1、GRE-练习十二及答案解析(总分：94.00，做题时间：90 分钟)一、单项选择题(总题数：52，分数：52.00)1.If r and 8 are positive integers，each greater than 1，and if 11(s-1)=13(r-1)，what is the least possible value of r+s?A. 2B. 11C. 2D. 24E. 26（分数：1.00）A.B.C.D.E.2.If the sum of five consecutive even integers is 70，what is the value of the grea
2、test of the five integersA. 12 B. 14 C. 18D. 20 E. 22（分数：1.00）A.B.C.D.E.3.In how many of the integers between 1 and100 does the digit 5 occur exactly once?A. 10 B. 18 C. 19D. 20 E. 21（分数：1.00）A.B.C.D.E.4.If p and r are prime numbers，which of the following must also be prime?A. pr B. p+rC. pr+1 D. p2
3、+r2E. None of the above（分数：1.00）A.B.C.D.E.5.A school district has 1，989 computers，which is approximately one computer for every 686 studentsOf the following，which is the closest approximation，in thousands，of the number of students in the sch001 district?A. 30B. 120C. 140D. 160E. 200（分数：1.00）A.B.C.D.
4、E.6.What is the least prime number greater than 83？A. 85 B. 87 C. 88D. 89 E. 91（分数：1.00）A.B.C.D.E.7. （分数：1.00）A.B.C.D.E.8.1113171923A decrease of l in which of the factorsabove would result in the greatest decrease in the product?A. 11 B. 13 C. 17D. 19 E. 23（分数：1.00）A.B.C.D.E.9.Which of the followin
5、g numbers is NOT the sum of three consecutive odd integers?A. 15 B. 75 C. 123D. 297 E. 313（分数：1.00）A.B.C.D.E.10.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. 1，624 B. 1，544C.
6、 1，434 D. 1，384E. 1，264（分数：1.00）A.B.C.D.E.11.If“and 6 are integers and a-b=6，then a+b CANNOT beA. 0B. less than 6C. greater than 6D. an even integerE. an odd integer（分数：1.00）A.B.C.D.E.12.If k is an integer and 5k20000，what is the greatest possible value of k?A. 6 B. 7 C. 8D. 9 E. 10（分数：1.00）A.B.C.D.
7、E.13.A dresser drawer contains 15 garmentsIf40 percent of those garments are blouses，how many are not blouses?A. 6 B. 8 C. 9D. 10 E. 12（分数：1.00）A.B.C.D.E.14.Of the followingwhich is closest toA. 1 B. 10 C. 70D. 100 E. 700（分数：1.00）A.B.C.D.E.15.One month Mary used of her monthly salary for a payment a
8、nd more than the car payment for rentWhat fraction of her mommy salary did Mary use that month for the car payment and rent combined?（分数：1.00）A.B.C.D.E.16.A positive integer with exactly two different divisors greater than 1 must beA. a primeB. an even integerC. a multiple of 3D. the square of a pri
9、meE. the square of an odd integer（分数：1.00）A.B.C.D.E.17.Seven is equal to how many thirds of seven?A. （分数：1.00）A.B.C.D.E.18.A certain spiral staircase is designed so that each step after the first one is turned 20counterclockwise from the one immediately below it，how many of the steps make up （分数：1.0
10、0）A.B.C.D.E.19.In a list of numbers，the first number is 3，the second is 4，and each subsequent humber is the sum of all the preceding numbers in the listIf the 20th number in the list is x，what is the 25th number in the list?A. 7x B. 16x C. 32xD. 35x E. 161x（分数：1.00）A.B.C.D.E.20.Which of the followin
11、g numbers is both a factor of 48 and a multiple of 6?A. 2 B. 8 C. 12D. 16 E. 18（分数：1.00）A.B.C.D.E.21. （分数：1.00）A.B.C.D.E.22.If p is a prime number greater than 11，and P is the sum of the two prime numbers x and y，then x could be which of the following?A. 2B. 5C. 7D. 9E. 13（分数：1.00）A.B.C.D.E.23.How m
12、any positive whole numbers less than 81 are NOT equal squares of whole numbers?A. 9B. 70C. 71D. 72E. 73（分数：1.00）A.B.C.D.E.24.If n is any prime number greater than 2，which of the following CANNOT be a prime number?A. n-4 B. n-3 C. n-1D. n+2 E. n+5（分数：1.00）A.B.C.D.E.25.Saplings are to be planted 30 fe
13、et apart along one side of a straight lane 455 feet longIf the first sapling is to be planted atone end of the lane，how many saplings are needed?（分数：1.00）A.B.C.D.E.26.3104 is greater than 4103 by what percent?A. 25% B. 75%C. （分数：1.00）A.B.C.D.E.27.Of the positive integers that are multiples of 30 and
14、 are less than or equal to 360，what fraction are multiples of 12?（分数：1.00）A.B.C.D.E.28.The sum of the first 50 positive integers is1，275What is the sum of the integers from 51 to 100，inclusive?A. 2，525 B. 2，550C. 3，25D. 3，775 E. 5，050（分数：1.00）A.B.C.D.E.29.If 7l is an odd integer，then n 2-1 must beA.
