GRE数学难题112道练习及解答.pdf

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1、Sixty-eight people are sitting in 20 cars and each carcontains at most A people.What is the maximumpossible number of cars that could contain exactly1 of the 68 people?c12348200000If n is any prime number greater than 2,whichf the following CANNOT be a prime number?E200000In 1988 Mr.Smith s annual i

2、ncome was greaterthan Mrs.Smithes annual income.In 1989Mr.Smiths annual income decreased by p percent,whereas Mrs.Smiths annual income increased byp percent,(p 0)Column AMr.and Mrs.Smithscombined annual incomein 19883Column BMr.and Mrs.Smithfscombined annual incomein 1989AHow many integers between 1

3、01 and 201 are equalto the square of some integer?4O TwoO ThreeO FourO FiveO SixCThe price of a certain stock was 12：dollars per share.5The price increased x percent to 15g dollars per share.Column A5kAColumn B20The reflection of a positive integer is obtained byreversing its digits.For example,321

4、is the reflectionof 123.The difference between a five-digit integerand its reflection must be divisible by which of thefollowing?000002A569EColumn A11 -0.03Column B1.03AThe original value of machine X is I/dollars,whilethe original value of machine/is 21/dollars.Bothmachines depreciate in value at a

5、 constant rate of10 percent of their original value per year.Column A Column BThe value of machine X The value of machine 丫after 3 years after 6 yearsBIf n is an odd integer,which of the following is thesquare of the next larger odd integer?O?2+1O+4O z?2+2z?+1O M+4O z?2+?+19D21一44-1 14-95-94-5If 55

6、percent of a group of people have brown hair and 80 percentof the same group do not have red hair,what fraction of those whodo not have brown hair have red hair?OOOOO10cK+3n =r VIn the equation above,K,r,s,尢 and v represent positive numbers.Multiplying which one of these numbers by 2 will reduce the

7、 valueof n to|of its present value?00000A certain money market account that had a balance of$48,000during all of last month earned$360 in interest for the month.At what simple annual interest rate did the account earn interestlast month?%7%7.58%8.59%000002EColumn AThe two-digit integer thatequals tw

8、ice the sum of3 its digitsAColumn B163When the even integer n is divided by 7,the remainder is 3.Column A Column BThe remainder when 10n is divided by 1414CA car travels at an average speed of 80 kilometers per hour during a 6-hour trip andaverages 75 kilometers per hour for the first A hours of the

9、 trip.Which of the followingdistance-versns-(me graphs is consistent with this information?2 4 6Time(in hours)2 4 6Time(in hours)oooooo060ooo54432128-3W05UD02 4 6Time(in hours)2 4 6Time(in hours)2 4 6Time(in hours)005o10875?里SWOPIUD0oooooo080ooo544321(sD-3UJ0妄U)-8U5S50A15GOVERNMENT AID TO FAMILIESWI

10、TH DEPENDENT CHILDRENThe number of households receivingmonthly benefits in 1960 was approximately what fraction of the numberreceiving monthly benefits in 1975?旦Wo5616271 1328350000I-I in actual-1-1 year dollarsAverage Monthly Benefit per Household1960 1965 1970 1975 1980 1985in 1960dollars(SUO=Ew)N

11、umber of Households ReceivingNote:Graphs drawn to scale.E4The“combined age“of a group of peopleis the sum of the ages of all of the peoplein the group.Which of the followinggroups had the greatest combined age in1986?O 20-year-old malesO 20-year-old femalesO 60-year-old malesO 60-year-old femalesO 8

12、0-year-old females17DThese questions refer to the following graphs,which are drawn to scale.Ages are in wholeyears completed by December 31.DISTRIBUTION OF THE UNITED STATES POPULATIONBY AGE AND SEX,1980 AND 1986D00000Approximately how many more 10-year-old children were there in 1980 than in1986?10

