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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?

这是说秘书打六封信,没一封信要 1 页或者两页。如果秘书总共打了 10 页,那么有多少封 信是两页? 解答:设有 x 封,则 2x+(6-x)=10,解得 x=4.
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?

题目意思是这 5 个数哪些可以是 2 个>1 的数的积,一个是奇数,一个是整数,只有 6 和 14 的 因数中有奇数,所以 C.
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?

是这样:(1970-1965)/1965
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

选 D,最大为 6,最小为-6.
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

答案错了,选 B p+(1-p)>=2p(1-p)^1/2

=>

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

还有截距为零的情况,所以 D.
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

意思是一个货币市场上个月共结余 48000,用它赚了 360 的利息,问以年单利计算每年利 率是多少? 360*12/48000=9%
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?

在小于 360 的 30 的公倍数中,也是 12 的公倍数的占多少?30N≤360, 得 N≤12,所以共有 12 个数满足题干. 又 12 与 30 的最小公倍数为 60,其实此题是求是 60 的倍数又小于等于 360 所占比例,同理求 出为 6 所以,6/12=答案 E
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

是呀,110/27=4.04,如果是 4 个班,那么总人数为 108,还剩 2 个。当然是 5 个班了。
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

这道题答案选的是 D,不明白怎么会无法确定呢?我是这样算的:16×0.2+(25*16-16)×0.15...这样对么?

因为 x 是个未知数,所以你无法确定它的值。
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

无法确定,没有告诉 1can 有多少克?
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

选 D,当 x=2,-2 时,余数为 2,-2,其它情况为 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

比较两个数的个位,6 不管多少次方个位都为 6,5 不管多少次方个位都为 5.
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

说的是 n 个大于零的奇数和。 当 n=2,1+3=4;n^2-1=3; 当 n=3,1+3+5=9;n^2-1=8; 当 n=4,1+3+5+7=16;n^2-1=15 所以选 A
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

后-前=a^7(a-1)+a^14(1-a) =(a^7-a^14)(a-1) 然后讨论,最后结果是后-前的差<0,但当 a=1 时,相等。所以选 D.
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

就是 N^2 的个位数不能为几,应该选 B 吧
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

这是比较 6 的 47 次方的个位数与 5 的 77 次方的个位数的大小。 6 的多少次方个位数都为 6,5 的多少次方个位数都为 5.所以前面大于后面。选 A。
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

我理解的阿:打折 20%后再打折 40%,结果等于打一个 X 折,比较 X 和 52 的关系 (100-20)*(100-40) = 48 X = 100 - 48 = 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?

奇数除 2 余数必为 1,偶数除 2 余数必为零,选 A
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?

这里 24 个学几何,40 个学生物,20 个全学。问两个都没学占多少比例。 单学几何的有 24-20=4 个,单学生物的有 40-20=20 个,所以学了这两门的任何一门的有: 20+4+20=44 个。所以没学的就是 80-44=36 个。 所以概率为:36/80=9/20.
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'

三角形 ABC 的面积:AC 的长度乘以 AB 的长度。 三角形 AB'C'的面积:1.2AC 的长度乘以 0.8AB 的长度=0.96 三角形 ABC 的面积 所以选 A
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~~

这是求下面哪个数能被 24 整除。 当尾数为 2, 时, 6 倒数第二个数应该为奇数。 当尾数为 0, 4,8 时,倒数第二个数为偶数。所以选 E。
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...

三个铅块,每个边长 10cm,熔了之后放在一矩形平底锅内.锅的底面积 20×30,高 15.问这三个 熔了的铅块倒进锅了有多深?
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

你理解错了,题目求连接街道两面的电话线有几根? 24 个?,因为有一边就 4 栋房子啊,4×6.
9 100x<y 1000x<2y 问:1100x y 这道题我是没有什么思路,请大家帮忙.

由上两式知道 x<y/500,所以 1100x<2.2y;但是不一定小于 y.所以无法确定。选 D
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

题目告诉了你等腰三角形有一个角是 40,问你相等的两个角的和和 120 比大小 如果 40 是顶角,那么两个相等角的和是 140 大于 120,如果是底角,那么两个相等角的和 是 80 小于 120,所以不能比较
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

这道题是问你在哪一位小数位 d 和 e 不同,e=5.039,所以是在第三位不同,所以小于四
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)

设 Y 上的高为 h,一半的面积为:1/2*1/2*y*h=y/4*h.所以比较的就是 h 和 x 的大小。因 为 h 是这个三角形的直角边,而 x 是斜边。所以 h 小于 x,所以 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

题目没有说明 x 的大小。有可能 X<6 .而除 A 外,其他答案都是不可能的。
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

理解成 3:2 的组合,就选 A 总体几率应该是 1/55
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?

这个数必须是个偶数,所以选 C。
1. 5 is 1/5 of x 比较 x 与 1 大小?

答案是 A 5 是 X 的 1/5,所以 X=5X5=25 大于 1
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

答案是 A,因为无论 Y 在哪里都坐落于圆上,既它到 O 的距离为 5>根号 20
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...

这道题是说 x,y 哪个不满足 y<2x。这里只有 E 符合。
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...

对呀你这样算出来的 k=1.1,人家问的是 k percent,所以要乘以 100,得 110.所以选 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...

可以列出方程式:y=-2(x-4)=-2x+8,当 x=0 时,y=8,即在 y 轴的截距为 8.选 A.
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...

