. 33E. 34（分数：1.00）A.B.C.D.E.22.RESULTS ON A HISTORY TESTClassNumber of StudentsT
20、aking Test Average*ScoreX 54 70Y 41 73Z 32 76*Arithmetic meanThe average(arithmetic mean)score for allof the students in the 3 classes iSA. less than 70B. between 70 and 73C. exactly 73D. between 73 and 76E. greater than 76（分数：1.00）A.B.C.D.E.23.LEAGUE RESULTSTeamNtimber ofGames WonABCDEX47922Accordi
21、ng to the incomplete table aboveIf each of the 6 teams in the league played each of the other teams exactly twice and there were no tiesHow many games did team X win?(Only 2 teams play in a game)A. 4 B. 5 C. 6D. 7 E. 10（分数：1.00）A.B.C.D.E.24.A total of 40 tourists went on a tripIf 18of the tourists v
22、isited site X，18 visited site Yand 8 visited both site X and site Y，how many visited neither site X nor site Y?A. 4 B. 10 C. 12D. 22 E. 28（分数：1.00）A.B.C.D.E.25.For which of the following sets of numbers is the product of the three numbers less than each member of the set?（分数：1.00）A.B.C.D.E.26.One in
23、teger will be randomly selected from the integers 11 to 60，inclusiveWhat is the probability that the selected integer will be a perfect square or a perfect cube?A. 0.1 B. 0.125 C. 0.16D. 0.5 E. 0.9（分数：1.00）A.B.C.D.E.27.A certain jar contains 100 jelly beans：50white，30 green，10 yellow，5 red，4purple，a
24、nd 1 blackIf a jelly bean is to be chosen at random，what is the probability that the jelly bean will be neither purple nor red?A. 0.09 B. 0.11 C. 0.55D. 0.91 E. 0.96（分数：1.00）A.B.C.D.E.28.The numbers 3，10，17，24，31，and 38 are the first six terms of an infinite sequence inwhich each term after the firs
25、t is 7 greater than the preceding termWhat is the 45thterm of the sequence?A. 308 B. 311 C. 312D. 315 E. 318（分数：1.00）A.B.C.D.E.29.In a class of 120 students，60 percent can speak French and the rest can speak only EnglishIf 25 percent of those in the class who can speak French can also speak English，
26、how many of the students in the class can speak English?A. 54B. 60C. 66D. 84E. 90（分数：1.00）A.B.C.D.E.30.What is the total number of different 5-digitnumbers that contain all of the digits 2，3，4，7 and 9 and in which none of the odd digits occur next to each other?A. 12 B. 10 C. 8D. 6 E. 1（分数：1.00）A.B.
27、C.D.E.31.A linen shop has a certain tablecloth that is available in 8 sizes and 10 colorsWhat is the maximum possible number of different combinations of size and color available?A. 9 B. 18 C. 40D. 80 E. 90（分数：1.00）A.B.C.D.E.32.An experiment has three possible outcomes，I，J，and KThe probabities of th
28、e outcomes are 0.25，0.35，and 0.40，respectivelyIf the experiment is to be performed twice and the successive outcomes are independent，what is the probability that K will not be an outcome either time?A. 0.36 B. 0.40 C. 0.60D. 0.64 E. 0.80（分数：1.00）A.B.C.D.E.33.What is the sum of the first 1，000 terms
29、of the sequence 0，0，1，2，1，0，0，12，1if the pattern 0，0，1，2，1 is repeated indefinitely?A. 200 B. 400 C. 800D. 1，000 E. 4，000（分数：1.00）A.B.C.D.E.34.Nine pieces of paper numbered consecutively from 1 to 9 are put into a hatIf one piece of paper is drawn a trandom from the hat，what is the probability that
30、it will have an even number?（分数：1.00）A.B.C.D.E.二、比较题(总题数：19，分数：19.00)35. （分数：1.00）A.B.C.D.36. （分数：1.00）A.B.C.D.37.An identification code read from left to right consists of 2 digits，a dash，3 digits，a dash，and then 4 digitsEach digit can be any number from 0 through 9（分数：1.00）A.B.C.D.38.SURVEY OF PET
