[讨论]我整理的10月MATH JJ－欢迎大家来对答案－答案更新（1－91）

lzger2000

讨论稿中好些没有更新，查看了讨论后，自己整理了一下，将题目不足部分补全（如有英文，尽量用英文；如有重题，以第一次出现为准），并列结果。欢迎指正。随时更新。

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1九月JJ的變形題,一个班90个鬼子选课，每人至少选一门，选A的有60，B的40，C的20，三门都选的5个，问只选两门的几个？

SA=20;讨论：请参见9月jj, <(60+40+20)-90>-5*2=20, 或用笨办法画图

 2.一家公司, 有拿business degree 的佔40%, 講法文的佔80%. 員工結構是, 要嘛會講法文, 要嘛有business degree, 要不就是兩者兼具, 求拿business degree的有多少比例是講法文

SA=50％

 3.有一題幾何圖, 長的很怪, 我算不出來面積... AB=BC=8, CD=2, B和C都是直角, AE=ED=13, 求他們的面積

SA=100; 讨论：连接AD,求梯形ABCD和三角形ADE的面积。梯形ABCD=(2+8)*8/2=40. 三角形ADE的面积求法是：底边AD=根号下(8-2)^2+(8)^2=10. 由E向AD引垂线，垂足为O,那么，OD=5, ED=13, 所以，OE=12, 因此，三角形ADE=12*10/2=60。
  所以，五边形ABCDE的面积=40+60=100

5.XY原料混在一起，XY的混和物需要1.5克的X和6.5克的Y，XY原料成本A元/克，兩個原料的成本在混和原料中佔同樣的比例，問X原料每克多少錢？
   

SA=8/3*A; 讨论：简单题。根据各原料成本在混合原料成本中所占的比例以及混合原料的价格，算出1.5g的X的成本。然后就可以求出每克的价钱；1.5X=1/2*(1.5+6.5)A, X=8/3A

7. (2)^-2/(1/2)^-3 (2的负2次方除以1/2的负三次方)

SA=1/32; 讨论：(1/4)/(8)=1/32

 8.Working alone, a small pump takes twice as long as a large pump takes to fill an empty tank. Working together at their respective constant rates, the pumps can fill the tank in 6 hours. How many hours will it take the small pump to fill the tank working alone?

SA=18; 讨论：设小泵用X小时，那么，大泵用X/2小时。1/[(1/x)+(1/1/2x)]=6, X=18

9. 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 odd digits occur next to each other?

SA=12; 讨论：满足条件的话，那么2，4两个数只能在2，4位。
  那么，p33*p22=12

10. One integer will be selected randomly from the integers 11 to 60, inclusive. What is the probability that the selected integer will be a perfect square or a perfect cube?

SA=0.1; 讨论：11-60中的完全平方数和完全立方数是：16，25，27，36，49。那么，概率就是5/50=0.1

11. 5 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?

SA=24; 讨论：先让一个人在位置上坐定，其余4个人来坐剩下的位置：P44因为排序和坐的位置没有关系，只和周围的人有关所以答案就是P44

12. The subset of [x, y, z] is x, y, z, xy, xz, yz, xyz. How many subsets of [x, y, z, w] contain w?

SA=8; 讨论：相当于有多少组合中含有W。1+C31+C32+C33=8

13. A three-digit code consists of digits from 0 to 9. If the first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot be 0 at the same time, how many codes are possible?

SA=152; 讨论：我分了两种情况：1. 第二位是0。C81*C91=72, 2. 第二位是1。C81*C10,1=80. Total=80+72=152

 14. A jar contains 12 balls, including three red and nine blue; another jar contains 20 balls, including eight red and 12 blue. If one ball is selected from each of the two bags, what is the probability that two blue balls will be selected?

