数学题求指教

蓝兰紫籽

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.




这题答案是C，但是lz真心觉得选e，？？？



How many different prime numbers are factors of the positive integer n ?b

(1) Four different prime numbers are factors of 2n.

(2) Four different prime numbers are factors of n^2.

答案选b，个人觉得是d啊

lz数学真心烂，求较详细的解答啊~~
看帖回帖的XDJM都700+~~~~

tsh0615

第一题：一个任务里面只有manager和director，你可以设manager的人数为X，average salary 为X'; director的人数为Y，average salary 为Y‘，总的average salary为Z
            根据条件1：X'=Z-5000
            根据条件2：Y’=Z+15000
            然后根据算平均数的方法得到以下等式：（Z-5000）*X+（Z+15000）*Y=Z*(X+Y)
            开括号，化简可得到X=3Y， 题目问的是比例，所以Y（director)的比例应该为25%

tsh0615

第二题，主要是弄清楚2的含义，条件（1）可能有两种情况，如果N本身的质因子没有2，比如105（3×5×7），那么2N的质因子有四个但是N的质因子只有三个。另外一种情况如果N的质因子有2，比如210（3×5×7×2），那么2N的质因子是四个，但是N的质因子也是四个，即是说从条件1不能确定N的质因子是3个还是四个
条件2，N的平方有4个质因子，因为N是其所有质因子的乘积的倍数，在平方的时候，N平方等于其所有质因子平方的倍数，很明显这个过程不能产生新的质因子（因为过程就是质因子平方，倍数平方），所以条件2是充分条件，条件1不是。

wilincl9321

no.1agree with tsh0615
no.2:
(1) 4 different prime numbers are factors of 2n --> if n itself has 2 as a factor (eg n=2*3*5*7) than its total # of primes is 4 but if n doesn't have 2 as a factor (eg n=3*5*7) than its total # of primes is 3. Not sufficient.

(2) 4 different prime numbers are factors of n^2 --> n^x (where x is an integer >or=1) will have as many different prime factors as integer n, exponentiation doesn't "produce" primes. So, 4 different prime numbers are factors of n. Sufficient.