大家帮帮忙，几道pp数学题，求教！

wowuname

1.For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by (–1)的k+1次乘上（1/2）的k次，if T is the sum of the first 10 terms in the sequence, then T is ___________(between 1/4 and 1/2)

2.On June’s credit card account, the overage daily balance for a 30-day billing cycle is the average (arithmetic mean) of the daily balances at the end of each of the 30 days. At the beginning of a certain 30-day billing cycle, Jane’s credit card account had a balance of $600, Jane made a payment of $300 on the account during the billing cycle. If no other amounts were added to or subtracted from the amount during the billing cycle, what was the average daily balance on Jane’s account for the billing cycle?

(1)  Jane’s payment was credited on the 21^st day of the billing cycle

(2)  The average daily balance through the 25^th day of the billing cycle was $540

D

3.If n and y are positive integers, and 450y=n的三次方，which of the following must be an integer?

(1)y/（3乘5乘2的二次方）    (2)y/(2乘5乘3的二次方)     (3)y/(3乘2乘5的二次方)

答案选（1）

4.Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

(1)  Machines X and Y, working together, fill a production order of this size in two-thirds the time that machine X, working alone does

(2)  Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone does

答案E

5.A certain city with a population of 132000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?

答案11000

6.The residents of Town x participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of Town x, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last weak?

答案12

过氧化氢

以下是引用wowuname在2007-1-16 20:16:00的发言：

1.For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by (–1)的k+1次乘上（1/2）的k次，if T is the sum of the first 10 terms in the sequence, then T is ___________(between 1/4 and 1/2)

这10个数依次是1/2,-1/4,1/8，每个数的绝对值都比前一个数的绝对值小，且一正一负交叉，把它们相加，就是一个数减去一个比它小的数，再加上一个更小的数，再减去一个更更小的数，……，所以最后的和一定比第一个数（1／2）小，比第一个数加上第二个数（1／2－1／4）大.

2.On June’s credit card account, the overage daily balance for a 30-day billing cycle is the average (arithmetic mean) of the daily balances at the end of each of the 30 days. At the beginning of a certain 30-day billing cycle, Jane’s credit card account had a balance of $600, Jane made a payment of $300 on the account during the billing cycle. If no other amounts were added to or subtracted from the amount during the billing cycle, what was the average daily balance on Jane’s account for the billing cycle?

(1)  Jane’s payment was credited on the 21^st day of the billing cycle

这样就可以知道前21天的balance和后9天的balance，当然充分了

(2)  The average daily balance through the 25^th day of the billing cycle was $540

前25天的平均数小于600,那么payment一定在前25天，后面5天每天的balance就是300,前25天的balance总和是540×25,后5天是300×5,求平均数很容易吧，充分

D

3.If n and y are positive integers, and 450y=n的三次方，which of the following must be an integer?

(1)y/（3乘5乘2的二次方）    (2)y/(2乘5乘3的二次方)     (3)y/(3乘2乘5的二次方)

答案选（1）

450＝3^2 * 5^2 * 2,450y是某个数的三次方，那么y一定是（3×5×2^2)这个数的倍数

4.Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

(1)  Machines X and Y, working together, fill a production order of this size in two-thirds the time that machine X, working alone does

(2)  Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone does

答案E

两个选项只提到了X和Y的倍数关系，没有提到HOURS，题目中也没有可以利用的HOURS，所以无法计算。

5.A certain city with a population of 132000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?

答案11000

设最小的为X，X＋Y1＋……＋Y10＝132000,显然当Y1＝……＝Y10＝1.1x时，X最小，得到12X＝132000

6.The residents of Town x participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of Town x, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last weak?

答案12

12只是一种可能性，不是唯一的可能，去看看standard deviation的定义吧，就可以排除其它选项了

gelisha

1.For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by (–1)的k+1次乘上（1/2）的k次，if T is the sum of the first 10 terms in the sequence, then T is ___________(between 1/4 and 1/2)

就是个首项是1/2，q=-1/2的等比数列求和，因为|q|<1 所以Sn=a1/1-q，得出Sn=1/3