SA=9/20; 讨论：(C91*C12,1)/(C12,1*C20,1)=9/20

15. What is the remainder when positive integer x is divided by 7 1). X+1 is divisible by 7 2). X+13 is divisible by 7

SA=D; 讨论：条件1：X+1=7a, X=7a-1, 可知，余数为6。条件2：X+13=7a, X=7a-13, 可知，余数为1。所以，D

16. A company has assigned a distinct 3-digit code number to each of its 330 employees. Each code number was formed from the digits 2, 3, 4, 5, 6, 7, 8, 9 and no digit appears more than once in any one code number. How many unassigned code numbers are there?

SA=6; 讨论：C81*C71*C61-330=6

 17. K=wxyz, where w, x, y, z are prime numbers. Not including 1 and K, how many factors does K have?

SA=14; 讨论：4+C42+C43=14

 18. Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?

SA=20; 讨论：设需要移走X个。30*18-14*(30-x)=20x, x=20

 19. In which quadrants do the roots of the equation lie, given x and y are integers: Y = (x-2)^2 -1

SA= Quad I, II, IV; 讨论：? Y = (x-2)^2 -1 Y=x^2+4-4x-1 Y=x^2-4x+3 Y=(x-1)(x-3) so, either x=y+1 or x=y+3 we can't determine what quadrant exactly x and y lie, so the answer would be E得到最後方程式後,可以用畫圖的方式解決,帶入 Y=0 求 X-intercept帶入  X=0 求 Y-intercept,然後話出圖形後,就可以發現這個曲線只會經過 Quad I, II, IV

20. At their respective rate, pump A can fill 1/2 of a tank in 3 hours, and pump B can fill 2/3 of the tank in 6 hours. Working together, how many hours will it take A and B to fill the tank?

SA=3.6; 讨论：A的效率：1/6，B的效率：1/9。AB一起工作，所用时间：1/[(1/6)+(1/9)]=3.6

21. The value of 1/11+1/12+1/13+...+1/20 will be

A. Less than 1/3

B. Less than 1/2

C. Greater than 1/2

D. Greater than 2/3

SA=D; 讨论：这个式子的和应该在1/2和10/11之间。也就是10倍最小数和10倍最大数之间。大于1/2是肯定的。 the median is 1/15;If you draw the y=1/x in the x-y plane,you may find that the mean should bigger than 1/15(maybe close to 1/14, or 1/13), so the sum will be bigger than 1/15*10,that's bigger than 2/3.17F has confirmed D by electric caculator

22. Maria invested a certain amount of money at r percent compounded annual interest rate. r=?1). She earned an interest of $200 in the first year. 2). She earned an interest of $220 in the second year

SA=C; 讨论：条件1：知道第一年的利息，但是，不知道本金，所以，不行。条件2：同条件1。两条件联立：设本金为X，利率是r，根据条件1，2列式子，可求。r=0.1。

23. In the xy-plane, line L passes through point (1,p). Does L have a positive slope? 1). L passes through point (-p, 13) 2). L passes through point (0,1)

SA=E; 讨论：两点确定一条直线。根据条件1和条件2可单独求出两条直线方程。方程1的斜率为：(13-p)/12.正负不能确定。方程2的斜率为：p-1。也不能确定。

1> a=(b-13)/p insufficient 2>b=1 insufficient, 3> both 1 and 2, a=-12/p insufficient

24. In a class of 120 students, 80 can speak English, 70 can speak Spain, 60 can speak French. If every student in the class can speak at least one of the languages, at least how many of students in class can speak all the three languages?

SA=10; 讨论：210-120=90（两门+三门的人）会两门的人最多是80人，就是把80个english分给70和60，剩50个人，因为总数是120，所以必要有10人分到前面两者中去，所以答案是10for example：70--spain&english;10--fench&english 剩下50--fench   那这50人里有10人必要分到前面二者中去，所以至少10人会三门.(Actually I dont understand...Try to remeber the answer)

25. At the same time, Ken invested x dollars at compounded annual interest rate of 4%, and Marlon invested y dollars at compounded annual interest rate of 6%. x/y=?1). At the end of the second year, Ken and Marlon earned same amount of interest. 2). At the end of the second year, Ken earns an interests of $400, and Marlon eared an interest of $500.