15、 a prime numberB. an odd integerC. divisible by 8D. a multiple of 2nE. a positive integer（分数：1.00）A.B.C.D.E.30.If x，Y and z are consecutive integers and xyz，which of the following must be true?xyz is evenx+y+z is even (x+y)(y+z)is oddA. None B. onlyC. only D. and onlyE. ，and （分数：1.00）A.B.C.D.E.31.At
16、 College C there are from 2 to 4 introductory philosophy classes each semester，and each 0f these classes has from 20 to 30students enrolledIf one semester 10 percent of the students enrolled in introductory philosophy failed，what is the greatest possible number who failed?A. 12 B. 10 C. 8D. 6 E. 3（分
17、数：1.00）A.B.C.D.E.32. （分数：1.00）A.B.C.D.E.33.The product of two consecutive positive integers CANNOT beA. a prime numberB. divisible by 11C. a multiple of 13D. an even number less than 10E. a number having 4 as its units digit（分数：1.00）A.B.C.D.E.34.The sum of n different positive integers is less than
18、100What is the greatest possible value of n?A. 10B. 11C. 12D. 13E. 14（分数：1.00）A.B.C.D.E.35.The number 1030is divisible by all of the following EXCEPTA. 250 B. 125C. 32 D. 16E. 6（分数：1.00）A.B.C.D.E.36.Each of the following numbers has two digits blotted out Which of the numbers could be the number of
19、hours in x days，where x is an integer?A. 25，06B. 50，26C. 56，02D. 62，50E. 65，20（分数：1.00）A.B.C.D.E.37.What is the remainder when 63is divided by 8?A. 5 B. 3 C. 2D. 1 E. 0（分数：1.00）A.B.C.D.E.38.The 10 households on a certain street have household incomes that range from$34，000 to$150，000 and an average(
20、arithmetic mean)household income of$60，000If the household with the highest income and the one with the lowest income are excludedWhat is the average household income for the remaining 8 households?A. $41，600B. $47，000C. $52，000D. $61，000E. $75，000（分数：1.00）A.B.C.D.E.39.If y is the average(arithmetic
21、 mean)of n consecutive positive integers，n1，what is the sum of the greatest and least of the seintegers?A. 2y B. ny C. （分数：1.00）A.B.C.D.E.40.How many of the positive integers less than 25 are 2 less than an integer multiple of 4?A. TWO B. Three C. FourD. Five E. Six（分数：1.00）A.B.C.D.E.41.When a certa
22、in number is divided by 7，the remainder iS 0If the remainder is not 0when the number is divided by 14，then the remainder must beA. 1B. 2C. 4D. 6E. 7（分数：1.00）A.B.C.D.E.42.A 12-inch ruler is marked off in Sixteenths of an inchWhat is the distance，in inches，from the zero mark to the 111th mark after th
23、e zero mark?（分数：1.00）A.B.C.D.E.43.Of the following，which is the closest approximation to（分数：1.00）A.B.C.D.E.44.If the range of the six measurements 140，125，180，110，165，and x is 80，which of the following could be the value of x?A. 60B. 85C. 190D. 220E. 245（分数：1.00）A.B.C.D.E.45.How many positive intege
