prep ds中用加权平均的思路的两题，特来请教

maomm

　

147.     14800-!-item-!-187;#058&010134

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.

133.     13609-!-item-!-187;#058&009567

At a certain company, the average (arithmetic mean) number of years of experience is 9.8 years for the male employees and 9.1 years for the female employees.  What is the ratio of the number of the company's male employees to the number of the company's female employees?

 

(1)  There are 52 male employees at the company.

 

(2)  The average number of years of experience for the company's male and female employees combined is 9.3 years.

我本来都是傻傻的列公式来算，但很费时，易错．后来在洋人网站上搜索到用ＷＥＩＧＨＴＥＤ　ＡＶＥＲＧＡＥ来做，但是还是不太懂，以前似乎数学课上没有学过，也ＧＯＯＧＬＥ了，但是解释得太专业，不明白．所以请数学牛牛能帮我用这两题解释一下．非常感谢．

zhu_eagle

其实吧，我有总结个公式，这类题：

(aX+bY)/(X+Y)=c  -->  (a-c)X=(c-b)Y  -->  X/Y=(c-b)/(a-c)  -->  X/(X+Y)和Y/(X+Y)

很明显，这个公式本身就是求加权平均。

所以，不知道你说的傻傻列公式列的是怎样的公式。如果就是这个，那么这就是加权平均的思想

133：设男生数X，女生数Y。得

(9.8X+9.1Y)/(X+Y)=9.3 

即(9.8-9.3)X=(9.3-9.1)Y

可得出X/Y，X/(X+Y),Y/(X+Y)  选B。

记得Prep上还有一题，也是男生数女生数，75%，78%什么的，记不清了。完全一样的题目。

147：稍微复杂一点，但是如果用上面给的公式发现是一类题目。只不过他直接给出了a-c=15000，c-b=5000

选C。

newaaron

多谢，很清晰的思路

bth

147:

M = # of manager
D = # of directors

Tm = Total salary of all managers
Td = Total salary of all directors

T = Tm + Td = Total salary of all employees
Total Avg salary of all employees = T / ( M+D)

Rephrased question? What is D/(M+D) ??

From (1) :
Tm / M = T / ( M+D ) - 5000

=> Tm/ M = ( Tm + Td) / ( M +D ) - 5000

=> ( Td*M - Tm*D ) / M*(M+D) = 5000 ...................eqn(a)

Cannot calculate D/(M+D)

Hence INSUFFICIENT

From (II):
Td / D = T / ( M+D ) + 15000

=> Td/ D = ( Tm + Td) / ( M +D ) + 15000

=> ( Td*M - Tm*D ) / D*(M+D) = 15000 .....................eqn ( b)

Cannot calculate D/(M+D)

Hence INSUFFICIENT

From (I) and (II) :

from eqn(a) and (b) ,

5000 * M * (M+D) = 15000 * D * (M+D)

=> M / D = 3

=> (M / D ) + 1 = 4

=> (M+D) / D = 4

=> D / ( M+D ) = 1 /4 = 25%

Hence, SUFFICIENT

Choice (C)

133:

1) There are 52 male employees

not sufficient, we don't get number of female employees

 

2)The average number of years of experience for the companys male and female employees combined is 9.3.

(9.8m+9.1f)/m+f=9.3

9.8m+9.1f=9.3m+9.3f

0.5m=0.2f

(m/f)=(2/5)

Sufficient

 

Hence B.

maomm

非常感谢,我拿回去好好琢磨琢磨

jackieli007

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