SA=D; 讨论：条件1：X(1+4%)4%=Y(1+6%)6%, 可求。条件2：X(1+4%)4%=400，Y(1+6%)6%=600，同样可求

26. A’s salary for any week is $600 plus 5% of the portion of A’s sales above $2000 for that week. B’s salary for any week is 10% of his sales for that week. For what amount of sales in a certain week would A and B earn the same salary?

SA=10000; 讨论：600+5%(s-2000)=10%s, S=10000

27. Which of points (4,6) and (-5,5) is closer to the origin?

SA=(-5,5); 讨论：点(4,6)到原点的距离是：根号60，点(-5,5)到原点的距离是：根号50，所以，点(-5,5)到原点的距离更近。

28. In a certain test, a student must answer 8 out of 10 questions. How many choices are there if at least 4 of the first five questions must be answered?

SA=35; 讨论：C₅⁴ C₅⁴+ C₅³=35

29. If x=3y, is x^2>y^2? 1). y+x<y*x; 2). X^2=9y^2

SA=A 讨论: 1> x is not 0, so sufficient, 2> when x=0, not sufficient

30.XYZWK五个数的算术平均值为Z,X+Y=Z.问W+K用Z表示是多少?

SA=3Z; 讨论：X+Y+Z+W+K=5Z, 将X+Y=Z带入，W+K=3Z 

[此贴子已经被作者于2006-10-16 12:23:17编辑过]

lzger2000

31.J,M,F三个人.各分有几个水果.J的水果数是M的2倍, J比F少6个. 若J给M10个果, F给M X 个果,那么J,M,F几个人的水果数就一样了.问M 原来有几个果?

SA=36讨论：. J=2M，J=F-6，J-10=M+10+X=F-X。

32.DS: What is the tens’ digit of integer X?

1). The tens’ digit of X-9 is 1

2). The hundreds’ digit of 10X is 2

SA=C; 讨论：条件1：任何数乘以10都是所有的位数增长一位。所以，可知，原来的个位是2。条件2：不能确定。如果Y的个位数<9，那么，十位数是2。如果Y的个位数=9，十位数就是1。所以两个条件可以确定是十位数是2

34.城里有电话分机，4位数，从3，8，5中选，其中3选2次，8，5选1次，问有多少种可能

SA=12; 感觉是以前的变体，我的解答P4,4/P2,2 ;讨论：我是按位置分类讨论。1)，3在1位。P3,3，3在2位，C21*C21，3)，3在3，4位，C21。Total=6+4+2=12

35. 投硬币正面朝上次数问题，正面概率不是1/2，是DS,两个条件都比较绕，要用特殊概率的公式列一下，我选的是D,不过下一道题的难度降低了，所以不确定是否正确，那个特殊概率的题一定要看

讨论：题目不全

36.DS, 一个数在30~40之间，能否知道value?1.被3除余2，2.被4除余3

SA=C; 讨论：WAY1条件1，2都单独不可以。因为满足的数字很多，例如：31，32，35等。两条件联立：可得到通项：X=12a+11。满足条件的数只有35通项公式的算法就是：用两个分公式第一项的最小公倍数作为通项公式第一项的，用两个分公式的最小相同值作为通项公式的第2项。举个例子：N=3a+2, N=5a+3, 则通项公式的第一项就是3a和5a的最小公倍数也就是15a. 通项公式的第二项就是当N=3a+2, N=5a+3这两个式子相等时的N的最小值，也就是8那么，通项就是N=15a+8 ; WAY2, x被3除余2，被4除余3，所以x+1就既被3整除又被4整除，也就是呗12整除，直接得出x=35 WAY3: LIST ALL POSSIBLE NUMBER

37.Pumps A, B, and C were used to fill a tank. If rate of A  is greater than rate of B, is rate of C greater than rate of B?