13、0,000200,000300,000400,0001,000,0005The population of females was greater in1980 than in 1986 for approximately whatpercent of the ages from 0 to 100 years?O 15%O 25%O 55%O 75%O 85%19BIn 1980 the ratio of the number of malesto the number of females was greatest forwhich of the following ages?20A0000

14、01030507090 x represents the greatest integer less than orequal to x and x represents the least integergreater than or equal to z.Column AColumn B1.4AThese questions refer to the following table.22APPARENT FAHRENHEIT TEMPERATURESDUE TO WIND-CHILL FACTOR(corresponding to actual temperatures and wind

15、speeds)WIND SPEEDS(miles per hour)ACTUAL TEMPERATURES(degrees Fahrenheit)-1001020305-15-5162710-34-2231615-45-315920-53-39-10425-59-44-15130-64-49-18-235-67-52-20-440-69-53-21-5If the actual temperature is 13 degreesFahrenheit and the wind speed is 14 milesper hour,then the apparent temperaturecould

16、 beO 5 degrees FahrenheitO -12 degrees FahrenheitO -20 degrees FahrenheitO -25 degrees FahrenheitO -32 degrees FahrenheitB6These questions refer to the following table.APPARENT FAHRENHEIT TEMPERATURESDUE TO WIND-CHILL FACTOR(corresponding to actual temperatures and wind speeds)WIND SPEEDS(miles per

17、hour)ACTUAL TEMPERATURES(degrees Fahrenheit)-1001020305-15-5162710-34-2231615-45-31-5920-53-39-10425-59-44-15130-64-49-18-235-67-52-20-440-69-53-21-523Which of the following can be inferred fromthe table?I.The apparent temperature for anactual temperature of 20 degreesFahrenheit and a wind speed of1

18、5 miles per hour is the same asthat for an actual temperature of30 degrees Fahrenheit and a windspeed of 40 miles per hour.II.At a constant wind speed,as theactual temperature increases,thedifference between the actual andthe apparent temperatures alsoincreases.III.At a constant actual temperature o

19、f-10 degrees Fahrenheit,the apparenttemperature decreases at a constantrate as the wind speed increases.O I only O II only O I and III onlyO II and III only O I,II,and IIIAThese questions refer to the following graphs,which are drawn to scale.An open dot meansthe point is not included.PRICE OF A BRA

20、ND X CANDY BARoooooooooo$e-op_u)WEIGHT OF A BRAND X CANDY BAR(sgun口)-&-From 1982 to 1987 the price of a Brand X candybar increased by approximately what percent?zo/o/ozo/oo/o/oo/o/ooooo457551200000c247These questions refer to the following graphs,which are drawn to scale.An open dot meansthe point i

21、s not included.PRICE OF A BRAND X CANDY BARoooooooooo0.0.0.0.0.0.0.0.0.0.$e=opu_)C DoudOF A BRAND X CANDY BAR0How many times between 1971 and 1991 did the price of aBrand 丫 candy bar increase while the weight decreased?25O OneO TwoO ThreeO FourO FiveBPRICE OF A BRAND X CANDY BARYearHow many times be

22、tween 1971 and 1991 did the price of aBrand X candy bar increase while the weight decreased?26O OneO TwoO ThreeO FourO FiveB8Of the 500 delegates attending a convention,200 areRepublicans and the rest are Democrats.One hundredof the delegates are vegetarians and,of those whoare not vegetarians,270 a

23、re Democrats.How manyof the vegetarian delegates are Republicans?27000003LI4。50hi：i70ES is a set of n consecutive integers.Column AColumn EThe mean of S28The median of SCAn airline must charge an 1 1 percent tax on the price of anairline ticket.The airline wishes to charge the whole-dollaramount of$

24、33.00 for the ticket,including the tax.Whatprice,to the nearest$0.01,should the airline set for theticket before the tax is added?O$385.37O$389.70O$390.09O$393.64O$422.0029cFrom the probability histogram,what isthe probability that x is either 1 or 2?30O 0.35O 0.45O 0.50O 0.70O 0.75D9These questions

