# 2011新GRE-数学满分不容易-要胆大心细

1. l1, l2 and l3 are three lines in space The number of points at which lines l1 and l2 intersect 2. The number of 1/4-inch lengths in a 4-inch length 1 The number of points at which lines l2 and l3 intersect

1。三条任意直线，L1 和 L2 的交点的个数与 L2 和 L3 的交点的个数没关。

2，是问 4 英尺中有多少个 1/4 英尺，应该是 16 个，所以是 A
3. The maximun number of solid cubes having edges of length 1/2 meter that can be placed inside a cubical box having inside edges of length 1 meter 4

3 边长为 1 的立方体里最多能放下几个边长为 1/2 的立方体，当然是 8 个咯
4. Cube C has volume 8 cubic centimeters The area of one of the faces of cube C 3 square centimeters

4 立方体体积是 8，那一个面的面积当然是 4 咯
5. Ms.Smith got an 8 percent cost-of-living raise of \$20 per week Ms.Smith's new weekly salary \$260

5 x*0.08=20，那 x+20=270>260
6. On a certain number live, 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.-3 E-11

6 应该是-11
7. For all real numbers a and b. if a?b=a(a+b), then a?(a?b)= A. a2+ab B a2+ab+a C a2+a+b D a3+a2b E a3+a2b+a2 注：a2 表示 a 平方，a3 表示 a 立方

7 新定义的运算 a?b=a(a+b), 那 a?(a?b)=a?(aa+ab)=a(a+aa+ab)=aa+aaa+aab
8.secretary typed 6 letters,each of which had either 1 or 2 pages.If the secretary typed 10 pages in all, how many of the letters had 2 pages? A1 B2 C3 D4 E5 答案是 D，题目我都看不懂，是啥意思呢？

9 how many of the five numbers above are each equal to the product of an integer and an odd integer that greater than 1? 这五个数是:2 6 8 14 16 a.none b.one c.two d.there e.four 我觉得这道题除了 2 不可能,其它四个数都有可能.可答案是 c,想问大家为什么?

10 这句话大家看该怎样列式子呢?这是一道图表题.

what was the approximate percent increase in personal income from 1965 to 1970? 是这样(1970-1965)/1965 还是(1970-1965)/1970 这样?

1 the sum of two numbers, x and y, equals twice their products. if x=3, what is the value of y? 这道题没大看懂?请问大家是这样么?x+y=2(x+y)

x+y=2xy,求 y.
2 if x is an integer and x2(x 的平方)<37,what is the greatest possible value of x minus the least possible value of x? 我觉得这道题 x 的最大值为 6,最小值为 0,所以选 6. a.5 b.6 c.10 d.12 e.36

3 三角形 ABC，角 B＝X 度，X>90 度，比较三角形的周长与 3 倍 AC 的长度的大小，答案是 B

AC 是最大边,所以 AB+BC+AC<AC+AC+AC(3AC).
2.0<p<1 比较 the greatest value of p(1-p)与 1／2 的大小，答案是 C

=>

p(1-p)<=1/4 < 1/2

4 for the line with equation y=ax+b,the x-intercept os twice the y-intercept 比较 the slope of the line 与 1／2 的大小，答案是 D，但算出来是－1／2 呀

5 a certain moneymarket account that had a balance of \$48000 during all of last monthearned \$360 in interest for the month. at what simple annual interestrate did the account earn interest last month? 答案是 9%,题目没看懂

6 Of the positive integers that are multiples of 30 and are less than or equal to 360,what fraction are multiples of 12? a.1/6 b.1/5 c.1/3 d.2/5 e.1/2 首先这道题我是对 multilples of ....不大明白,这是什么意思啊?其次这道题怎么解呢?

