04年1月数学机井总结 2004

04年1月数学机井总结
2004-01-29 00:45:05 转自www.mba8.com

1.DS：if m/n=7/15, mn=?
A)m，n都为正整数 B)m,n 的最大公约数为3

2.ds: Y>0?
1)XY>0
2)XY^2>0
MY CHOICE: C
3.集合S为8个连续整数集合，集合T是S中每个整数加4以后，以及S中的每个整数减4以后的整数集合。问T比S多多少个整数？
1）4 2）8 3）2
MY CHOICE: 2) 8
ps：这道题可以变化一下，比如问T与S的交集有多少个整数，大家可以做做。

4. 3男3女中选4个人，问4个人中男女相等的概率？
MY CHOICE: 3/5

5. 1/(9-4*根号5）
MY CHOICE: 9+4*根号5

6. A1=2, A2=5, An=A(n-1)-A(n-2), n>=1,问该数列的前100项的和？

7.条件：
1) X和Y两个机器可以用来生产产品，同样生产W的产品，X要比Y多花2小时
2) X和Y两个机器一起生产3小时的话，可以生产出三分之四W（4W/3）的产品
问题：
如果要X单独生产2W产品的话，需要花费多长时间？

8.tax fare, the first 1/7mile charges 1.52dollars, then 0.33dollars for each additionally 1/7miles or partly .ask the fares of a 4.6-mile trip.(answer: 12.08 dollars)

9.一个调查，人数是60，对三种冰淇淋----v,s,c的偏好，其中3/5的人将v排在最后，2/15的人将v排在c前面， 3/10的人将v排在s前面，问将v排在最前面的人数。（答案：2人）

10.tax fare, the first 1/7mile charges 1.52dollars, then 0.33dollars for each additionally 1/7miles or partly .ask the fares of a 4.6-mile trip.(answer: 12.08 dollars)

11.一个调查，人数是60，对三种冰淇淋----v,s,c的偏好，其中3/5的人将v排在最后，2/15的人将v排在c前面， 3/10的人将v排在s前面，问将v排在最前面的人数。（答案：2人）

12.3150与一个整数y相乘后是一个数的平方，问y最小为几？
A. 2 B.3 C.4 D.7 E.14
答案为14

13.x^2+bx+c=0,哪个条件使根为正？
条件一：b>0
条件二：c>0
我觉得答案为E

14.DS x+y>0么？
条件一：x/(x+y)>0
条件二：y/(x+y)>0
我的答案为C

15.一个跑步的速度为10mile/hour，一个走路的速度为6mile/hour,两人同方向前进，当跑步的pass走路的10分钟后经过一个东东，问走路的那个比跑步的多用多少分钟才能经过那个东东。

16.1995年w公司中x产品占50%，1996年x产品比1995年增加了30%，而其他产品不变，问1996年x产品占w公司的份额。

17.5个产品中有2个坏的，问从中取两个都是好的概率?(3/10)

18.7^548除以10的余数(7)

19.一个三角形（有图），一个角为60度，另一个角为45度，其中45度对的那条边为10，问60度对的那边是多少？（居然考正余弦，faint!）

20.y=根号下（9-x），x,y都为正整数，问x,y各为多少？
条件一：x<8
条件二：y>1
答案为D

21.某人存了笔钱x，每个月末这笔钱增加d，问5个月后总额是否大于20？
条件一：x>10(不确定，反正是大于一个数)
条件二：d>5
答案为B

22.有個圓形內有兩條弦互相平行，且長度相等，求圓形內的這兩條弦所圍成的面積是多少？弦的長度是根號2，這兩條弦的中點連成一條線，長度也是根號2。

23. 一個書店賣新書和二手書。新書一本賣13元，舊書一本賣5元，有一個學生共買了67元。書店賣一本新書的利潤是成本的30%，舊書的利潤是100%，求書店賣給這個學生賺得的利潤是多少？

24.s, r, t, u are integers. which one has the same standard deviation as s, r, t, u ?
(a) |s|, |r|, |t|, |u|
(b) s+1, r+1, t+1, u+1
(c) 2s+s, 2r+2, 2t+2, 2u+2
(d) s^2+4, r^2+4, t^+4, u^2+4

25. 一台車平均時速80,問是否第一小時時速 > 90 ?
A. 第一個小時後時速 < 70
B. 一共開了兩小時

26..一个正方形,边长为4，P,Q为对边上两点，问PQ的长度范围：
应该是4
27.. one hundredth of 1 percent is ?

