急问 GMATPrep 几道数学题. 过两天就考了

lguo1

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

(1) The average (arithmetic mean) salary of the managers is $5,000 less than the average salary of all employees
(2) The average (arithmetic mean) salary of the directors  is $15,000 greater than the average salary of all employees.

I chose E.  But the given correct answer is C.  百思不得其解.


2.   If n and t are positive integers, what is the greatest prime factor of the product nt?

(1) The greatest common factor of n and t is 5
(2) The least common multiple of n and t is 105.

The given correct answer is B.  这题我是试出来的.  想问问有没有数学证法?

 

rio

1.设m个manager的平均工资a，d个director的平均工资b,

    (am+bd)/(m+d)-a=5000

    b-(am+bd)/(m+d)=15000

将数字替换掉就得到：am-bm=3ad-3bd,从而：m=3d

2.因为你要找的是质因子，nt中必然包含组成n,t的所有因子以及质因子，在105（最小公倍数中）则包含了所有组成n,t的质因子，因此就是7了

lguo1

明白了. 多谢 rio!