24、rs less than 20 are equal to the sum of a positive multiple of 3and a positive multiple of 4?A. TwoB. FiveC. SevenD. TenE. Nineteen（分数：1.00）A.B.C.D.E.46. （分数：1.00）A.B.C.D.E.47.What is the greatest positive integer n so that 2”is a factor of 1210?A. 10 B. 12 C. 16D. 20 E. 60（分数：1.00）A.B.C.D.E.48.Of t
25、he following，which is greatest?（分数：1.00）A.B.C.D.E.49.The numbers in a table are arranged in 10rows and 4 columns such that one number is placed at the intersection of each row and columnHOW many numbers are contained in the table?A. 14 B. 40 C. 400D. 104 E. 410（分数：1.00）A.B.C.D.E.50.Of the following，
26、which is most nearly equal to ?（分数：1.00）A.B.C.D.E.51.If n=pqr，where P，q，and r are three different positive prime numbers，how many different positive divisors does n haveincluding 1 and n?A. 3 B. 5 C. 6D. 7 E. 8（分数：1.00）A.B.C.D.E.52.For which of the following pairs of integers is the least common mul
27、tiple of the integers minus their greatest common divisor the greatest?A. 3，12B. 5，6C. 10，20D. 11，12E. 15，30（分数：1.00）A.B.C.D.E.二、比较题(总题数：42，分数：42.00)53. （分数：1.00）A.B.C.D.54.Whenx+2 is divided by 5 the remainder is 3（分数：1.00）A.B.C.D.55.k is an integer greater than 1（分数：1.00）A.B.C.D.56.n=7?193（分数：1.00
28、）A.B.C.D.57.n is a positive integer（分数：1.00）A.B.C.D.58.When the even integer n is divided by 7，the remainder is 3（分数：1.00）A.B.C.D.59.A printer numbered consecutively the pages of a book，beginning with 1 on the first pageIn numbering the pages，he printed a total of 189 digits（分数：1.00）A.B.C.D.60. （分数：
29、1.00）A.B.C.D.61.23(784) 24(783)（分数：1.00）A.B.C.D.62. （分数：1.00）A.B.C.D.63.m，p，and x are positive integers and mp=x（分数：1.00）A.B.C.D.64. （分数：1.00）A.B.C.D.65.In a new housing development，one house sold for$140，000and all the rest sold for$100，000 each（分数：1.00）A.B.C.D.66.x is the sum of the first 25 posit
30、ive even integersy is the sum of the first 25 positive odd integers（分数：1.00）A.B.C.D.67.The average（分数：1.00）A.B.C.D.68. （分数：1.00）A.B.C.D.69.The product of“ two integers is 6（分数：1.00）A.B.C.D.70.In a certain twodigit nun2berthe unitsdigit is twice the tensdigit（分数：1.00）A.B.C.D.71.A Knumber is a positiv
31、e integer with the special property that 3 times its unitsdigit is equal to 2 times its tensdigit（分数：1.00）A.B.C.D.72. （分数：1.00）A.B.C.D.73. （分数：1.00）A.B.C.D.74.d=561.165（分数：1.00）A.B.C.D.75.On a trip，Marie drove 200 miles in 5 hours using gasoline that cost her$149 per gallon（分数：1.00）A.B.C.D.76. （分数：1
32、.00）A.B.C.D.77. （分数：1.00）A.B.C.D.78.Richards salary，which is greater than$10，000，is 75 percent of Sandras salaryTeds salary is 80 percent of Richards salary（分数：1.00）A.B.C.D.79. （分数：1.00）A.B.C.D.80.n=7193（分数：1.00）A.B.C.D.81. （分数：1.00）A.B.C.D.82.d=5.03894 and is the decimal expression for d rounded to