1). To fill the tank, A and B together takes half of the time taken by C

2). To fill the tank, B takes 3/4 of the time taken by C

SA=D; 讨论：条件1：A+B=2C，C=(A+B)/2,  A+B>2B，所以，C>B.条件2：C=3B/4，C<B.

38.一个数列，后项是前几项相加之和，比如a2=a1,a3=a1+a2,已知n>=3,an=p,问a(n+2)等于多少？

SA=4P; 讨论：an=a1+a2+...+an-1=p。an+1=a1+a2+...+an=2p，an+2=a1+a2+...+an+1=2p+2p=4p; WAY2由题设可以推出：An=2An-1

39.For integer n, f(n) denotes the remainder when n is divided by integer k. Is k greater than 10?

1). f(k+32)=8

2). f(k+42)=6

SA=A; 讨论：条件1：(K+32)=ka+8, K=24/(a-1) ,  k 必須大於8 並且是整數, 所以k=12或24 条件2：k+42=ka+6, k=36/(a-1) , K必須大於6並且是整數, 所以k有可能為9或者12，18

1). f(k+32)=8

2). f(k+42)=6

SA=A; 讨论：条件1：(K+32)=ka+8, K=24/(a-1) ,  k 必須大於8 並且是整數, 所以k=12或24 条件2：k+42=ka+6, k=36/(a-1) , K必須大於6並且是整數, 所以k有可能為9或者12，18

1). f(k+32)=8

2). f(k+42)=6

SA=A; 讨论：条件1：(K+32)=ka+8, K=24/(a-1) ,  k 必須大於8 並且是整數, 所以k=12或24 条件2：k+42=ka+6, k=36/(a-1) , K必須大於6並且是整數, 所以k有可能為9或者12，18

40.（有图）以原点、（6，0），（0，4）组成的三角形被y=c的直线截成面积相同的两部分，问c=?.

SA=4-2√2讨论：（1）先求过点（6，0）和（0，4）的直线的公式y=-2/3x+4 (2)再求与直线y=c的交点，即解这个方程组，可以得到x=3(4-c)/2 (3)利用两个面积相等的条件得到一个方程2*{[6(4-c)/4]*(4-c)/2}=4*6/2，求解便可以得到c所以，C=4+(-)2根号2。4+2根号2舍弃; WAY2根据相似三角形

[此贴子已经被作者于2006-10-15 16:41:25编辑过]

lzger2000

41.X and Y are two positive integer, y=(x-9)^0.5, what is the value of Y? (1) X>8(2)Y>1

讨论：条件1：X取值不同，y值也不同。条件2：也不能知道y得知。两条件联立：也不能求。这题也怪怪的。觉得出的没有什么意义啊。大家讨论吧

42.f(x)=(x^2)(1-x)^2, f(1-x)=?

SA= f(x); 讨论：将1-x带入：f(1-x)=[(1-x)^2][1-(1-x)]^2=f(x)
   

43.If a man had earned $14,000 more in June, the pay for June would be twice as much as May. Was the pay for June greater than May? (1)…(2) He earned more than 12,000 in June.

讨论：条件2：12000+14000=2M，M=13000，也就是说，五月份至少赚了13000。她六月份赚得比12000多并不能说明他的工资一定比五月份的13000多。所以，条件2不可以

44.一组连续的正整数，最小的是3，问有几个数？（1）the average mean is 6 ; （2）the range = average mean

SA=D讨论：条件1：最小数是3，连续，平均数是6。等差数列求和：a1=3，an=a1+n-1，Sn=n(a1+an)/2=n(5+n)/2. 平均数=6，Sn/n=(6+n)/2=6, n=7. 条件2，an-a1=Sn/n，有n=(5+n)/2，n=7