28.. 3男3女中选4个人，问4个人中男女相等的概率？

29. 求所有城市市民的年龄平均数：(DS)
* 每个城市的市民的年龄平均数：
*每个城市的市民人数；

30..音乐会，6个曲目，其中3个必须连续但不限顺序，求总共排法？

31.0.999999/1.00001—0.999991/1.00003

32.x^2+bx+c=0,哪个条件使根为正？
条件一：b>0
条件二：c<0
我觉得答案为B,注意!刚才看道这个jj, C的条件不一样的!!

33.DS x+y>0么？
条件一：x/(x+y)>0
条件二：y/(x+y)>0

34. 7^548, divided by 10, what is reminder (my ans 1)

35. wxyz<0, w,x,y,z 是在x轴上从左到右排列的4个点，问下面那个比对对（ wx>0, xy>0,.....my anw xy>0)

36.三角形 KLM 在第一象限 ,LM在x轴上（L左M右）问面积
a:等边三角形 b: M（12，0）（my anw: E)

37.买第1-5本书8元/本，买第6--10本7元/本，买10本以后6元/本，摩人买两次，第一次共花32元，第二次化61元，问如果他一次就买所有的书，花多少钱？（my ans 87)

38.in a group, 50%male and 40%female older than 35岁， 42%的人in this group older than 35, 问female 占总人数的 percentage.

39.(1.00001*0.99999)-(1.00002*0.99998)=? (my 10^-10,你们再算一下对不对）

40.(870)^n , 问千位数=0？ 1.:n<6 2.:n>3 (my anw b )

41.和12月jj85题相似，我以为所有数加或减同一数 sd不变。

42.圆里有两条平行等长的旋，长2根号2，两旋之间距离2根号2（通过圆心的，有图），问两旋围城的面积。

43.1到24的连续乘积，10得n次方是他的因子，n可能的最大值是多少。

44.红黑两种书在架上, 红X本, 黑Y本, 抽两本书, 没有红的可能性?
A: X:Y=1:2
B: 共多少本
Answer is C.

45.A 单独做 X 比 B 多 2 Hours, A, B together, can finish 4/5 X in Y hours, A 单独做 2X, how long?

46.问y=ax+b的斜率是否大于2？
（1）a>3
(2)b>5
我选A

47.几何题：一个园，被两条平行线分割，两条线距离是2根号2，它们被园所截的长也是2根号2，求它们截园的那个阴影面积。
答案：4+2pai

48.81的x次方=1/27的y次方，问y,x的表达式
答案：y=-4/3x

49.当集合里的数同时加减相同的数值，标准方查不变

50.坐标中两点 (-1,3)(2,-1)为一SQUARE 的对角线的两个终点，求此随SQUARE 的周长。

51.ONE PERSON WORK IN 2 WEEKS, A and B week. 已知如果一星期工作40个小时，工资为10￥PER HOUR, IF 加班的话，加班工资为15。另外，知道此人在A星期没有干满40小时，而在B星期有加班。问在B星期收入多少？
（1）在 B工作的时间比A的时间多20 小时，在B星期赚的钱比A多250￥
（2）在 B 工作的时间是A的 11/6，赚的钱是A的几分之几

52.car's speed is 10 mile/ hour, walker's speed is 6 mile/hour, after the car passed the walker 10 minutes, the car reach a fountain, ask after car passed the fountain, how long the walker takes to reach the fountain in minute?

53.一个人买东西，他将每样东西的价格都四舍五入到 1￥，（注意此处的英文表达，容易理解错） near around 1 $, 我理解的就是价格都为整数，问此人花的钱是否在10￥以内？
（1）买的ｉｔｅｍｓ的60％的价格总和 WITHIN 5 ￥
（2）共买了15 个 ITEMS
此题我选E。

54.一个数可以表达为 2^n 5^n, n is positive integer, 此数是1x2x3....x24 的因子，问n 的最大值？
my ans is 4

55.平行和主谓一致

56.一长方形内接两个全等菱形，已知长方形周长18根号2，求菱形周长。

57.DS: m,n 为两整数，m divided by 5 后，余 r , n divided by 5 后余 s. 问s=r?
1) m-n is even
2) m+n is odd.

58.给出一个柱形图，横坐标是六至十二月的平均每日用电量。纵坐标是千瓦。每月头600度电每度$0。14，超过的每度$0。11。求八月的cost.