25、 refer to the followinginformation.The average(arithmetic mean)quiz score isclosest to which of the following?00000sc9Pmsjo-qEnN31CFrom the set of 6 letters A,B,C,D,E,and F,there are20 different 3Te甘er subsets that could be selected.Column A Column BThe number of 3-letter 10subsets that include32 th

26、e letter FCThese questions refer to the followinginformation.Thirty hospital patients who had beentreated for the same illness were given anew treatment in a research study.Theywere then asked to evaluate whether fivesymptoms,H,L,P,T,and I/,were madebetter or worse by the new treatmentcompared to th

27、e old treatment.For eachsymptom,each patient used one of fiveratings：2：much better1 ：somewhat better0：neither better nor worse-1 ：somewhat worse-2：much worseFor each symptom,the sum and standarddeviation of the ratings are listed below.RATINGS FOR SYMPTOM HRating210-1-2Number ofPatients712rstIn the

28、Ratings for Symptom H table shown,which of the following could be rt s,and 七,respectively?0000010For each symptom,the sum and standarddeviation of the ratings are listed below,SymptomSum of30 RatingsStandard Deviationof 30 RatingsH121.4。L350.69P-330.79T-260.431/20.89EIf(7,3)is the center of the circ

29、le,then the radius of the circlecould be equal to which of the following?34C00000If z+2y=2 and(x+y)2=9,which of thefollowing is a possible value of y?-8-53-23-25。00-。035E11These questions refer to the following graph,which isdrawn to scale.In what month was gas use in one ofthe years nearly double t

30、hat for thesame month in the other year?eqnQ00L103LECJUGSnseC DA HOUSEHOLDS MONTHLY GAS USE FOR 1987 AND 1988O FebruaryO JulyO AugustO SeptemberO October-g A n g1 C L O o 8BThe figure represents a rectangular level plot ofland,subdivided into identical rectangular gardens.Column AThe total number of

31、 feet offencing,indicated by the solidlines,needed to separate eachof the gardens37Column BThe total number offeet in the perimeterof the plotBThe curvature of a circle is defined to be the reciprocalof the radius of the circle.Column AThe curvature of acircle with circumference 357r38AColumn BThe c

32、urvature of acircle with circumference 36T T12The length of a rectangular box is A inches longer than thedepth,and the width of the box is 1 inch less than the length.The depth of the box is between 2 inches and 4 inches.Column A Column BThe volume of the box 200in cubic inches39DIf n is an integer

33、and 99 z?2 10?O x+(w/-10)y+10O x+(wz-10)+yO 10 x+10(H/-y)O 10 x+y(w/-10)O 10 x+wyD54The jewels in a certain tiara consist of diamonds,rubies,and emeralds.If the ratio of diamonds to rubies is?and6othe ratio of rubies to emeralds is|,what is the leastnumber of jewels that could be in the tiara?620371

34、245600000D55I8Column AThe area of the triangularregionColumn BThe area of the circularregionD56If 3 cars have traveled a total of 180,000 miles andthe distance traveled by each car differs by at least1 mile from the distance traveled by either of theother 2 cars,what is the minimum possible numberof

35、 miles traveled by the car with the most mileage?0000060,00160,00261,00091,000180,000A57These questions refer to the following graph.NUMBER OF CAT LICENSES AND DOG LICENSESISSUED IN TOWN X1985-1990450400350300250200150100500E581985 1986 1987 1988 1989 1990KSM Cat I I DogAccording to the graph,which

36、of thefollowing statements must be true?I.For each of the years 1986through 1990,the number of catlicenses issued was greaterthan that of the previous year.II.In Town more householdshad dogs in 1986 than in 1985.III.For at least one of the yearsshown,the number of catlicenses issued was more thanl|t

37、imes the number of doglicenses issued.I onlyII onlyIII onlyI and III and III00000I9How many 4-digit numbers begin with an odd digitand end with an even digit?000002505002,0002,5005,000D59Column Ay (79)(80)(81)(82)A60Column B6,400In a bowl that contains 20 marbles,7 are green,6 are red,and the remain

