12月数学机井总结(2)
34. y=1/(3-6/(x-4)), What is x defined as?
I 4
II 6
III 8
35. 有一个连续数的集合,问7是否在这个集合里面
a) -7在里面
b) 9在里面
36. A rectangle ABCD area is 84, point E is on line AB and AE/EB = 4/3, point F is on line DC, what is area of triangle AFE?
37.一个圆圆心在(0,0),一直线y=x,k同时在圆上和线上,问k坐标:
答案:(跟号2 除以1,跟号2 除以1)
38.JJ本月题99到301间的偶数的和
答案:20200
方法:99到301间的偶数的和=100到300间的偶数的和,等差数列求和=(A1+An)*N/2=(100+300) * 101/2=20200
39.JJ本月题 (X^ N) / (X-1)= X ^ (N-1) + X ^ (N-2) + …+1, 且7^8= 一个具体的数值C,问7^9=?
答案:
方法:假设X=7, N=9, 那么7^9 / 6 = 7^8 + 7^7+7^6+…+1
假设X=7, N=8, 那么7^8 / 6 = 7^7+7^6+…+1
因为 7^8=C,所以 7^7+7^6+…+1 = C/6
综合以上=〉 7^9 = 6(C+C/6)=7C/6
说明:具体公式可能略有偏差,但方法是这样的,请大家掌握此类方法,勿记答案。
40.ABCDEFG中随便取3个,但是AB不能在一起,问可能性?
答案:C(7,3)-5
41.圆柱体CAN, 半径=R,高=H, 若另一个圆柱体积相同,r=2/3 R, 那么高h为多少?
9/4h
42.DS: 两个数列S,T,S 由偶数组成,T由奇数组成,两个数列个数相同,问S的MEDIAN 和T的算术平均值谁大?
(1) S,T 为连续的数
(2) S的算术平均值大于T的
43. 452*36*17
7 个数字中,哪个数字增加1,乘积增加小于1000?
A. 1
B. 2
C. 5
D. 7
E. 4
44. N 有几个不同的质数?
A. N 是7200的因子
B. 180 是N的因子
45. M, P, T 是positive integer, m
A. T-P=P-M
B. Forgot
46. 一个序列,从第三位数起,每个数都与它前面连续的两个数的和有关,the number is the sum of the 2 numbers in the sum is odd or ½ if the sum of the 2 numbers are even, the forth number is 7 and the fifth number is 5, what is the first number?
47. Give the English definition of standard deviation, 2 or 3 lines, there are 4 numbers, 9, 8, 7, 4, ask the standard deviation of these 4 numbers?
48. X, Y 是正整数,X 是3的倍数吗?
A. X-Y 是3的倍数
B. X-2Y是3的倍数
49. N除以3的余数是多少?
A. N除以2 余1
B. N+1除以3 余2
50. 正方体内有以内切球,直径为6,求正方体内最长的一条对角线长度
51.一正方形,10 <长< 20, 5<宽<9, 求周长范围
52.
A. S, T 关系
B. t > 1
题目记不清,但是通过A, 求出T 有两值1,2,根据B,可确定T=2, 则答案选C
53. 卖门票 on Monday & Tuesday, children’s ticket $7 each, adult $10 each, children’s number on Tues is twice the number on Monday, adult’s number on Tues is ½ the number on Monday, the total revenue on Monday is $2700, revenue on Tuesday is $2400, what’s the children’s number on Monday?
54. –2
55.3个不同的旗子排列视为一个信号,有四面不同的旗子,可排成几个信号?
56.从50加到100的和?
57.孩子们拿笔,either 3 pens , 2 pencils, or 1 pen, 3 pencils, the average pen number is 1.6, what’s the average pencils number? (the number is not accurate)
58. lottery $16 billion, separate as gifts, government payment, and expense, give the relation of payment and gift & the relation of payment and presentation, ask the payment in $ amount
59. 7 red tomatoes, 5 green tomatoes, ask the probability of all 3 tomatoes are red ….
60. 某数的80%是多少? (具体叙述忘了,但翻译过来就是求这个式子)
61. Is xy >x^2y^2
A. 14X^2=3
B. Y^2=1
62. Mary 和 Tom 同时从a地出发到b地,问Mary 比 Tom早到几分钟?
A. a地到b地距离100miles.
B. Mary的小时速度 比 Tom小时速度快5 miles.
63. r>1, r * = 1-(1/r) what’s the value of : r * - (r-1)*
64. Is xyz>0
A. XY>0
B. YZ>0
65. A (0,3) B (-2,0), C在AB上,C的横坐标是-5,求纵坐标?(数不准,有图)
66.People in Senior only is 16, ppl in physics only is 24. ppl in senior only + ppl both in senior and physics = ppl in physics only. What’s the percentage does ppl both in senior and physics account for all senior ?
67. 一个三角形x,y,z,分别为三个外角,确定x的度数?
A. x=y
B. x=z
68. DS 根据账户里的钱付费用问题,$400 之内付1。5%,超出部分付1.2%, 求某人上月账户里有多少钱?
(题目叙述长,数不准)
69. 溶液问题:10单位混合物,含有30%的A,70%的B,问要取去多少单位的混合物,换成A,使新的混合物中A、B各占50%?
[确认]20/7
[思路]设要取去X单位的混合物,解方程X*70%=10*(70%-50%)可得。
70. 集合题:参加股东会的人中62%为股东,47%为公司员工,问参加会议的是股东中不是员工的比例?
[确认]53%
[思路]62%-(62%+47%-100%)=53%