45.科学家在研究一群侯鸟geese，30％male。During the scientific experiment some geese migrated, and 20% of them were male. 问， what is the ratio of the migrating rate for male geese to the migrating rate for felmale geese?题目给了个公式 the migrating rate for a certain sex=the number of geese of that sex which migrated during the experiment/ the total number of geese of that sex

SA=7/12; 讨论：30%是m，70%是f。设研究总数是x，那么，20%x是m，80%是f。根据题目所给公式：(20%x/30%)/(80%x/70%)=7/12

46.n=101~150, 1/n的和在什么范围之内？

SA=1/3~1/2; 讨论：应该在50倍最大数和最小数之间。也就是50*1/101~50*1/150

47.X>-1, 1/X^2  +  1/(X^2-4)=0, X的范围？A: -1~0 ;B: 0~1; C: 1~2; D..

SA=C; 讨论：将上式整理，得：X^2=2, X=+(-)根号2。因为x>-1, 所以，X=-根号2舍去。x=根号2在1~2间

48. A is cycling around a track at a speed of 15 mph. B starts at the same time at a speed of 12 mph. If A and B move at the same direction and the track is 1/2 mile long, how many minutes after they start will A pass B if?

SA=10; 讨论：设时间为X。15/60*X-0.5=12/60*x。x=10

50. A fish tank is half full of water. If 10 gallons of water were added, the tank would be 7/8 full. What is the capacity of the tank?

SA=80/3; 讨论：设能装X升。X/2+10=7X/8。X=80/3

52. Terry receives 10z coins in addition to what she already had. She now has 5y+1 times as many coins as she had originally. In terms of y and z, how many coins did she have originally?

SA=2z/y; 讨论：原有X。 10z+x=(5y+1)x, X=2z/y

53. The price of a item decline by 67% every 6 months. At the rate, approximately how many years will it take for the $81 item to reach $1?

SA=2; 讨论：81(1-67%)^x=1, 1/3^x=1/81, X约等于4。则，需要用24个月也就是2年。

54. Set A has 20 numbers and B has 40 numbers. Is the range of B greater than 45?

1). The range of A and B combined exceeds 50

2). Range of B is greater than range of A

SA=E; 讨论：条件1：不能确定。因为是两个集合在一起的范围大于50，不能判断单独的一个范围。条件2：B的范围大于A，也不可以，因为没有说可不可以重复。两条件联立：范围还是不能确定。

55. Sequence 2, 7, 22,…after the first three terms, each term is three times the previous term plus 1, a(n+1)=3an + 1. What is the sum of tens digit and tens digit of the 35 term?

SA=1; 讨论：我多写了几项，发现，十位数的规律是0,0,2.6，四位数循环。个位数就是2.7循环。所以，35项的个位数：(2+7)*17+2=155, 留5，进15。十位数：(0+0+2+6)*8+0+0+2=66. 再加上进位66+15=81，留1进8。所以，十位数是1

56.250人参与某个调查，调查问题有两个，对每个问题的回答有yes，no和no opinion三种，原题给出一个表格列出两个问题三种答案共六种情况下的人数，别的数字机不清，只记得对第一问题回答no的有100人，对第二问题回答no的有40人，另外告诉对两个问题都回答no的有60人，问只对某一个问题回答no的人数。这题很怪，也没说对哪个问题回答no，答案有60， 120，140，其他记不清
   

讨论：？

57.给出三行数列

0/1                                              1/1

0/1                   1/2                      1/1

0/1        1/3       1/2        2/3         1/1

As the figures shows, after the first line, the number of fractions in each of the following lines increased. The denominator of the added number is the sum of the denominators of the up-right and up-left fractions, and so does the numerator, for example, 1/4=0+1/1+3. Which line will contain 6/11 and 5/9

SA=7; 讨论：我的方法比较麻烦，因为是数出来的。有一行包括1/2，6/11，5/9，6/11就是1/2和5/9的中间数。所以，可知5/9是1/2和另一个数的中间数。依此类推，可知，题目所求的那行是第7行