33、 the nearest thousandth（分数：1.00）A.B.C.D.83. （分数：1.00）A.B.C.D.84. （分数：1.00）A.B.C.D.85. （分数：1.00）A.B.C.D.86. （分数：1.00）A.B.C.D.87. （分数：1.00）A.B.C.D.88.x percent of 24 is 12（分数：1.00）A.B.C.D.89. （分数：1.00）A.B.C.D.90.In each of the years 1983 and 1984，the total number of automobiles sold in the United Stat
34、es was 1.2 million more than in the previous year?（分数：1.00）A.B.C.D.91.The least common（分数：1.00）A.B.C.D.92. （分数：1.00）A.B.C.D.93.When integer n is divided by 9，the remainder is 2（分数：1.00）A.B.C.D.94. （分数：1.00）A.B.C.D.GRE-练习十二答案解析(总分：94.00，做题时间：90 分钟)一、单项选择题(总题数：52，分数：52.00)1.If r and 8 are positive int
35、egers，each greater than 1，and if 11(s-1)=13(r-1)，what is the least possible value of r+s?A. 2B. 11C. 2D. 24E. 26（分数：1.00）A.B.C.D.E. 解析：若 r 和 s 都是大于 1 的正整数(positive integer)，且有 11(s-1)=13(r-1)，问 r+s 的最小值是多少?“the least possible value”是“最小值”的意思。一个数要想被另一个数整除必须含有对方所含有的质数因子。由题中的已知条件可得：*s-1 必为一个大于零的整数，所以等式
36、右项中的 13(r-1)必能被11 整除，而 13 很明显不能被 11 整除因此 r-1 必须能被 11 整除，而 r 最小值为 12由此可得出 s 的最小值等于 14，也即 r+s 最小值等于 26。2.If the sum of five consecutive even integers is 70，what is the value of the greatest of the five integersA. 12 B. 14 C. 18D. 20 E. 22（分数：1.00）A.B.C. D.E.解析：若 5 个连续偶数(consecutive even integer)的和为 70
37、，则 5 个数中数值最大的数是多少?5 个连续偶数构成了一个公差等于 2 的等差数列。对于等差数列有如下性质：a n-m+an+m=2an。对这 5 个连续偶数应用此公式可得：a 1+a5=a2+a4=2a3，因此这 5 个数的和=5a 3=70，所以 a3=14，最大数=a 5=(14+4)=18。3.In how many of the integers between 1 and100 does the digit 5 occur exactly once?A. 10 B. 18 C. 19D. 20 E. 21（分数：1.00）A.B. C.D.E.解析：在 1 至 100 之间的数字
38、中。5 仅在它们中出现 1 次的整数有多少?解答本题的关键是考生一定要记住 5 只能在这些数字中出现 1 次，5 在其中出现两次的数字应排除掉，即5 要么在个位，要么在十位个位与十位都出现 5 的数字(55)应排除掉。个位上有 5 的数字是：5，15，25，35，4565，75，85 和 95；十位上有 5 的数字是：50，5152，5354，56，57，58 和59，一共是 18 个。4.If p and r are prime numbers，which of the following must also be prime?A. pr B. p+rC. pr+1 D. p2+r2E. N
39、one of the above（分数：1.00）A.B.C.D.E. 解析：若 p 和 r 是质数(prime number)，则下面哪一个也一定是质数?此题可用排除法。质数就是除了 1 和它本身之外，没有其他因子的数，因此(A)选项是显然不正确的；由5+7=12 可以断定(B)也是错误的，实际上两个质数的和为偶数；57+1=36 可否定(C)是错误的；3 2+52=34可断定(D)也是错误的。5.A school district has 1，989 computers，which is approximately one computer for every 686 studentsOf
40、 the following，which is the closest approximation，in thousands，of the number of students in the sch001 district?A. 30B. 120C. 140D. 160E. 200（分数：1.00）A.B.C. D.E.解析：一校区有 1989 台计算机，大约为 68.6 名学生一台，以千为单位，下面哪一项最接近校区的学生数?此题比较简单，大多数的考生都会这样来解这道题：由平均 68.6 人一台电脑可得该校区共有198968.6136，445140，000 名学生，但是考生要注意的一点是，本题