7 A certain teacher has a total ofat least 110 students enrolled in her classes.if the teachers has anaverage (arithmetic mean) of exactly 27 students enrolled per class.what is the least possible number of classes that the teacher couldhave? a.3 b.4 c.5 d.6 e.7 我觉得这道题就是用 110 除以 27 就好了,可是答案是选 c 的

8 a delivery service charges \$0.02 per ounce for the first 16 ounces ofa shipment and \$0.15 for each additional ounce of theshipment,(1pound=16ounce)

the delivery charges for x shipments weighing a combimed total of the pounds

vs 567.00

9 the cost per gram of carrots if 3 cans of carrots cost \$0.90 the costper gram of onions if 5 cans of onions cost \$1.50

10 X is an integer, and the remainder when 2X is divided by 4 is 0. The remainder when X is divided by 4 0

1 Let[X]=3, if X is an odd integer; let[X]=6, if X is an even integer. r and s are integers, 3r is odd and 5+s is odd. [r] 2 the value of the units' digit in 6^47(6 的 47 次方) 77 次方) [s] the value of the units' digit in 5^77(5 的

3r 是奇数说明 r 为奇数，所以[r]等于 3，5+s 为奇数，说明 s 为偶数，所以[s]=6

3 for all numbers r and s, where s/=(不等于)0, r#s=10r/s. 0.01#0.01 1

0.01#0.01=10*0.01/0.01=10,大于 1.
4 1<n<5,n is an integer. the sum of the first n odd integers that are greater than zero n^2(n 平方)-1

5 a^7+a^15 比较大小题 a^8+a^14 注是 a 的 7 次方,类推呵呵

6 A total of \$480 is ina certain cash register. All of the money is in one-dollar and five-dollar bills, and there are 30 more one-dollar bills than five-dollar bills. The sum of 30 and the number of five-dollar bills in the cash register 105

let x be the number of one-dollar bill y be the number of five-dollar bill x+5y=480-----1 x=y+30--------2 subsitute 2 in to 1 6y = 450 so y=75 30+75=105
7 If N is an integer, then the units digit of N 平方 cannot be

a0 b2 c4 d5 e6 谁能把题目翻译以下？谢谢

8 the value of the units' digit in 6 的 47 次方 哪个大呀？这种题怎么做呀？ 还有，黄皮书的答案是全对的吗？怎么有些明显好怪的，望指点哈~ the value of the units' digit in 5 的 77 次方

9 two successive discounts of 20percent and 40percent are equavilent tp a single discount of X percent. X 同问此题，不明白题目说什莫 52

10.已知：y=x^2-16x+64 比较"the least value of y"和"0"的大小 答案是 C, y 没有最小直呀？

y=(x-8)^2,所以 y 的最小值为 0.
1 比较"The remainder when a positive odd integer divided by 2"和"The remainder when a positive even integer is divided by 2" 答案是 A, 我觉得应该是 B 呀？

2 If x,y,and z are consecutive positive integers, with x<y<z and x+y+z an even number, which of the following could be the value of z? A.1 B.2 C.4 D.5 E.8 答案是 D,如果是 D 的话，那么 3+4+5 也不是奇数呀？我觉得 C 和 E 怎么都对呀？

even 是偶数的意思，三个连续的整数相加为偶数，则中间的书必为偶数，两边的就为奇数 了。所以选 D。
3 In a group of 80 students,24 are enrolled in geometry , 40 in biology, and 20 in both. If a student were randomly selected from the 80 students, What is the probability that the strdent selected would NOT be enrolled in either course? 我没头绪 没学过概率，怎么办呢？

4 triangular garden ABC is redesigned by increasing the length of AC by 20 percent to point C' and decreasing the length of AB by 20 percent to B'. the area of the original garden ABC the area of the redesigned garden AB'C'

5 一个三角形的三边分别是 11，5，13，怎么判断 13 的边所对的角是钝角？ 假设 11， 5 是两条直角边，斜边的平方等于 146 小于 13 的平方，所以 13 对的边是钝角 Rectangle R has an area of 60 square units and a perimeter of 64 units. The length of the shortest side of R is x and the length of the longest side of R is y. 问 x/y 大还是 1/15 大？ 这种题怎么算呀，答案是一样大

xy=60 x+y=32.得出：x=30,y=2 和 x=2,y=30.因为 y 大于 x，所以 x=2,y=30
6 Each of the following numbers has two digits blotted out.Which of the numbers could be the numbers 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 P.S. * 代表 blotted digit 咋做呀～～