59.给出一个柱形图，横坐标是working hours,纵坐标是人数。求working hours 的median.

60.DS, 不放回抽样，共有English and Spanish 良种，抽两本，问抽得at least one english book的概率。
1）english 与spanish 的比是1：3
2）书的总数少于20本

61.scientist studies the migration trend of a group of geese. The group contains 30% male geese. Among the geese that later on migrated, 20% are male. What is the ratio of migration factor for male geese to the migration facotr for female geese? (migration factor for sex X = number of migrated individual with sex X/total number of individuals with sex X)
Solution: Assume total geese X, of which Y migrated.
The answer is simple [(20%Y)/(30%X)]/[(80%Y)/(70%X)] = ...

62.Some guy has 6 albums of anthology from which he read one poem at least. All peoms in the albums are different. Did he read more than 6 poems from at least one of the album?
a) he has read 22 poems in total.
b) the numbers of poems he read from each album are all distinct.
Anwser: C

63. k, l, m are positive integers, does k has more prime factors than m
a) k = 30l
b) m = 10^k
Answer: C

64.sqrt{2sqrt(63) + 2/[8 + 3sqrt(7)]}
Answer: 4

65.two right cylinders, A and B. radius of A is 2 times radius of B. height of A is half the height of B. If B's radius is x and B's height is y. What is the difference between surface area of A and that of B.
Solution:
A's suface 2*pi*(2x)^2*(y/2) + pi*2*(2x)*(y/2)
B's surface 2*pi*x^2*y + pi*2xy
Difference = A's - B's

66.三角形, 有图, 一底角60度,另一底角45度角, 45度角所队边长10,求60度角所队边长为多少.
答案: 5根号6

67.某人去商店买东西,1/2买了a, 1/3 for b, 1/10 for c, and the rest $6 for candy. ask the total.
ans: 90

68.five letters d, i, i, g, t,排列组合，且两个ｉ不相邻，求有多少种做法。
我的答案：３６

69.坐标系中，有八个点，(4,5) (5,4); (-4,5)(-5,4);(4,-5)(5,-4); (-4,-5)(this one is not sure); (0,-6)
问从这八个点中任取一个点，ｘ+2y>0的概率是多少？　答案有1/8,1/4,etc

70.速度50miles per hour, if traveled 700feet, ask how many seconds used. 1mile=5280feet

71.81^x=1/(27^y), ask y in terms of x. ans: y=-4x/3

72.有一块地长15FEET，宽10FEET，用6INCH的SQUARE来铺，最少用多少块？（1FEET = 12 INCH） --》我的答案是600

73.N>K?
(1) N < 5K - 30
(2) K<30
我选的E

74.有12个数字，不是偶数，就是可以让5整除，其中又5个可以让2整除，由8个可以让5整除，问多少个可以被10整除？

75.what is the sum of a certain pair if consecutive odd integers?
(1) at least one of the integers is negative
(2) at least one of the integers is positive
ans: c

76.if y is the smallest positive integer such that 3150 multiplied by y is the square of an integer, then y must be:
a.2 b. 3 c.7 d. 4 e. 14
ans: e.14

77.the surface of a certain planet reflects 80 percent of the light that strike it. the clouds around the planet then absorb 40 percent of the reflected light. what percent of the light that strikes the planet is reflected from the surface and passes trough the clouds without being absorbed?
ans: 40%

78.if x>1 and y>1, is x (1) x^2/(xy+x)<1
(2) xy/(y^2-y)<1
ans: e

79.in a meeting of 3 representatives from each of 6 different companies, each person shook hands with every person not from his or her own company . if the representatives did not shake hands with people from their own company, how many handshakes take place?
ans:135

80.from a group of 3 boys and 3 girls, 4 children are to be randomly selected. what is the probability that equal numbers of boys and girls will be selected?
ans: 3/5

81.the first roll of a cinema has 16 seats, the roll immediately after the first roll has 2 more seats than the first roll. every roll has two more seats than the roll immediately in front of it. the last roll of has 64 seats. how many seats does this cinema have?
ans: 1000

82.in the parallelogram shown, pq=4, qr=6,angleqps is 30 degree, what is the area of pqrs?

q ______________r
/l /
/ l /
p /__ l__________/s

83.a scientist recorded the number of eggs in each of the 10 birds' nests, what was the standard devition of the numbers of eggs in the 10 nests?
(1) the averge (arithmetic mean) number of eggs for the 10 nests was 4
(2) each of the 10 nests contained the same number
ans: b