59.
            What is the remainder when 7^468 is divided by 10?

SA=1; 讨论：7^x的个位数是7.9.3.1循环。468可以被4整除。所以，其的个位数是1。

60. AB=2, CD=BD, BC=1, 问角ACD＝？

此主题相关图片如下：

SA=30 讨论：根据题目可知，三角形BCD是等边三角形。所以，CD=1，AD=1，那么三角形ADC是等腰三角形。角ACD=30

[此贴子已经被作者于2006-10-15 15:18:06编辑过]

lzger2000

61.平行四边形ABCD，给出ACD坐标，问B坐标。

讨论：题目不全

一条抛物线y=x(6-x),有一点P在抛物线与x轴之间，问坐标不可能是哪个？

讨论：抛物线与X轴的交点是0，6。只要将点的横坐标带入求一下纵坐标，然后和所给的纵坐标相比就可以了

62. DS：[d] represents the least integer larger than or equal to d, is [2d]=0?
条件1: [d]=0
条件2: [3d]=0

SA=B; 讨论：d有可能是0或者-1/3<d<0条件1：d应该小于等于0，大于-1。[2d]=-1也是可能的，所以，不行。条件2：同作者的d取值范围。可以

63.
   What is the remainder when x^4-y^4 is divided by 3?

1). x-y is divisible by 3.

2). When x+y is divided by 3, the remainder is 2

SA=A; 讨论：A, x^4-y^4=(x+y)(x-y),被3除，条件1可以。条件2单独不行。

1). x-y is divisible by 3.

2). When x+y is divided by 3, the remainder is 2

SA=A; 讨论：A, x^4-y^4=(x+y)(x-y),被3除，条件1可以。条件2单独不行。

1). x-y is divisible by 3.

2). When x+y is divided by 3, the remainder is 2

SA=A; 讨论：A, x^4-y^4=(x+y)(x-y),被3除，条件1可以。条件2单独不行。

1). x-y is divisible by 3.

2). When x+y is divided by 3, the remainder is 2

SA=A; 讨论：A, x^4-y^4=(x+y)(x-y),被3除，条件1可以。条件2单独不行。

1). x-y is divisible by 3.

2). When x+y is divided by 3, the remainder is 2

SA=A; 讨论：A, x^4-y^4=(x+y)(x-y),被3除，条件1可以。条件2单独不行。

64.The blue region shown above is a rectangular rug with area of 110 square feet. The length is 1 foot greater than the width. If the rug covers a rectangular floor and distance between edges of floor and rug is 1 foot, what is the area of the uncovered floor?：同100

SA=46; 讨论：设内长方形宽为X，X(X+1)=110,X=10. 则，外长方形面积：12*13=156，所求面积为：156-110=46

65.  There are four points in line L and five points in line P, where L is parallel to P. By linking the 9 points, how many triangles can be formed?

SA=70; 讨论：C41*C52+C51*C42=70

67.一个三位数的整数，如已知个位分别加9，4的结果，判断十位数（DS题）

讨论：题目不全

68.10<n<40，且n/4余3，n/5也余3，n/6余几？

讨论：n=4a+3,且，n=5a+3，则有通项：n=20a+23，因为，10<n<40，所以，n只能等于23。那么，n/6余数是5

69.7的（4n+3）次方与6的（n）次方的乘积，除以10余几（n不等于0）？

SA=8; 讨论：7的（4n+3）可以写成(7^4)^n*7^3, 7的（4n+3）次方与6的（n）次方的乘积=(7^4*6)^n*7^3, 从尾数看，永远都是8。所以，余数就是8。WAY2:设N＝1

70.a跑完1公里比b多用了2秒，b的速度是75km/h，问a的速度。

SA=72; 讨论：3600/a=3600/75+2， a=72

71.一个外语club有15个人，a、b、c三种语言，三种都会的一个人，会a的1/3，会b的2/3，会c的3/5，问会2种的共几人。

SA=7; 讨论：15=5+10+9-X+1-3我猜題目有給錯一個條件答案選項只有 0 1 2 3 4

74. Peter invested $10,000 in a certain account. If he earned interest of $180, $190, and $200 in the first, second, and third quarter, respectively, what amount of interest should he earn in the fourth quarter so that the annual interest rate for the year will be 8%?