41、只是让求近似解，因此可以通过取近似值的办法来大大简化计算过程，19892000，68.67,3，由此可以口算出该校区学生人数为140 千。6.What is the least prime number greater than 83？A. 85 B. 87 C. 88D. 89 E. 91（分数：1.00）A.B.C.D. E.解析：比 83 大的最小质数(prime number)是多少?因为质数是只有 1 和它本身而不再有其他因子的数，而(A)、(B)、(C)和(E)均有其他因子，所以此题的正确答案为(D)。7. （分数：1.00）A.B.C.D.E. 解析：在上述求和中，若 X 和 Y
42、 表示 09 中的一个数字(包括 0 和 9)，则 X=由上面的加式可知，十位没有向百位上进位，由此可以推出 X=0，或 X=1。若 X=1，则表明个位没有向十位进位，显然无论 y 等于几都不会有 7+Y=1 成立；因而 X 只能是 0，则 Y=3。正确选项为(E)。8.1113171923A decrease of l in which of the factorsabove would result in the greatest decrease in the product?A. 11 B. 13 C. 17D. 19 E. 23（分数：1.00）A. B.C.D.E.解析：上式中哪一
43、个因子(factor)的值减小 1 将导致该式的乘积减少最大?设 n 为上式中的任一个因子，则当 n 减少 1 时，其乘积将减少*，所以 n 越小时减少的越多。9.Which of the following numbers is NOT the sum of three consecutive odd integers?A. 15 B. 75 C. 123D. 297 E. 313（分数：1.00）A.B.C.D.E. 解析：下列哪一个不是 3 个连续奇整数(consecutive odd integer)的和?设 3 个连续奇整数分别为 2n+1，2n+3，2n+5，其中 n 为正数，则
44、3 个连续奇整数的和=(2n+1)+(2n+3)+(2n+5)=3(2n+3)，因此 3 个连续奇整数的和必为 3 的倍数。本题中只有(E)不是 3 的倍数。10.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. 1，624 B. 1，544C. 1，434 D. 1，384E. 1，264（分数：1.0
45、0）A.B. C.D.E.解析：若某公司购买计算机终端总计花费$540，400，且每一台计算机终端花费$350，那么公司购买了多少台终端?根据计算机终端的总额和单价可得终端数量为：$540，400/$350=1544。11.If“and 6 are integers and a-b=6，then a+b CANNOT beA. 0B. less than 6C. greater than 6D. an even integerE. an odd integer（分数：1.00）A.B.C.D.E. 解析：若 a 和 b 是整数，且 a-b=6，那么 a+b 不能是：由题可得：a=b+6*a+b
46、)=2b+6所以 a+b 必然是偶数。12.If k is an integer and 5k20000，what is the greatest possible value of k?A. 6 B. 7 C. 8D. 9 E. 10（分数：1.00）A. B.C.D.E.解析：若 k 是整数，且 5k20000，那么是的最大值(greatest possible value)是多少?先把 20000 化成乘积的形式：20000=2104=2(25)4=2354因为 522 55 3，所以是最大能取 2+1=6。13.A dresser drawer contains 15 garments
47、If40 percent of those garments are blouses，how many are not blouses?A. 6 B. 8 C. 9D. 10 E. 12（分数：1.00）A.B.C. D.E.解析：一梳妆台的抽屉中有 15 件衣服，若那些衣服的 40%是上衣，那么有多少件不是上衣?根据题意可得：15(1-40%)=9 件14.Of the followingwhich is closest toA. 1 B. 10 C. 70D. 100 E. 700（分数：1.00）A.B. C.D.E.解析：下列选项中，哪一项最接近*因为题目只是要求求近似值，且五个选项的
48、数相差较大，因此考生可以按照下面的方法取各数的近似值进行计算：*15.One month Mary used of her monthly salary for a payment and more than the car payment for rentWhat fraction of her mommy salary did Mary use that month for the car payment and rent combined?（分数：1.00）A.B. C.D.E.解析：某月 Mary 用月薪的*来支付车款，房租比车款多*。Mary 这个月用于支付车款和房租的钱占其月薪的比
49、例为多少?考生在解此题要注意对比较级的正确理解。More than 前后两事物才是比较体，more 前的分数“1/4 是后者(payment for the car)的 1/4，而不是总体(salary)的*，因此车款和房租两者占月薪的比例为：*16.A positive integer with exactly two different divisors greater than 1 must beA. a primeB. an even integerC. a multiple of 3D. the square of a primeE. the square of an odd integer（分数：1.00）A.B.C.D. E.解析：仅有两个不同的大于 1 的因子的正整数一定是：大多数考生在做本题时都用了排除法，虽然用排除法也可把本题做对，但是这种方法却是不对的。考生在解答本题时一定要正确理解题意，该题问的是具有两个大于 1 的不同因子的数一定是什么样的数，并不一定这样
