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标题: 明天要考了，急请教3道PP2上的数学题，怎么也搜不到 [打印本页]

作者: earvin 时间: 2007-12-27 13:46
标题: 明天要考了，急请教3道PP2上的数学题，怎么也搜不到

If S in the infinite sequence S1=9, S2=99, S3=999,…, Sk=10k-1,…, is every term in S divisible by the prime number P?

1 P is greater than 2

2 at least one term in S is divisible by P.

The weights of four packages are 1, 3, 5 and 7 pounds, respectively. Which of the following CANNOT be the total weight, in pounds, of any combination of the packages?

9, 10, 12, 13, 14

If n is a positive integer and r is the remainder when (n-1)(n+1) is divided by 24, what is the value of r?

(1), n is not divisible by 2; (2), n is not divisible by 3

作者: chonheinrich 时间: 2007-12-27 14:45

1，选E，e.x.可能是3，也可能是11.

2，14不可能，你怎么也加不出14来。

3，选E，e.x.:n=5时，r=12；n=7时，r=0.

作者: cloudymind 时间: 2007-12-27 16:39

(1) n = 2k+1, (n-1)(n+1) = 2k(2k+2)= 4k(k+1) is divisible by 8

(2) n= 3k+1 or 3k+2, (n-1)(n+1) = 3k*(3k+2) or (3k+1)(3k+3), both are divisible by 3

If we combine (1) and (2), then n is surely divisible by 24. Thus the remainder r is always 0.

The answer should be (C)

作者: chonheinrich 时间: 2007-12-27 17:00

err……我以为是被24除的余数……我的阅读能力…………

作者: earvin 时间: 2007-12-28 00:17
多谢二位，但是第二题，如果其他为0，2个7kg的包不就是14吗？

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