[原创] 十月七日机井 数学部分11道题

ondesert

谢谢楼主

taojm2001

Thanks! These days only you give us some JJ

taojm2001

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

But my answer is D, because x is positive integer, 余数 only can be 1.

taojm2001

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?

my answer is 152, because the second and the third digit cannot be 0 at the same time, so when the second digit is 1, the third digit could be 0-9

[C(8,1)C(1,1)C(9,1)+C(8,1)C(1,1)C(10,1)=152]

ll_422

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, ==>余数为1

KEY D

十八木耳

lz大好人！！！

molayyifangsu

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

解:4(2/3/5/7) 因为Z可以是相同或不相同的质数且10>质数>0,则相同的质数的K的因子则有4个即为2.3.5,7;若用整数的整除特性则还是2,3,5,7．估计这题我是严重错误！请指教如何详解此题！

 

這題的意思應該是假使K是wxyz的乘積,而wxyz都是質數。我們假定K=2*3*5*7=210

210的因子個數總共：(1+1)(1+1)(1+1)(1+1)=16  (1,2,3,5,7,6,10,14,15,21,30,35,42,70,105,210總共16個)

題目問不包括1及K本身，也就是不包括1及210,則16-2=14 ,答案即是 14~~

Echoxlx

以下是引用tomwalkson在2006-10-8 0:35:00的发言：

哎呀呀，看我是多么糊涂啊，我总是出现这种极为搞笑的错误，还比如236-30=36！！！！就因为这，我的prep总得49分，很多都是这种弱智错误。怎么办啊，我脑子真个秀豆啊

Echoxlx

以下是引用ll_422在2006-10-8 8:23:00的发言：

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, ==>余数为1

KEY D

同意！

Echoxlx

以下是引用molayyifangsu在2006-10-8 8:53:00的发言：

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

解:4(2/3/5/7) 因为Z可以是相同或不相同的质数且10>质数>0,则相同的质数的K的因子则有4个即为2.3.5,7;若用整数的整除特性则还是2,3,5,7．估计这题我是严重错误！请指教如何详解此题！

 

這題的意思應該是假使K是wxyz的乘積,而wxyz都是質數。我們假定K=2*3*5*7=210

210的因子個數總共：(1+1)(1+1)(1+1)(1+1)=16  (1,2,3,5,7,6,10,14,15,21,30,35,42,70,105,210總共16個)

題目問不包括1及K本身，也就是不包括1及210,則16-2=14 ,答案即是 14~~

这题思路可这样：

每个质数：c41个

两个质数的乘积：c42个

三个质数的乘积：c43个

总个数：c41+c42+c43=14个