SA=230; 讨论: SA：10,000*8%-(180+190+200)=230

75. 91-93年的average salary是A元(一个数字，忘记了)，公司的target是未来3年每年的平均工次升幅是x%，问96年的平均工资是多少

SA：A(1+x%)3 

77．投资X元以10%利率，然后投资Y元以一个B的利率，二人的利息相等,问B是多少？(1) X=1000; (2) Y=2/X

SA：B; 讨论: 10%X=YB; 条件1：没有告诉X和Y的关系。不可以。条件2：有X，Y的关系。可以

 78. Symbol © denotes that when integer K is even, ©K=K-1, when integer K is odd, ©K=K+1. If a and b are integers, is ©a*©b even?

1). a is odd

2). b is odd

SA  

1). a is odd

2). b is odd

SA  

 78. Symbol © denotes that when integer K is even, ©K=K-1, when integer K is odd, ©K=K+1. If a and b are integers, is ©a*©b even?

1). a is odd

2). b is odd

SA  

1). a is odd

2). b is odd

SA  

79.The sum of the integers from 1 to n is n(n+1)/2. What is the sum of the even numbers between 99 and 301

SA=20200,往里套就行了

80:x+y除5余1,x+z除5余2,y+z除5余3,问x+y+z初5余几?

SA=3; 讨论: x+y=5a+1, x+z=5b+2, y+z=5c+3. 则，x+y+z=5(a+b+c)/2+3. x+y+z初5余3

[此贴子已经被作者于2006-10-16 12:28:36编辑过]

lzger2000

82.长方形油画加宽为1的画框面积为m,如果加宽为2的面积为m+52,问周长

SA=40; 讨论: 设长x，宽y。根据已知，(x+2)(y+2)=m, (x+4)(y+4)=m+52, 则，周长=2(x+y)=40 

83:送快件第一个$x,以后每个$y，X=?$

条件1:送2个总费用$5

条件2:送7个一共$10

SA=B; 讨论：这个满阴的,隐含条件是整数,因为题目说了"刀拉",~~不懂，怎么只能是整数 

85一个数离10-3次放近还是10-2次近

条件1;此数离10^-4比10^-1近; 条件2:此数离10^-3比10^-1近

SA=E; 讨论: 条件1：因为10^-4和10^-1包含了10^-3还有10^-2，所以，无法比较。条件2：同理。两条件联立，也是一样的。

86:甲容器含10%某成分,乙含15%,现甲拿200单位,乙拿300单位放一起,新溶液比例多少

SA=13%; 讨论: (10%*200+15%*300)/(200+300)=13% 

87:某部门扩招按人头每一人多招2人,告诉你这部门人数占公司的百分比2/11,问现在百分比

SA=40%.讨论: 部门a人，公司11a/2, 现在百分比3a/(11a/2+2a)=40% 

89. what is the value of 3/5 of 1/2 of 7

讨论: 2.1 

90.Jean earn $15 for each of the first 8 days, and then double the amount for the next days. how much is earned for 10 days?