7 Three solid cubes of lead, each with edges 10 centimeters long, are melted together in a level, rectangular-shaped pan.The base of the pan has inisde dimesions of 20 centimeters by 30 centimeters, and the pan is 15 centimeters deep.If the volume of the solid lead is approximately the same as the volume of the melted lead,approximately how many centimeters deep is the melted lead in the pan? 这道题实在没大看懂,盼望牛人解释...

8 On Elm Street are 6 houses on oneside of the street and 4 houses on the other.Each pair of houses on Elm Street is connected by exactly one telephone line. The total number of each lines that connect houses on opposite sides of Elm Street 这道题我是思÷这么想的:(6-1)+(4-1)=8 而答案选的是 A. 12

9 100x<y 1000x<2y 问:1100x y 这道题我是没有什么思路,请大家帮忙.

10 三角形 RST is isosceles and 角 RST=40 问 the sum of the measures of the two angles of 三角形 RST that have equal measure 和 120，哪个大？ （题目讲啥？）答案是不能比较

1 d=5.03894,and e is the decimal expression for d rounded to the nearest thousandth. 问 the number of decimal places where d and e differ ，和 4 比较 ，哪个大？（这个也不晓得题目在讲 啥）答案是 4 大

2 n is an odd integer, and S is the finite sequence of consecutive integers1,2,3,4,...,n The number of terms of S that are odd The number of terms of S that are even

n 为奇数时，S 序列中奇数数量多于偶数。
3 ab>0 (a^2+b^2)/a+b a+b

(a^2+b^2)/a+b=a+b-2ab/a+b 当 a,b 都大于零时，前者小于后者；当 a,b 都小于零时，前者大于后者。
4 图画不出来。 。一个三角型，2 条边为 X，一条边为 Y，边 Y 上的高把三角形分成两半，问一半的面积和 xy/4，哪个大？ (答案是 xy/4 大）

5 The water level in a tank is lowered by 6 inches, then raised by 8 inches, and then lowered by 4 inches. If the water level was x inches before the changes in level, which of the following represents the water level, in inches, after the changes? a. X-1.5 答案选 A B.X+1.5 C.X-6.5 D. X+6.5 E. X-18.5

6 If the cube of n is 180 greater than the square of n, then n=? A. 10 答案选 E B.9 C.8 D.7 E. 6

n 三次方值比 n 平方值大 180，如果解不出来，一个个带入就行了。
7 一个边长为 3 feet 的立方体顶面 ABCD 由对角线 AC 将立方体分开两个相等的部分，问分开的一部分每 个面的总面积和 36 square feet 之间的大小？答案为：Ａ，但是我算出来应该是相等？？

5 个面， 应该是大于 36， 有一边是 3sqrt(2)
8 A certain five-number committee must be assembled form a pool of 5 women---A,B,C,D,E, and three men—X,Y,Z, what is the probability that the committee will include B,C,E,Y and Z? A.1/30 B. 1/25 C.2/35 D. 1/15 E.3/32

9 Diane completed each of her exercise in 25 seconds and rested for 55 seconds between the exercise sets. What is the ratio of the amount of time it took her to complete an exercise set to the amount of time she rested between the sets? (A)5:6

(B) 5:11 (C) 6:11 (D) 11:5 (E) 11:6 答案是 B

25/55=5/11
10 Which of the following CANNOT be a factor of (A)6 (B)8 (C) 27 (D) 42 (E) 54 答案是 C 2^i*3^j where i and jare positive integers?

1. 5 is 1/5 of x 比较 x 与 1 大小?

2. 一个圆上有一点(Z,y)，半径是 5 The circle above with center O has a radius of 5 圆上的点(Z,y)的 y 与 20 开根号比较

3 which of the following points（x,y）is not on the graph of y<2x? A.(-3,-7) B.(3,3) C.(2,-9) D.(2,2) E.(2,5) 首先是要问大家这是一个什么样子的 graph 呢?然后是对折刀题没有什么思路...

