1。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

the answer is C

求思路，谢谢

2。if there are more than two numbers in a certain list, is each of the unmbers in the list equal to 0?

1)

the product of any two numbers in the list is equal to 0.

2) the sum of any two numbers in the list is equal to 0

the answer is B, why 1) is not sufficient?

3. alice's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. the total amunt of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save. if all the money that she saved lat year was from her take-home pay, what fraction of her take-home pay did she save each month?

1/2; 1/3; 1/4; 1/5; 1/6

the answer is 1/5, why?

4. if d is the standard deviation of x,y,z, what is the standard deviation of x+5,y+5, and z+5

d; 3d; 15d;d+5; d+15

the answer is d. why?

thank you

这道题好像跟GWD还是FF一道题一样的。

（1）n=2k+1

(2)n=3s+1或3s+2

（1）（2)综合,n可能为n=6m+1或n=6m+5,后者也可写成n=6m-1（关于通项如不清楚，请参见此贴：

所以(n-1)(n+1)＝6m(6m+2)=12m(3m+1)，因为m和3m+1必然一奇数一偶数，所以12m(3m+1)可被24整除，故r为0；

或者(n-1)(n+1)＝(6m-2)6m=12m(3m-1)，因为m和3m-1必然一奇数一偶数，所以12m(3m-1)可被24整除，故r为0；

(1)有可能1，0，0也满足条件啊

设每月saved为X,did not save为Y,则12X=3Y,4X=Y

fraction of her take-home pay did she save each month:X/(X+Y)=X/5X=1/5

关于标准方差的定理：序列中每一个数都加上一个常数，标准方差保持不变的！！！

3 times the amount of that portion of her monthly take-home pay that she did not save

这句话怎么理解？Puzzled

the total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save

一年所存钱的总额是每个月拿回家的钱当中没有存的部分的3倍

设一个月拿回家的钱为m，每个月存钱的比例为x，则未存的部分就是1-x，根据题义，方程应该是

12*m*x=3*m*（1-x）

恩恩 谢谢了 不过如果这样的话是不是可以直接设总数为m，存的钱为x，方程直接是

12*x=3*（m-x)