31、S IN HOUSEHOLDSIN AN APARTMENT COMPLEXKind of PetNumber ofHouseholdsDog 25Cat 41Other 19No Pet 44（分数：1.00）A.B.C.D.39.The average(arithmetic mean)of 3different positive integers is equal to the average of 5、7、8、9 and 11（分数：1.00）A.B.C.D.40.The geometric mean of any two positive numbers x and（分数：1.00）A
32、.B.C.D.41.COMPARISON OF TEST SCORES FORTWO CLASSESNumberof ScoresMeanScoreMedianScoreClass A15 80 84Class B30 74 72（分数：1.00）A.B.C.D.42.Each person at a party shook hands exactly once with each of the other people at the partyThere was a total of 21 handshakes exchanged at the party（分数：1.00）A.B.C.D.4
33、3.The median of 10，15，x and y is 18.5，and xy（分数：1.00）A.B.C.D.44.The average(arithmetic mean)of x，y，and6 is 3（分数：1.00）A.B.C.D.45.M(r，s，t)denotes the average(arithmetic mean)of，r，s，and t，and M(x，y)denotes the average of x and y（分数：1.00）A.B.C.D.46. （分数：1.00）A.B.C.D.47.The median of the positive integer
34、s l，m，n，r，and s is 10，where lmnrs（分数：1.00）A.B.C.D.48.S is a set of n consecutive integers（分数：1.00）A.B.C.D.49.Regions sharing a common border are to be different colors（分数：1.00）A.B.C.D.50.For each positive integer n，（分数：1.00）A.B.C.D.51.A precinct is divided into four wards as shownThe two northern wa
35、rds have exactly 30 Democrats each and the two（分数：1.00）A.B.C.D.52.The average(arithmetic mean)of 50measurements is 34.6，and the least and（分数：1.00）A.B.C.D.53.The probability that event R will occur is 0.38（分数：1.00）A.B.C.D.GRE-练习十五答案解析(总分：55.00，做题时间：90 分钟)一、单项选择题(总题数：35，分数：36.00)1.The odds in favor of
36、 winning a game can be found by computing the ratio of the probability of winning to the probability of not winningIf the probability that Pat will win a game is （分数：1.00）A. B.C.D.E.解析：赢得一场比赘的口能性可以通过计算获胜的概率与不获胜概率的比值得到，若 Pad 赢得比赛的概率为*，那么 P 赢得比赛的可能性是多大?Pad 赢得比赛的概率为*，那么他不赢得比赛的概率为*，由题意可得：Odds=P(win):P(n
37、ot win)=*2.The 4 beads in a bag are identical except that 2 are red and 2 are blueIf 2 beads are to be simultaneously and randomly selected，what is the probability that they will both be blue?（分数：1.00）A. B.C.D.E.解析：一个袋子中有 4 个相同的珠子，其颜色为 2 红 2 蓝。若同时随机地取出 2 个珠子。问这两个珠子同为蓝色的概率是多少?第一个珠子为蓝色的概率是*第二个仍为蓝色的概率是
38、*听以两个同为蓝色的概率是：*3.In a series of races，10 toy cars are raced，2cars at a timeIf each car must race each of the other cars exactly twice，how many races must be held?A. 40 B. 90C. 100 D. 180E. 200（分数：1.00）A.B. C.D.E.解析：在一系列比赛中，有 10 辆玩具汽车进行比赛，每场比赛有 2 辆汽车参加。若每辆汽车必须和其他的各辆汽车比赛两次，问一共要举行有多少场比赛?10 辆车中，每辆车与另一辆车
39、比赛一次，共有*次，表示从 10 辆汽车中任选 2 辆车比赛，共 45 次；而比赛 2 次，则共有 2*=90 次。4. The figure above shows a rectangular play area in which one child stands at B while another child runs back and forth along the entire side ADIf the running child is in a position randomly located along side AD at a given time，what is the
40、probability that the two children are at most 50 feet apart at that time?（分数：1.00）A.B.C.D. E.解析：左面图形表示一个长方形的娱乐区，有一个小孩站在 B 点，同时另一个小孩在 A 和 D 之问来回跑动。若跑步的小孩在 AD 边上的位置在任一时刻都是随机的，两个小孩最多相距 50 英尺的概率(probability)是多少?根据题意可知，两个孩子的位置及点 A 在任意时刻都可构成一个直角三角形，直角三角形的斜边长就是两个孩子之间的距离，两个孩子的距离不超过 50 英尺，即直角三角形的斜边不超过 50 英尺，
41、AB=30 英尺，根据勾股定理可知，跑步的小孩离 A 点的距离应不超过 40 英尺时，才能使他们之间的距离不超过 50 英尺。而跑步的小孩在 AD 上的位置是随机的，因此两个小孩最多相距 50 英尺的概率是*5.A certain computer program generates a sequence of numbers P1，P 2，P n，by the rules P1=1，P 2=1，and for n3，P n=Pn+1+pn-2，Which of the following equals P 5?A. 10 B. 11 C. 14D. 15 E. 17（分数：1.00）A.B.
