GRE数学难题

GRE数学--难题解析（一）
1. On a certain number line, if -7 is a distance of 4 from n and 7 is a distance of 18 from n then n=
(A) 25 (B) 11 (C)- 3 (D) 11 (E)-11
2. The diagram represents a rectangular garden. The shaded regions are planted in flowers, and the unshaded region is a walk 2 feet wide. All angles are right angles. The sum of the of the feet shaded regions 2,800 square areas
3.The map shows the only roads that connect the four towns and shows the distance along each road.
The road distance between Austen The road distance between Coaltown
and Seburg and Woodland
4.How many positive integers less than 20 are equal to the sum of a positive multiple of 3 and a positive multiple of 4?
(A) Two (B) Five (C) Seven (D) Ten (E) Nineteen
5.Which of the following symbols should be substituted for to make both of the
statements above true for all integers n such that -2< n≤3?
(A) ≤ (B) < (C) = (D) > (E) ≥
6.In 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) 134 (D) 125 (E) 106
7.In 1984 median income for a person in the 55-64 age category was in which of the following intervals?
(A) less than $10,000 (B) $10,000-$19,999 (C) $20,000-$24,999
(D) $25,000-$34,999 (E) $35,000-$49,999
A sample of employees were tested on data-entry skills for one hour, and the number of errors (x) they made and the percent of employess (p) making x errors were recorded as follows.
8. What was the median number of errors in the sample?
(A) 3 (B) 3.5 (C) 4 (D) 4.5 (E) It cannot be determined from the information given.
d=7.56872 and d1 is the decimal expression for d rounded to the nearest thousandth.
9. The number of decimal places where d and d1 differ 4
10. In a certain country, a person is born every 3 seconds and a person dies every 10 seconds. Therefore, the birth and death rates account for a population growth rate of one person every
11. Of the positive integers that are multiples of 30 and are less than or equal to 360, what fraction are multiples of 12?
12. The figure above shows a large square formed by fitting three L-shaped tiles and one small square title together. If a rectangular floor 10 feet by 12 feet is to be tiled in large squares of this design, how many L-shaped tiles will be needed?
(A) 810 (B) 405 (C) 270 (D) 135 (E) 45
13. The daily rate for a hotel room that sleeps 4 people is $39 for one person and x dollars for each additional person. If 3 people take the room for one day and each pays $21 for the room, what is the value of x?
(A) 6 (B) 8 (C) 12 (D) 13 (E) 24
14. A positive integer with exactly two different divisors greater than 1 must be
(A) a prime (B) an even integer (C) a multiple of 3
(D) the square of a prime (E) the square of an odd integer
x>z
y>z
15. x+y z
x > y and xy≠0
2AF=AB=BD=DE=AE
17. The sum of the area of triangular The area of rectangular
region ABF and area of region BCEF
triangular region CDE
18. Each of the following numbers has two digits blotted out. Which of the numbers could be the number of hours in x days, where x is an integer?
(A)25, 06
(B)50, 26
(C)56, 02
(D)62, 50
(E)65, 20
20. The median score for the class is
(A)76 (B)77 (C)78 (D)79 (E)80
21. If 5 points were added to each score, which of the following would NOT be affected?
(A)The highest score
(B)The mean for all scores
(C)The median for the seniors' scores
(D)The mode for the juniors' scores
(E)The standard deviation for all scores
22. If the mean score for the juniors were known, which of the following could be calculated from the information given?
I. The range of the scores for the seniors
II. The median score for the juniors
III. The mean score for the seniors
(A)None (B)I only (C)III only (D)I and II (E)II and III
23. If in an experiment the probabilities of obtaining the values
are, respectively, then the expected value is defined
as For the values and their corresponding
probabilities in the table above, what is the expected value?
(A)350 (B)320 (C)300 (D)270 (E)250
24. The standard deviation of the sample The standard deviation of the sample measurements 0, 1, 2, 4, and 8 measurements 0, 1, 3, 5, and 9
25. What is the total number of different 5-digit numbers that contain all of the digits 2, 3,4,7 and 9 and in which none of the even digits occur next to each other?
(A)72 (B)100 (C)120 (D)60 (E)48
Water is to be poured at a rate of 2.5 gallons per minute into a 500-gallon tank that initially contains 50 gallons of water.
