[原创] 十月十日 数学机井更新至五十四

findjuhl

40. How many arrangements of A, B, C, D, and E are there, such that B and D are not adjacent? Each letter is used exactly once.

41. 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?

0/1----------------------------------------1/1

0/1----------------1/2---------------------1/1

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

0/1  1/4  1/3 2/5  1/2   3/5   2/3   3/4  1/1

42. 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?

43. 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%?

44. 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?

45. 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

46. If x and y are integers, |x|*|y|=?

1). xy=10

2). x*|y|=-10

47. Symbol [d] denotes the least integer greater than or equal to d, is [2d]=0?

1). [d]=0

2). [3d]=0

48. 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

49. Beside one more prime factor, integer x and 770 has same prime factors. What is the least value of x/770?

50. 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?

Choices include (301*302/2-99*100/2)/2 E/P>

51. In the figure shown above, if line y=c divided the triangle equally, c=?

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

53. A 4-letter code consists of letters a, b, c. To form a code, letter a was used twice and b, c used one times. How many such codes are possible?

54. 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

注意：大部分题和国内JJ相同

[此贴子已经被作者于2006-10-10 16:02:03编辑过]

pvdpvdpvd

謝了大哥 頂一頂

liuyang1984

板凳，嘿嘿

shqco

顶

ll_422

thanks. findjuhl

 

yaomao

40. How many arrangements of A, B, C, D, and E are there, such that B
and D are not adjacent? Each letter is used exactly once.
 P₅⁵-2P₄⁴=72
 

 

41. 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?

中间长方形的长宽分别为11，10
 （11+2）（10+2）-110=46
 

0/1----------------------------------------1/1
 0/1----------------1/2---------------------1/1 
 0/1-------1/3------1/2---------2/3--------1/1
 0/1  1/4  1/3 2/5  1/2  3/5   2/3   3/4  1/1

42. 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?
 应该是7哈
 

43. Peter invested $10,000 ina 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%?
 10000*8%-180-190-200=230

44. 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?
 4C₅²+5C₄²=40+30=70

45. 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
 D

46. If x and y are integers, |x|*|y|=?
 1). xy=10
 2). x*|y|=-10
 D
 

47. Symbol [d] denotes the least integer greater than or equal to d, is
[2d]=0?
 

1). [d]=0

2). [3d]=0
 B

由1）得：-1<d<=0
 由2）得:-1/3<d<=0

48. 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
 A
 x^4-y^4= （x^2-y^2）（x-y）（x+y）
 

49. Beside one more prime factor, integer x and 770 has same prime
factors. What is the least value of x/770?
 

770的质因子有：2，5，7，11

X比770多一个质因子，
 所以X/770最小就是3
 

50. 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?

Choices include (301*302/2-99*100/2)/2 ?E/P> 
 101（100+300）/2=20200
 

51. In the figure shown above, if line y=c divided the triangle
equally, c=?
 4-2√2

52. What is the remainder when 7^468 is divided by 10?
 1
 

53. A 4-letter code consists of letters a, b, c. To form a code, letter
a was used twice and b, c used one times. How many such codes are possible?
 P₄⁴/2=12

 54. 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
 A
 

注意：大部分题和国内JJ相同

[此贴子已经被作者于2006-10-11 13:04:51编辑过]

findjuhl

以下是引用yaomao在2006-10-10 18:02:00的发言：

  

你是数学系毕业的吧？太牛了，也！

[此贴子已经被作者于2006-10-10 18:11:40编辑过]

rainman714

45. 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

请教一下  为什么我觉得选D啊  所有的奇数加1不是都是偶数吗?  那么偶数和其他整数的积不也是偶数吗

yaomao

以下是引用findjuhl在2006-10-10 18:11:00的发言：

  

你是数学系毕业的吧？太牛了，也！

不是得哈，

是很关注LZ的帖子，有新题就做了哦

 

yaomao

以下是引用rainman714在2006-10-10 18:18:00的发言：

45. 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

请教一下  为什么我觉得选D啊  所有的奇数加1不是都是偶数吗?  那么偶数和其他整数的积不也是偶数吗

呀，对的，该是D

[此贴子已经被作者于2006-10-10 18:36:21编辑过]