12月数学机井总结

1. X is a positive integer. 2-height of X is defined as the greatest negative integer n where 2^n is a factor of X. K and M are two positive integers. Whether 2-height of K is greater than 2-height of M?
a. K is greater than M
b. K is even times of M
(Key: B)

2. X, Y and Z are three different prime numbers. How many factors does X*Y*Z have? (Key: 8)

3. XY>Z?
a. XYZ>1
b. XYZ^2=1
(Key: C)

4. XYZ>0?
a. XY>0
b. YZ>0
(Key: E)

5. 7^3*7^4=? (Key: 7^7)

6. A is 25% less than B and B is 25% less than C. How much percent is A less than C? (Key: 1/3)

7. A can finish one job in X hours. A does this job three times as fast as B does. If A and B work together, how many hours can they finish the job? (Key: 3X/4)

8.能否确定N?， 条件是
1 (69+N)^1/2，(94+N)^1/2 是连续整数
2 (94+N)^1/2，(121+N)^1/2 是连续整数
我答D

9.还有就是两条平行线，一条有5个点，一条4个点问能组成多少个直角三角形
我答70个

10. 一个正三角形，边长5，中间内切一圆，问圆的面积

11. 在坐标系中有3点P(2,1),M(5,1),N,(5,5).问从P->M->N的距离比从P直接到N的距离大多少

12. R,S,T为正整数，问T/S^2是否是整数？ 1）T/RS是整数 2）R/S是整数

13. 0.6是0.0015的多少倍？（400）

14. 唯一的jj：有一box,厚度of the plastic 是1，inner三个边长为x,y,z，求plastic 的体积。(x+2)(y+2)(z+2)-xyz把式子展开就是了。

15.有一梯形ABCD，AD=CD，P为AD上一点，求梯形面积。
(1)PD=5 (2)BC=8 (数字不准确) 我选E

16.有12个什么DD,其中3个defective,某人买2个randomly,问neither is defective的概率?

17.一直角三角形,直角顶点为(0,3),一点为(-4,0),另一点为(b,0),求b?

18.2个数的积为48,其中一个比另一个大2,求大的那个数? (8)

19.一个半圆的street,直径为1mile,7个点把这个半圆分成相等的8段,某人以15mile/hour从最左一点开始走,问3分钟后他在哪2点之间? (好象是在第四段)

20. 一公司A业务占总收入的25%，B业务占t%,C业务占余下的，B业务收入是150，000 C业务是总收入-225，000 求t=?
My Answer: 50%

21. 在电话厅前排队，J前有13个人，问队伍总共多少人
（1） C后有16个人
（2） C前J后有3个人
My Answer: C

22. A circle inscribed² in an equilateral triangle with side length = 10. What is the area of inscribed circle?

23. 机经的题目，W到X到Y到Z，三个送信人，一个速度70mile/分钟，一个速度80mile/分钟，一个速度100mile/分钟，总长750mile 求X到Y长，
答案是240

24. x = (10 的100 次方), if (x的x次方) = (10 的k 次方), what is k?
My Answer: k = 200. (Not sure if my answer is correct)
Old JJ:
X=10^100，有X^X= 10^K， 问K等于多少
remeo评价意见：10^102

25. If X is between 4497 and 4509, which number is closest to 23/(30X)?
My Answer: 3451

26. A right triangle is on top of a square. Square side is 100, right triangle sides are 60, 80 and 100 (common side with the square). How many bags of fertilizer to cover entire area? (1 bag covers 2000 sq. feet.)
My Answer: 7 bags.

27. Make a code of different letters from 10 letters (A,B, ….). What’s the ratio of 5 letter code to 4 letter code?
My Answer: P(5, 10)/P(4, 10) = 6

28. r+s+t 是偶数么？
(1)r+s是偶数
(2)s+t是偶数

29. 有线段AC，AC上的一段AB正好是某圆柱体的体对角线(有图，看图会很清楚，我的描述可能不大清楚)，能求出AC的长么？
(1)BC=2
(2)AC有3/4长度在圆柱体内

30. 1998 sales increases x percent from 1997, 1999 sales decreases x percent from 1998, 1999 is 9 percent less than 1997. What is X?
My Answer: 30 percent

31. R=S(100)/P, in the equation, R is the real salary of a person, S is the current salary, and P is a kind of index. Whether the person K\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\'s real salary now is more than the real salary of 1967? (1)K\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\'s current salary now is 94% more than that of 1967
(2) the index of 1967 is 100 and the index of now is 182

32. a, b are nonnegative numbers and (a-b)/(a+b)=1/2, which one of the following must be true?
作者答案及思路：(Choice C: a>b)

33. A和B两个工程，A占2/3，B占余下的，B要花的时间是7/5 as much as A 问B花的时间占总共时间多少，
我的答案好象是7/17