这道题的意思是:当学校演出所卖的票比剧院的容量多 150 个时,需要演两场。如果卖票

数等于参加的人数,那么每场演出的人数为剧院容量的 2/3.问剧院的容量? 设剧院容量为 x,得: (x+150)/2=2/3 *x,得出 x=450,选 E.
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?

这句话是说:18 个不重叠的圆的总面积为多少?每个圆的直径为 2. 所以 18 个圆的面积为:18 派,大于 36,所以选 A
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

设错了 X 个题,则对了 40-X 个,总分为 40-X(对的题数)-1/3X(错的 1/3)=20 解出来 X=15
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

我的理解是,oil 和 vinegar 的比例是 2:3,即放 2 份的 oil 要放 3 份的 vinegar,但由于并 没有涉及水的比率也并不知道配制 1 杯 sd 需要多少 oil 或 vinegar 或水, 所以无法判断配制 10 杯 sd 需要多少杯水。
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?

我的理解是,一块 box 有两层,每层有 27creams,题中说口味是 packedinrows,又给出了 一个 9 个 flavors 的排列, 我认为这一层是 3 行这样的排列, 按此计算, 每层有 3*2 个 vanila, 一块 box 有 2*3*2 个 vanila,所以 200boxes 有 200*2*3*2=2400 个 vanila 的 creams。
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

八边形的面积分解成一个正方形+4 个矩形+4 个等边直角三角形, 此题那个正方形的面积为 为竖边与横边的乘积为 1,斜边为根号 2,所以直角三角形的两条直角边为 1,这样 4 个三 角形的面积为 1*1/2*4=2。4 个矩形面积为 1*1*2+1*1*2=4,所以总面积为 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)

第一项太麻烦,化简为 xy/(x+y),而第二项合并为(x+y)/xy,由于未知 x+y 与 xy 的大小关 系,无法比较原题中二者的大小。
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

这是说 1/2*2/3*3/4*.......n/n+1,这里 n 小于 20.所以乘完以后为:1/n+1=1/20.所以相等。
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

这是求 x^2+x-380=0,求得 x=20.所以选择 A
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!

这道题的解法为:x=w+1,y=w+2,z=w+3.所以(w+x)(x+y)(y+z)=(2w+1)(2w+3)(2w+5), 这三个数都为奇数,三个奇数相乘还为奇数。所以除 2 必余 1.
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

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:125/1000=1/8.
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?

一个三位正整数它是奇数,并且没有 5:首先第一位有 8 个数适用,第二位有 9 个数适用, 最后一位有 4 个数适用。所以总共有 9*8*4=288 个,一个四位正整数开始的是奇数,末位 是偶数“:第一位有 5 个数适用,第二和第三位有 10 个数适用,第四位有 5 个数适用,所 以总共有 5*10*10*5=2500,所以后者大于前者。
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!

这道题是说:一个打印者数连续的页数,从第一页的 1 开始.数这些页数,它总共打了 189 个数。 首先:1-9 的单位数一共有 9 个,所以 189-9=180 为两位数,180/2=90,说明一共有 90 个两位数,从 10 到 99.所以比 100 小。
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?

这是问的是 n 是 5 和 9 的乘积,但并没有说是几个 5 和 9 的乘积,而且还有可能还有其它 的数,所以不一定是 45.
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

尾数为 3 的数的幂的个位数一定以 3,9,7,1 循环。所以 3^5 的个位数为 3. 5^3 的个位 数为 5. 所以 3*5 的个位数为 5. 所以 N 的个位数为:2*5 的个位数为 0. 所以前者大于后者。
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

这题的意思是:如果 n 为一个整数,那么 n 的平方的个位数不能是哪个? 因为没有两个相同的数相乘为 2,所以选 2.
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??)

最大的差为: 80*15-13*60=420, 最小的差为: 15*80-18*60=120.所以 412 在这个范围内。
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?

一个三位正整数它是奇数,并且没有 5:首先第一位有 8 个数适用,第二位有 9 个数适用, 最后一位有 4 个数适用。所以总共有 9*8*4=288 个,一个四位正整数开始的是奇数,末位 是偶数“:第一位有 5 个数适用,第二和第三位有 10 个数适用,第四位有 5 个数适用,所 以总共有 5*10*10*5=2500,所以后者大于前者。
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!

这道题是说:一个打印者数连续的页数,从第一页的 1 开始.数这些页数,它总共打了 189 个数。 首先:1-9 的单位数一共有 9 个,所以 189-9=180 为两位数,180/2=90,说明一共有 90 个两位数,从 10 到 99.所以比 100 小。

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?

这是问的是 n 是 5 和 9 的乘积,但并没有说是几个 5 和 9 的乘积,而且还有可能还有其它 的数,所以不一定是 45.
中的 integer 如果 前面 没有加 positive 或 minus OR negative ,是不是 都算作是 正的整数啊?

不是,没说的话,按整数处理包括正和负
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

这道题是这样解的: 问你它们两个至少有一人可以解码的概率。 你只要算出他俩都不能解码 的概率,然后 1 减就是答案了。 Lin 不能解码的概率为:1-0.8=0.2;Mark 不能解码的概率为:1-0.7=0.3 俩人都不能解码的概率为 0.2*0.3=0.06 所以至少有一个可以解码的概率为:1-0.06=0.94.


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