42、 C.D.E.解析：44。某计算机程序根据规则 P1=1，P 2=1，并且对于 n3，P n=Pn-1+2Pn-2产生一系列数字P1，P 2，P n问下面哪一项等于 P5?解答本题时只要把数字代入规则即可：P3=P2+2P1=1+2=3P4=P3+2P2=3+2=5P5=P4+2P3=5+6=116.The buyer of a certain mechanical toy must choose 2 of 4 optional motions and 4 of 5optional accessoriesHow many different combinations of motions an
43、d accessories are available to the buyer?A. 8 B. 11 C. 15D. 20 E. 30（分数：1.00）A.B.C.D.E. 解析：一购买机械玩具的顺客必须从 4 个可选择的机械装置中选择 2 个，且从 5 个附件中选择 4 个，问共有多少种不同机构装置和附件的组合可供这个顾客选择?从 4 个机械装置中选出两个的组合数为*，而从 5 个附件中选出 4 个的组合数为*，所以总的组合数为*7.In a graduating class of 236 students。142took algebra and 121 took chemistryWha
44、t is the greatest number of students that could have taken both algebra and chemistry?A. 21 B. 27 C. 37D. 121 E. 142（分数：1.00）A.B.C.D. E.解析：一个 236 名学生的研究生班，有 142 人选修代数，121 人选修化学，问最多有多少人既修代数又修化学?本题也即求两个集合交集的最大值，交集中的元素数小于或等于较小的集合中的元素数，所以最多有 121个同时选了两门课。8.If one number is chosen at random from the first
45、 1，000 positive integers，what is the probability that the number chosen is multiple of both 2 and 8?（分数：1.00）A.B. C.D.E.解析：若从前 1000 个正整数中随机选出一个数，问该数是 2 和 8 的倍数的概率是多少?在 1 至 1000 中，8 的倍数有 125 个，因为 2 和 8 的最小公倍数为 8，则该数是 2 和 8 的倍数的概率为：*9.The odds that a certain event will occur is the ratio of the probab
46、ility that the event will occur to the probability that it will not occurIf the odds that Pat will win a prize are 4 to 3，what is the probability that Pat will not win the prize?（分数：1.00）A.B.C. D.E.解析：某事件发生的可能性(odds)为这件事将发生的概率与这件事不发生概率的比值。若 Pat 赢得一项奖的可能性为 4 比 3，Pat 赢不到该奖项的概率是多大?*10.For which of the
47、following lists of number is the median equal to the average(arithmetic mean)?A. 3，4，7 B. 1，10，19 C. 7，7，10，12D. 0，1，1，5 E. 0，2，3，4（分数：1.00）A.B. C.D.E.解析：下面哪一列数的中数(median)等于其(算术)平均值?五个选项中只有(B)的中数是 10，平均数也是 10。11.k ak pk1 100 0.102 200 0.253 300 0.204 400 0.255 500 0.20If in an experiment the probabi
48、lities of obtaining the values a1，a 2，a 3，a 4， and a 5are p1，P 2，P 3，P 4 and P5，respectively，then the expected value is defined as a1p1+a2p2+a3p3+a4p4+a5p5For the values and their corresponding probabilities in the table above，what is the expected value?A. 350 B. 320 C. 300D. 270 E. 250（分数：1.00）A.B.
49、 C.D.E.解析：若在某个实验中，得到值 a1，a 2，a 3，a 4和 a5的概率分别为 p1，p 2，p 3，P 4和 p5，那么期望值(expected value)被定义为 a1p1+a2p2+a3P3+a4p4+a5p5，对于上面表格中的值及其相应的概率，问其期望值是多少?由题中所介绍的 expected value 的求法，考生可直接把表格中的数据代入公式计算：1000.1+2000.25+3000.2+4000.25+5000.2=32012.What iS the sum of the first 2，003 terms of the sequence 0，2，7，1，0，2，7，l，0，2，7，1，if the pattern 0，2，7，1 is repeated throughout the sequence?A. 503 B. 2，010 C. 2，013D. 5，009 E. 20，030（分数：1.00）A.B.C.D. E.解析：若整个序列 0，2，7
