[原创] 十月七日机井 数学部分11道题

flaviajzx

20T

应该是16吧，还有1

mayleila

去掉1和k本身啊，所以应该是14。

谢谢楼主，这么多jj,不容易啊，我也是9号考，大家加油！！

liuyang1984

楼上的，明天加油啊

对了，别忘了带jj回来哦

[此贴子已经被作者于2006-10-8 14:51:53编辑过]

liuyang1984

以下是引用猪小弟在2006-10-8 1:50:00的发言：

11. 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?
速度设定有问题，应该是小的速度是v，大的速度是2v，答案应该是18小时。

12. 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?

具体算法：由于偶数只能插中间，即1 3 5三个位置，有顺序排列，所以应该是P(3,3)，剩下两个数是P(2,2)，所以答案是P(3,3)*P(2,2)=12

16. 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?
该题目分为两种情况：
1、第二位是1：C81*C101
2、第二位是0：C81*C91
所以答案为：C81*C101+C81*C91=152种，注意原文给出的条件and the second and third digits cannot be 0 at the same time

18. 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

1) x+1=7a, x=7a-1,余数为1

2）x+13=7a, x=7a-13, 余数为6或1

选A
1) x+1=7a, x=7a-1,余数为6
2）x+13=7a, x=7a-13=7(a-2)+1, 余数为1
所以答案为D

补充一道：

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

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
这道题目是一条抛物线，开口向上，在X轴截距是1和3，画图可知，该图形不能出现在第三象限，不知是否这个意思。

以上谨代表个人意见，请大家多指正。

totally correct!!~

mecca7a

14. 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?

问一下这题的解法，谢谢！

mecca7a

已经看过了yaomao女侠的解法！

shqco

楼主这个月的贡献真是大呀,

shqco

这些题好象都见过,呵呵,看来这个月只要细心,再把以前的题过一下,还是可以过关的.顶

rainbow1983

11. 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?
答案应该是9小时。

16. 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?
该题目分为两种情况：
1、第二位是1：C81*C101
2、第二位是0：C81*C91
所以答案为：C81*C101+C81*C91=152种，注意原文给出的条件and the second and third digits cannot be 0 at the same time

18. 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
1) x+1=7a, x=7a-1,余数为6
2）x+13=7a, x=7a-13=7(a-2)+1, 余数为1
所以答案为D

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

总个数：c41+c42+c43=14个

补充一道：

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

Y = (x-2)^2 -1

Y=x^2+4-4x-1

Y=x^2-4x+3

Y=(x-1)(x-3)
这道题目是一条抛物线，开口向上，在X轴截距是1和3，画图可知，该图形不能出现在第三象限.

1). X+1 is divisible by 7

2). X+13 is divisible by 7
1) x+1=7a, x=7a-1,余数为6
2）x+13=7a, x=7a-13=7(a-2)+1, 余数为1
所以答案为D

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

总个数：c41+c42+c43=14个

补充一道：

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

Y = (x-2)^2 -1

Y=x^2+4-4x-1

Y=x^2-4x+3

Y=(x-1)(x-3)
这道题目是一条抛物线，开口向上，在X轴截距是1和3，画图可知，该图形不能出现在第三象限.

captain_ma

18. 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
1) x+1=7a, x=7a-1,余数为6
2）x+13=7a, x=7a-13=7(a-2)+1, 余数为1
所以答案为D