prep数学求助……

snowwarm

以为数学不用复习，刚直接上了prep，泪奔……错了9个，下面3个是看了还不明白的，求助！

多谢！！！

Each employee on a certain task force is either a manager or a director. What percent of the employees on the task force are directors?

(1) The average (arithmetic average) salary of the managers on the task force is 5000 less than the average salary of all employees on the task force.

(2) The average (arithmetic mean) salary of the directors on the task force is 15000 greater than the average salary of all employees on the task force.

答案：Both statement together are sufficient, but neither statement alone is sufficient.

完全不知道怎么算。。。

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

Of the 75 houses in a certain community, 48 have a patio. How many of the houses in the community have a swimming pool?

(1) 38 of the houses in the community have a patio but do not have a swimming pool.

(2) The number of houses in the community that have a patio and a swimming pool is equal to the number of houses in the community that have neither a swimming pool nor a patio.

答案：Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

我怎么觉得应该两个statement合起来呢。。。

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

For every positive even integer n, the function h(n) is defined to be the product of all the even intergers from 2 to n, inclusive. If p is the 

smallest prime factor of h(100)+1, then p is

A. between 2 and 10

B. between 10 and 20

C. between 20 and 30

D. between 30 and 40

E. greater than 40 (correct)

完全不知道怎么算。。。

wxsimon

第二个的答案错了吧，应该是选B而不是A

wxsimon

第二题

第一个条件不能单独退出

再看第二个条件

设公共部分，既有patio又有swimming pool的为x，有swimming pool但没有patio的是y，那么有swimming pool的就是x+y

由条件可得，x（二者都没有）+48+y=75

所以x+y就求出来了。

画个韦恩图会更清楚

写得仓促，仅供参考哈！

geekland

1.  you may solve this question by listing two formulas:
(No. of M*Avg. Sm + No. of D*Avg. Sd)/(No. of M+No. of D)=Avg. Sm+5000,
and (M* Avg.Sm + D* Avg.Sd)/(M+D)=Avg.Sd - 15000

Then divide the former by the later, you may get the ratio as the question requires.

2. Combined Wenn Diagram and condition A , it can be inferred that 10 is the overlap number of pool and patio,  so you can get the number of pool. (don't assume there are some houses have neither  patio nor pool)

3. Sorry for this one, I am struggling too.

Good luck!

wxsimon

以下是引用geekland在2009/8/17 6:57:00的发言：
1.  you may solve this question by listing two formulas:
(No. of M*Avg. Sm + No. of D*Avg. Sd)/(No. of M+No. of D)=Avg. Sm+5000,
and (M* Avg.Sm + D* Avg.Sd)/(M+D)=Avg.Sd - 15000

Then divide the former by the later, you may get the ratio as the question requires.

2. Combined Wenn Diagram and condition A , it can be inferred that 10 is the overlap number of pool and patio,  so you can get the number of pool. (don't assume there are some houses have neither  patio nor pool)

3. Sorry for this one, I am struggling too.

Good luck!

为什么我们不考虑二者都无的情况呢？

snowwarm

Thx~

snowwarm

以下是引用geekland在2009/8/17 6:57:00的发言：
1.  you may solve this question by listing two formulas:
(No. of M*Avg. Sm + No. of D*Avg. Sd)/(No. of M+No. of D)=Avg. Sm+5000,
and (M* Avg.Sm + D* Avg.Sd)/(M+D)=Avg.Sd - 15000

Then divide the former by the later, you may get the ratio as the question requires.

2. Combined Wenn Diagram and condition A , it can be inferred that 10 is the overlap number of pool and patio,  so you can get the number of pool. (don't assume there are some houses have neither  patio nor pool)

3. Sorry for this one, I am struggling too.

Good luck!

Sorry我怎么还是没懂……我也是这么列的方程，但是两者相除，不就成了：Avg. Sm+5000＝Avg.Sd - 15000了么……题目问的是M/D呀……

snowwarm

第三题，找了个答案，share一下：

Let's first consider the prime factors of h(100). According to the given
function, h(100) = 2*4*6*8*...*100

By factoring a 2 from each term
of our function, h(100) can be rewritten as
2^50*(1*2*3*...*50).


Thus, all integers up to 50 - including
all prime numbers up to 50 - are factors of h(100).

Therefore,
h(100) + 1
        cannot have any prime factors 50 or below,
since dividing this value by any of these prime numbers will yield a remainder
of 1.

Since the smallest prime number that can be a factor of h(100) + 1
has to be greater than 50, The correct answer is E.