28. The percent of the tank's capacity 60 percent
that will be filled 1 hour after water
begins to be poured in
29. In the figure above, if x, y, and z are integers such that x<y<z, then the least and the greatest possible values of x+z are
(A)59 and 91 (B)69 and 135 (C)91 and 178 (D)120 and 135 (E)120 and 178
30. The figure above shows the dimensions of rectangular box that is to be completely wrapped with paper. If a single sheet of paper is to be used without patching, then the dimensions of the paper could be
(A)17 in by 25 in (B)21 in by 24 in (C)24 in by 12 in (D)24 in by 14 in
(E)26 in by 14 in
31. In the table above, what is the least number of table entries that are needed to show the mileage between each city and each of the other five cities?
(A)15 (B)21 (C)25 (D)30 (E)36
32. A store currently charges the same price for each towel that it sells. If the current price of each towel was to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?
(A)$ 1 (B)$ 2 (C)$3 (D)$ 4 (E)$ 12GRE数学--难题解析（二）
33. Pat will walk from intersection X to intersection Y along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from X to Y can Pat take that have the minimum possible length? (A)Six (B)Eight (C)Ten (D)Fourteen (E)Sixteen
34．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 those policies having incorrect electric record, 75% also having incorrect electric 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)0.80 (B)0.94 (C)0.75 (D)0.88 (E)0.92
35. There are 1200 respondents to a poll, each favoring their preference for candidates A, B,
and C. 54% favored A, 48% favored B, and 42% favored C, and there is 30% favored both A and B. what's the largest possible number of respondents favoring C, but not C & B, nor C & A?
(A)25% (B)30% (C)28% (D)38% (E)40%
36. Out of 100 ladies attending the church fete, 85 had a white handbag; 75 had black shoes;
60 carried an umbrella; 90 wore a ring. How many ladies must have had all four items?
(A)15 (B) 35 (C)5 (D)10 (E)25
37. The sergeant had fewer than 500 men to line up on parade. He tried arranging them in rows of three, but found there was one leftover. Then he tried them in rows of four, then five and six, but always there was one leftover. Finally, he tried them in rows of seven, and, to his relief, saw that the rows were exactly even. How many soldiers were lined up on parade?
(A)308 (B)241 (C)296 (D)245 (E)301
38. The vicar returns from his allotment with a small bag of tomatoes. To the first parishioner he meets he gives half the tomatoes plus half a tomato, to the second he gives half what he has left plus half a tomato and to the third he gives half what he has left plus half a tomato. He has then distributed all his bag of tomatoes. How many tomatoes did he initially have in the bag?
39. The median salary of A, B, C, D, E is $20000, the range of these five people's salary is less than $50000. We have already known that the salaries of A, B, C are $20000, $40000, $50000, respectively. What is the probable average salary of these five people?
(A)$20000 (B)$32000 (C)$18000 (D)$23000 (E)$31000
40. 一个样本在一个标准方差内的概率是0.68, 两个标准方差内的概率是0.95。

一样本
mean=18.6，标准方差是6，求：该样本在6.6-12.6内占的概率是多大？
(A)0 (B)0.68 (C)0.27 (D)0.36 (E)0.135
41. 有一组数平均值为9，标准方差为2，另一组数平均值为3，标准方差为1，问第一组数在(5,11)中的数占总数的比例和第二组在(1,4)中的数占总数的比例谁大？
42．How many pairs of integer solutions satisfy?
43. 0-9组成三位电话号码，第一位不能是0或1，三位数中相邻两位不能是同一个数，问有多少种方法？
44. 从1，2，3，4，5，6，7，8，9中选出三个数字组成一个三位数，这三位数的digits 中有两个相同，另一个digit与其它两个都不同，问有多少个这样的三位数？
(A)73 (B)144 (C)216 (D)36 (E)54
45．A, B, C, D, E, F排在1,2,3,4,5,6六个位置上，问A不在1，B不在2，C不在3，
共有多少种排法？
(A)720 (B)426 (C)180 (D)216 (E)320
46．Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x-and y-coordinates of P, Q, and R are to be integers that satisfy the inequalities -4≤x≤5, 6≤y≤16. How many different triangles with these properties could be constructed?
(A)110 (B)1100 (C)9900 (D)10000 (E)12100
47. A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box. What is the probability that the sum of the three numbers on the balls selected from the box will be odd?
(A)1/4 (B)3/8 (C)1/2 (D)5/8 (E)3/4
48. 一直线L过点A(5,0), B(0,2)，坐标原点为O，点P(X,Y)为三角形OAB中一点，问：Y<X 的概率为多少？
(A)1/4 (B)3/8 (C)1/2 (D)5/8 (E)5/7。