38、der are blue.Two marblesare to be drawn at random from the bowl withoutreplacement.Column AColumn EThe probability that onemarble is green and theother marble is redThe probability that onemarble is green and theother marble is blueB61If the sum of four consecutive even integers is 340,then the aver

39、age of the two larger integers is356788888800000D6220These questions refer to the following graph.AFEDERAL GRANTS TO THE ARTS AND THE HUMANITIES(in millions of dollars)1982 1983 1984 1985 1986 1987 1988In 1987,$30 million of the total amountof federal grants to the arts was appropriated to match fun

40、ds raised throughprivate sources.What was the ratio offederal matching funds to federalnonmatching funds in that year?47011123tototototo1333400006Note:Drawn to scale.B63The 20 people at a party are divided into nmutually exclusive groups in such away thatthe number of people in any group does notexc

41、eed the number in any other group bymore than 1.Column A Column BThe value of n if 6at least one of thegroups consists of3 peopleD64Twenty-seven people applied for a certain managerial job.Accordingto one report,the first interview narrowed the field down to fewer than7 candidates.Another report cla

42、imed that the first interview eliminatedfewer than 23 applicants from consideration.If both reports are true,and if x applicants were eliminated by the first interview,what are thepossible values of x?0000001o122220 and 21 only21 and 22 only21,22,and 23D652lTo obtain an FHA mortgage for$50,000 or mo

43、re,the homebuyer must have a down payment equal to 4 percent of thefirst$25,000 of the mortgage amount and 5 percent of theportion in excess of$25,000.At settlement the buyer paysa mortgage-insurance premium equal to 3 percent of themortgage amount.What is the maximum FHA mortgage,ifany,a buyer can

44、obtain if the buyer has only$6,000 availablefor the down payment and insurance premium?ooooo$62,500$71,875$78,125$125,000The home buyer cannot obtainan FHA mortgage.C66A$550 donation to a community fund is to be divided among threeorganizations.The hospital is to get twice as much as the communityre

45、creation center and three times as much as the volunteer fire company.How much of the donation is to go to the community recreation center?00000$50$75$100$150D67If T?is a positive integer,then+denotes anumber such that 乃+/7+1 .Column A Column B20+l下5O The quantity in Column A is greater.O The quanti

46、ty in Column B is greater.O The two quantities are equal.O The relationship cannot be determinedfrom the information given.D6822A certain holiday is always on the fourth Tuesdayof Month X.If Month X has 30 days,on how manydifferent dates of Month X can the holiday fall?00000FourFiveSixSevenEightD69H

47、ow many positive integers can be expressed as aproduct of two or more of the prime numbers 5,7,11,and 13 if no one product is to include the sameprime factor more than once?00000EightNineTenElevenTwelveD)TOThese questions refer to the following data.IN SELECTED SCIENCES IN COUNTRY X,1985 AND 19903,5

48、003,0002,5002,0001,5001,000NUMBER OF GRADUATE STUDENTS WITH RESEARCH FELLOWSHIPSIn 1990 for which of the selected sciences did the greatest percent of its graduatestudents have research fellowships?O BiologyO ChemistryO Computer scienceO EngineeringO Physics23GRA D UA TE STUD E NTS IN SE LE C TE D S

49、C IE NC E SIN C OUNTRY X,1990Number ofGraduate StudentsNumber withResearch FellowshipsB iology3,6912,700C hemistry2,4981,959C omputer Science2,1961,310E ngineering6,9203,114Mathematics2,450889Physics2,8241,614B71wf x,yf and z are all integers such that1 w x y z and w xyz=210.Column Aw+zColumn B10O T

50、he quantity in Column A is greater.O The quantity in Column B is greater.O The two quantities are equal.O The relationship cannot be determinedfrom the information given.B72击9 of 2.8 is000000.001260.01260.1261.2612.6D73Seven one-dollar bills are to be distributed amongLucia,Gomez,and Domingo so that