求教: 两道PREP上的题!!!!

steffie

求教求教,都是DS的,没有思路

1. Is the Integer n odd?

1)n is divisible by 3

2)2n is divisible by twice as many possible integers as n

2 when positive integer n is divided by 3, the remainder is 2, and when positive integer T is divided by 5, tje remainder is 2, and what is the remainder when product nt is divided by 15?

1) n-2 is divisible by 5

2) t is divisible by 3

[此贴子已经被作者于2007-1-16 21:13:48编辑过]

steffie

NN快出来啊

steffie

再问两道:

1. how many integers n is ,2^n=n^2

Answer is 二个, but I only find 2, what is the onther one?

2. In the xy-plane, does the line with equation y=3x+2 contain the point (r,s)?

1)  (3r+2-s)(4r+9-s)=0

2) (4r-6-s)(3r+2-s)=0

DS: the answer is C, but I think both lead two 3r+2-s=0, why not D?

gelisha

求教求教,都是DS的,没有思路

1. Is the Integer n odd?

1)n is divisible by 3

2)2n is divisible by twice as many possible integers as n

满足1的可为6 or 9, 2中 设n为奇数，n的因数为2,则2n的因子数为：[ 2的指数(此时为1)+1]x[那个奇数的指数(此时为1)+1] =4,满足。 若n为偶，则n因数中至少有一个2，假设只有一个2，提取出这个2后剩一个奇数，此时n的因数为4，2n的因子数为[ 2的指数(此时为2)+1]x[那个奇数的指数(此时为1)+1] = 6，不满足 Answer B

2
when positive integer n is divided by 3, the remainder is 2, and when
positive integer T is divided by 5, tje remainder is 2, and what is the
remainder when product nt is divided by 15?

1) n-2 is divisible by 5

2) t is divisible by 3

题是不是应该是“when positive integer n is divided by 3, the remainder is 2, and when
positive integer T is divided by 5, the remainder is 3,”  Answer C

gelisha

以下是引用steffie在2007-1-16 21:13:00的发言：

再问两道:

1. how many integers n is ,2^n=n^2

Answer is 二个, but I only find 2, what is the onther one?

还有4

2. In the xy-plane, does the line with equation y=3x+2 contain the point (r,s)?

1)  (3r+2-s)(4r+9-s)=0

2) (4r-6-s)(3r+2-s)=0

DS: the answer is C, but I think both lead two 3r+2-s=0, why not D?

因为两个条件各自还会有另一个解满足条件（4r+9-s=0,4r-6-s=0），只有合起来才能保持唯一性

steffie