SA=180; 讨论: 8*15+2*15*2=180; 应该不会这样理解8*15+2*8*15+4*8*15=840  

91. Square ABCD, some point E, making AE=DE=AD. what is <BCE??同97：一个正方形，以底边为边的等边三角形在正方形内，三角形在正方形内的点与正方形另外两点连接，问右上的角范围是多少

SA=15; 讨论：90-(180-30)/2
    

[此贴子已经被作者于2006-10-15 14:51:49编辑过]

simona

大沙发！！！！

谢谢辛苦了！！

很有用呢

lzger2000

呵呵 希望后面的也有人做呢 我就指着它奔51了

findjuhl

支持阿！

支持lz继续整理至最新的！

minnie1016

谢谢，其他都对的，下面的题目，好像有些问题：

5. XY原料混在一起，XY的混和物需要1.5克的X和6.5克的Y，XY原料成本A元/克，兩個原料的成本在混和原料中佔同樣的比例，問X原料每克多少錢？
  

3/16A

15. What is the remainder when positive integer x is divided by 7 1). X+1 is divisible by 7 2). X+13 is divisible by 7

A

21. The value of 1/11+1/12+1/13+...+1/20 will be

A. Less than 1/3

B. Less than 1/2

C. Greater than 1/2

D. Greater than 2/3

C

24. In a class of 120 students, 80 can speak English, 70 can speak Spain, 60 can speak French. If every student in the class can speak at least one of the languages, at least how many of students in class can speak all the three languages?

0

32.DS: What is the tens’ digit of integer X?
         

1). The tens’ digit of X-9 is 1
        

2). The hundreds’ digit of 10X is 2
       

B

55。 SA=1; 55. Sequence 2, 7, 22,…after the first three terms, each term is three times the previous term plus 1, a(n+1)=3an + 1. What is the sum of tens digit and tens digit of the 35 term

7

56.250人参与某个调查，调查问题有两个，对每个问题的回答有yes，no和no opinion三种，原题给出一个表格列出两个问题三种答案共六种情况下的人数，别的数字机不清，只记得对第一问题回答no的有100人，对第二问题回答no的有40人，另外告诉对两个问题都回答no的有60人，问只对某一个问题回答no的人数。这题很怪，也没说对哪个问题回答no，答案有60， 120，140，其他记不清
         

是不是 100+40-60？？

79.一个定义式表示K之前所有数字的和为n(n+1)/2，问99~301之间所有的偶数和

301*302/2-99*100/2

欢迎大家讨论阿

[此贴子已经被作者于2006-10-15 13:54:34编辑过]

lzger2000

能问你的思路吗，或请指出我思路的错误。

5. XY原料混在一起，XY的混和物需要1.5克的X和6.5克的Y，XY原料成本A元/克，兩個原料的成本在混和原料中佔同樣的比例，問X原料每克多少錢？
  

3/16A

15. What is the remainder when positive integer x is divided by 7 1). X+1 is divisible by 7 2). X+13 is divisible by 7

A

21. The value of 1/11+1/12+1/13+...+1/20 will be

A. Less than 1/3

B. Less than 1/2

C. Greater than 1/2

D. Greater than 2/3

C

24. In a class of 120 students, 80 can speak English, 70 can speak Spain, 60 can speak French. If every student in the class can speak at least one of the languages, at least how many of students in class can speak all the three languages?

0

32.DS: What is the tens’ digit of integer X?
         

1). The tens’ digit of X-9 is 1
        

2). The hundreds’ digit of 10X is 2
       

B

我写错了，应该为C，已更新

55。 SA=1; 55. Sequence 2, 7, 22,…after the first three terms, each term is three times the previous term plus 1, a(n+1)=3an + 1. What is the sum of tens digit and tens digit of the 35 term

7

56.250人参与某个调查，调查问题有两个，对每个问题的回答有yes，no和no opinion三种，原题给出一个表格列出两个问题三种答案共六种情况下的人数，别的数字机不清，只记得对第一问题回答no的有100人，对第二问题回答no的有40人，另外告诉对两个问题都回答no的有60人，问只对某一个问题回答no的人数。这题很怪，也没说对哪个问题回答no，答案有60， 120，140，其他记不清
         

是不是 100+40-60？？

79.一个定义式表示K之前所有数字的和为n(n+1)/2，问99~301之间所有的偶数和

301*302/2-99*100/2

可以检验一下，你的公式不等于20200，所以不对

[此贴子已经被作者于2006-10-15 17:01:55编辑过]