84.the base of a retangular solid tank is a square, the length of each side of the square is 4 meters, the altitude of the tank is 6, if there is 16 cube meters water in the tank, what is the rate of the volume of water in the tank to the volume of the retangular solid tank?
ans: 1/6

85. is n more than m?
a. n is more than 2m-1 b. m is more than 1

86. ask what is the unit digit of n?
a. n is divided by 5, reminant is 3
b. n divided by 4, no reminant

87.some money deposit to bank, ask for the simple interest rate
a. each $70 , get $2.10 interest.
b. each $20 , get $0.66 interest

88.$20.000 deposit into bank, compand quarterly, ask for this compand interest.
a.the intrest in 2nd quarter is 1.1 times more than the first quarter.
b. the intrest in 2nd quarter is 2 dollars more than the first quarter.

89. s=0.abc. ask s is more than 2/3?(old jj)
a.a+b is more than 14
b. a+c is more than 15

90. six musicians put into order, 3 of them have to be put together(their order does not matter), ask how many ways?

91.a1=3, a2=5, a(n+1)=an-a(n-1), ask s100=?(old jj)

92.buy wines, first 5 bottle $8each bottle, from 6 to 10(inclusive) $7each, more than 10 is $12 each. buy seperate $32 and $61, ask if buy together how much need to pay.(old jj)

93. 1/(9- 4xsqurt5) old jj

94. x is more than 3 but less than 100, ask how many prime squres are in 3/x. ( 9 and 25 only)

95.two identical square in one rectangular, the perimeter of rectangular is 18xsqurt2, ask the perimeter of each square(old jj, but old jj but rhombus instead of identical square)

96. 3男3女中选4个人，问4个人中男女相等的概率？

97.音乐会，6个曲目，其中3个必须连续但不限顺序，求总共排法？

98.买第1-5本书8元/本，买第6--10本7元/本，买10本以后6元/本，摩人买两次，第一次共花32元，第二次化61元，问如果他一次就买所有的书，花多少钱？（ans 87)

99. A1=3， A2=5， An=An-1 – An-2 ， pls add A1， A2 to A100，ask the result
Answer： 7

100.一个长方形长150米，宽100米，问用0。5米边长的正方形，来覆盖，要用多少？

101.(数据可能不准)
数轴上四点A,B,C,D(从小到大),AD=10,问长问短BC=?
1>AB=6
2>CD=5
我的答案:C

102.PS比较大小
R=-根号下(0.0025), S=-根号下(1/1600), T=-[根号下(0.04)]/2
我的答案:T
103. One ball will drop from a certain height. The height it will reach after rebounding from the floor is 75 percent of the previous height. The total travel is 2146cm when it touchs the floor on third time. Ask for the original height?
a)400cm
b)500cm
c)600cm
d)700cm
e)800cm
Answer: c

104.Jan's 160. change 4w/3 to 5w/4.
my Answer: D, 12

105.DS, the sum of four consecutive odd numbers is 12 less than the sum of four consecutive even numbers, ask for the least among the odd numbers?
a) the sum of four consecutive odd numbers is 48.
b) the sum of four consecutive even numbers is 60.
my answer: D.

106. one rectangle with perimeter of 18*Sqr2 is inscribed by two identical squares(there is a picture which shows: the two squares are turned 45 degree so that one vertex of a diagonal of one square touches one vertex of a diagnoal of the other inside the rectangle, and the rest of vertex of each diagonal of two squares just touches the edge of length and width of the rectangle. I hope that I made it clear), ask for the perimeter of a square?
my answer: 12.
2*(a^2) = ((1/2)*L)^2, 2*(a^2) = w^2, 2(L+w)=18*Sqr2, get a=3

107. 3x + 7y = 9, ask for ratio?
my answer: -3/7

108. pick up 2 from 12 items, the order does not matter, How many
selections are there?
My answer: C(2, 12) = 66.

109. sb A finishes the first 10 miles with speed of 40miles/hr, and the rest of 20 miles with speed of 60miles/hr, ask average speed?
my answer: 51.4

110. DS. two kinds of balls in a box, A and B, pick two balls from the box,
ask the probability that at least one A ball is picked?
a) A:B=3:1
b) the total balls in the box is less than 20.
My: e

111. which of following satisfy f(ab)=f(a)f(b)?
My: f(x)=Sqr(x)

　

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