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GMAT prep problem - Weighted avg.

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by adi_800 » Sat Aug 28, 2010 2:58 am
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.

A) The average salary of the managers on the task force is 5,000 less than the average salary of all employees on the task force.

B) The average salary of the directors on the task force is 15,000 greater than the average salary of all employees on the task force.


Answer is C..
I did this problem algebraic way..
But many people from other forum have used d concept weighted average...
What is this concept of weighted avg and how can we apply it here...
I dont want algebraic way..I want to know this concept of weighted avg...
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by sanju09 » Sat Aug 28, 2010 5:11 am
adi_800 wrote: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.

A) The average salary of the managers on the task force is 5,000 less than the average salary of all employees on the task force.

B) The average salary of the directors on the task force is 15,000 greater than the average salary of all employees on the task force.


Answer is C..
I did this problem algebraic way..
But many people from other forum have used d concept weighted average...
What is this concept of weighted avg and how can we apply it here...
I dont want algebraic way..I want to know this concept of weighted avg...

An average that depends on the comparative weight of each constituent, rather than caring for each constituent by the same token, is the weighted average.

Grades are habitually worked out using a weighted average. Given that training counts 10 percent, grills 20 percent, and question paper 70 percent.

If Maria has a training grade of 92, a grills grade of 68, and a question paper grade of 81, then

Maria's's overall grade = (0.10)(92) + (0.20)(68) + (0.70)(81) = 79.5

Coming to your question adi_800, I too agree that each statement here alone is not sufficient. After that is the biggest catch in this problem, another prompt question: what do we at least need to know? Should we say the ratio manager to director either way could answer the stem? I think yes. The exact question is

If there are d directors and m managers, what is d/ (d + m) equal to?

So, I think that if d to m is known, question is inimitably answered.

Since the average salaries of directors and managers could be taken as the representatives of their individual mass in our question, so we can temporarily fix d and m as: d is 15000 more than the mean of d and m; and m is 5000 more than the mean of d and m.

Simplified as d = ½ (d + m) + 15000 and m = ½ (d + m) - 5000, Can't we find d/m now? Let's try it later


[spoiler]C[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



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