4 A bicycle registration costs \$2.5 in city x and \$3.0in city y.At these rate, the cost of 4 registration in city x is k percent of the cost of 3 registration in city y k 90 这道题我是这样想的,4×2.5=k*3*3.0,课答案选的是 A...

5 In a rectangular coordinate system, line k has x-intercept 4 and slope -2 the y-intercept of k 2 这道题是因为我不能理解 x(y)-intercept 的意思...

6 When it was found that 150 more tickets for the school play were sold than the seating capacity of the auditorium.It was decided to have two performances.If the total number of tickets sold was equal to the total number who attended and if the auditorium was 2/3 full for each of the two performances, what is the seating capacity of the auditorium? A.100 B.200 C. 225 D.300 E.450 这道题我没什么思路,请牛人给出解释.主要是读题时头都大了...

7 the total area of 18 nonoverlapping circular regions,each having a diameter of 2 inches 36 square inches 答案选Ａ 我怎么觉得是Ｄ呢？ 题目到底是什么意思？

8 the scores reported for a certain mutip;e-choice test were derived by subtracting 1/3 of the number of wrong answers from the number of right answers .On a 40 question test,if none of the questions was omitted and the score reported was 20. how many wrong answers was there? 5 10 15 25 30 选 c

9 The tenths digit of .....是指十位数吗? The tenths digit of 为十分位，即小数点后第一位。 10 Olive oil, vinegar, and water were combined to make 10 cups of salad dressing. The oil and vinegar were mixed in the ratio of 2 parts oil to 3 parts vinegar. 10. The number of cups of water used in the salad dressing 这题什么意思? 5

1 A candy assortment consists of seven flavors of chocolate-coveredcreams packed in two-layered boxes with 27 creams in each layer. Theflavors are always packed in rows so that the flavor varies with eachpiece in the following order, vanilla, orange, cherry, vanilla,raspberry, lime, pecan, cherry, lemon. How many chocolate-coveredvanilla creams are needed to pack 200 boxes of the assortment? (A) 600 (B) 1,200 (C) 1,800 (D) 2,400 (E) 3,600 这题看着晕的要命,不知道怎么回事?

2 一个八边形,内角相等,横边得竖边长都为 1,斜边长为根号 2,面积是多少.答案是 7

3 X 是大于 1 的整数,下面哪个大. 3x+1 ; 4x

. (注,答案是无法比较大小)

3x+1-4x=1-x，说明 x<1 时答案为 A，x=1 时答案为 C，x>1 时答案为 B 所以选 B，答案错误！
4 X＞1, Y＞1 下面哪个大：1/(1/x+1/y); 1/x+1/y (注,答案是无法比较大小)

5 S is the set of all fractions of the form n/n+1, where n is a positive integer less than 20. The product of all the fractions that are in S 1/20

6 A retail business has determined that its net income, in terms of x, the number of items sold, is given by the expression x2+x-380. （第一项是 x 的平方）

The number of items that must be sold for the net income to be zero

10

7 w, x, y, and z are consecutive positive integers and w<x<y<z. The remainder when (w+x)(x+y)(y+z) 1 答案是 C ， 不理解。题也不理解， 答案也不理解啊！

8 新东方数学黄皮书的 section65 中的第 9 题 the three small rectangles have the same dimensions, ps/rs 是否 大于 1/2？

2/3，大于 1/2 小矩形设短边长为 1，则小矩形的长边长为 2； 所以大矩形的短边长 PS=小矩形的长边长=2，大矩形的长边长 RS=小矩形短边长+小矩形 长边长=3； 因此 PS/RS=2/3>1/2
9When 9 students took a zoology quiz with a possible score of 0 to 10,inclusive, there average (arithmetic mean) score was 7.5. If a tenthstudent takes the same quiz, what will be the least possible averagescore on the quiz for all 10 students?

