In a workforce the employers are either managers or directors. What is the percentage of directors?
A) The average salary of managers is $5,000 less than the total average salary.
B) The average salary for directors is $15,000 more than the total average salary.
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aditiniyer
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Let's call the average salary of the managers, M, the average salary of the directors, D, and the overall average, A.aditiniyer wrote:IEach employee of 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 5000 less than the average salary of all the employees on the task force.
(2) the average (arithmetic mean) salary of the directors on the task force is 15000 greater than the average salary of all the employees on the task force.
Statement 1: on a number line, we'd have:
M------A
Gap:5000
But we have nothing about D, so alone this is not sufficient.
Statement 2: on a number line, we'd have:
A--------------D
Gap:15000
But we have nothing about M, so alone this is not sufficient.
Together we have:
M-----A--------------D
Gap:5000 ----- 15,000
This tells us that the ratio of the Directors:Managers is 5,000:15000 = 1:3. If there is 1 director for every 3 managers, there is 1 director for every 4 people in the company. So together the statements are sufficient. The answer is C
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Clearly, neither statement on its own is sufficient.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.
The two statements combined constitute a MIXTURE problem: two ingredients (managers and directors) are combined to form a mixture (all of the employees on the task force).
To evaluate the two statements combined, use ALLIGATION -- a great way to handle mixture problems.
Let M = managers, D = directors, and T = the entire task force.
Step 1: Draw a number line, with the two ingredients (M and D) on the ends and the mixture (T) in the middle:
M---------------T---------------D
Step 2: Calculate the distances between the averages.
Since the managers' average is 5000 less than the average of the entire task force, and the directors' average is 15,000 more than the average of the entire task force, we get the following distances between the averages:
M-----5000------T----15000------D
Step 3: Determine the ratio in the mixture.
The ratio of M to D in the mixture is the RECIPROCAL of the distances in red.
M : D = 15000:5000 = 3:1.
Since M : D = 3:1, there are 3 managers for every 1 director.
Thus, of every 4 employees, 1 is a director, implying that directors/total = 1/4 = 25%.
SUFFICIENT.
The correct answer is C.
For two other problems solved with alligation, check here:
https://www.beatthegmat.com/ratios-fract ... 15365.html
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Hi aditiniyer,
GMAT questions are always carefully worded, so you have to pay attention to the specific question that is ASKED. Here, we're asked for the PERCENTAGE of a workforce that are directors (we're NOT asked for the NUMBER that are directors). This prompt is asking us for a percentage/ratio/fraction, so we don't necessarily need to know the exact number of managers and directors to correctly answer it.
1) The average salary of managers is $5,000 less than the total average salary.
This Fact doesn't tell us anything about how the number of managers relates to the number of directors.
Fact 1 is INSUFFICIENT
2) The average salary for directors is $15,000 more than the total average salary.
This Fact doesn't tell us anything about how the number of managers relates to the number of directors.
Fact 2 is INSUFFICIENT
Combined, we have data that relates the average salaries of managers to the average salaries of directors...
-The average salary of managers is $5,000 less than the total average salary.
-The average salary for directors is $15,000 more than the total average salary.
The two Facts, when combined, define the relationship of number of members in each category. Here's are two examples:
If we have 3 managers, then their 3 average salaries will bring DOWN the average (3)($5,000) = $15,000. That $15,000 would be 'offset' by the salary of 1 director (since the director's salary is $15,000 ABOVE the average). In this example, there is 1 director out of 4 total employees = 1/4 = 25%
If we have 6 managers, then their 6 average salaries will bring DOWN the average (6)($5,000) = $30,000. That $30,000 would be 'offset' by the salary of 2 directors (since the director's salary is $15,000 ABOVE the average). In this example, there is 2 director out of 8 total employees = 2/8 = 1/4 = 25%
The answer to the question will always be 25%.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
GMAT questions are always carefully worded, so you have to pay attention to the specific question that is ASKED. Here, we're asked for the PERCENTAGE of a workforce that are directors (we're NOT asked for the NUMBER that are directors). This prompt is asking us for a percentage/ratio/fraction, so we don't necessarily need to know the exact number of managers and directors to correctly answer it.
1) The average salary of managers is $5,000 less than the total average salary.
This Fact doesn't tell us anything about how the number of managers relates to the number of directors.
Fact 1 is INSUFFICIENT
2) The average salary for directors is $15,000 more than the total average salary.
This Fact doesn't tell us anything about how the number of managers relates to the number of directors.
Fact 2 is INSUFFICIENT
Combined, we have data that relates the average salaries of managers to the average salaries of directors...
-The average salary of managers is $5,000 less than the total average salary.
-The average salary for directors is $15,000 more than the total average salary.
The two Facts, when combined, define the relationship of number of members in each category. Here's are two examples:
If we have 3 managers, then their 3 average salaries will bring DOWN the average (3)($5,000) = $15,000. That $15,000 would be 'offset' by the salary of 1 director (since the director's salary is $15,000 ABOVE the average). In this example, there is 1 director out of 4 total employees = 1/4 = 25%
If we have 6 managers, then their 6 average salaries will bring DOWN the average (6)($5,000) = $30,000. That $30,000 would be 'offset' by the salary of 2 directors (since the director's salary is $15,000 ABOVE the average). In this example, there is 2 director out of 8 total employees = 2/8 = 1/4 = 25%
The answer to the question will always be 25%.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
