求助数学题~

jessie_yhy

If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of aⁿ, what is the value of a ?

 

(1)  aⁿ = 64
                

 

(2)  n = 6

答案：B

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 mean) salary of the managers on the task force is $5,000 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 $15,000 greater than the average salary of all employees on the task force.

答案：c

 

 

 

SunnyNeil

第一题：

前8的product可以分解为(2^7)(3^2)(5^1)(7^1)，同时又是aⁿ的倍数

所以aⁿ中a是2、3、5或7中的一个或多个，但是相应的不能大于8分解出的最高次幂

所以：A错误，N=3.a=4;N=6,a=2……；B正确，N=6时，a不可能是3，5或7，只有a=2符合条件

第二题：

设X=number of directors,Y=number of managers,the average salary of all employees =K

question is X/(X+Y)=?

根据两个条件，我们可以得出等式：[(K+15000)Y+(K-5000)X]/(X+Y)=K

这个方程就是平均工资等于平均工资，解出答案：15000Y=5000X即X:Y=3:1