(A) 6.5 (B) 6.75 (C) 7.0 (D) 7.25 (E) 7.5

KEY:题目是 the least( possible average),是问十个人最低能考到的分数,而不是问选项中哪 个分数出现的几率最低,如果理解为后者那么选 a, 因为 a 的几率为 0,但是题目的本意是前者, 所以 7.5*9/10=6.75,选 B.
10 d=561.165 比较 the tenths digit of 100d，和 the tenths digit of d/100，答案是一样大。 不懂 the tenths digit 是否指得是十位上的数字？

the tenths digit 是第十分位的数，100d=56116.5,d/100=5.61165，第一个的十分位为 5， 第二个的十分位为 6。所以选 B。
1 If one number is chosen at random from the first 1,000postiveintegers, what is the probability that the number chosen ismultiple ofboth 2 and 8? 从 1 到 1000 中选出的同时是 2 与 8 的乘积的数概率是多少? 答 案是 1/125 我的解法是这样的:: 只有满足 8*2 62/1000. 错在哪儿呢? 8*4...........8*124 可以满足,也就是只有 62 个,概率就应该是

2. How many 3-digit positeve integers are odd and do not contain the digit " 5" ? How many positive 4-digit integers begin (on the left) with an odd digit and end with an even digit?

3.A printer numbered consecutively the pages of a book ,beginning with1on the first page .In numbering the pages,he printed a total of189digits. 与 100 比较？什么意思呀？ 看不懂啊，郁闷！

4 certain integer n is a multiple of both 5 and 9.Which of the following must be true ? I. n is an odd integer. II. n is equal to 45. III. n is a multiple of 15 答案 是 只有 第三个 对 ， 第二个 为什么不对呢？

5 the number of prime numbers greater than 40 and less than 50 the number of prime numbers greater than 10 and less than 20

40 到 50 的质数有：41，43，47. 10 到 20 的质数有：11，13，17，19.所以后者大于前者。 Ms.Smith got an 8 percent cost-of-living raise of 20\$ per week.
6 Ms.Smith's new weekly salary \$260

20/0.08=250,小于 260.选 B。
71<n<5,n is an integer The sum of the first n odd integers that are greater than zero (n^2)-1

n=2, 前 2 个大于 0 的奇数为 1、3，所以和为 1+3=4 (n^2)-1=3 n=3, 前 3 个大于 0 的奇数为 1、3、5，所以和为 1+3+5=9 (n^2)-1=8 n=4, 前 4 个大于 0 的奇数为 1、3、5、7，所以和为 1+3+5+7=16 (n^2)-1=15 所以前者大于后者。

8 M＝3^5*5^3 N=2*3^5*5^3 the value of the units' digit of M the value of the units' digit of N

9 if n is an integer,then the units digit of n^2 cannot be a.0 答案为 b b.2 c.4 d.5 e.6

10 Rack A holds 80 pairs ofslackswith prices ranging from \$12 to \$15 a pair, and rack B holds 60pairs ofslacks with prices ranging from 13\$ to 18\$ a pair. If all theslacks aresold, what is the greatest amount by which the revenue fromthe slacksof rack A could possibly exceed the revenue from the sale ofslacks onrack B 412 没理解好(80*15-13*60??)

1. How many 3-digit positeve integers are odd and do not contain the digit " 5" ? How many positive 4-digit integers begin (on the left) with an odd digit and end with an even digit?

2.A printer numbered consecutively the pages of a book ,beginning with1 on the first page .In numbering the pages,he printed a total of 189digits. 与 100 比较？什么意思呀？ 看不懂啊，郁闷！

3certain integer n is a multiple of both 5 and 9.Which of the following must be true ? I. n is an odd integer. II. n is equal to 45. III. n is a multiple of 15 答案 是 只有 第三个 对 ， 第二个 为什么不对呢？

4 Lin and Mark each attempt independently to decode a message. If the probability that Lin will decode the message is 0.80, and the probability that Markwill decode the message is 0.70, find the probability that at least oneof them will decode the messge