From GMAT prep
Each employer on a certain task force is either a manager or Director. What percent of the employees on task force are directors?
1. Average salary of managers on task force is 5000 less than average salary of all employees on task force.
2. Average salary of directors on task force is 15000 more than average salary of all employees on task force.
Correct Answer is C.
Thanks.
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- RonPurewal
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First off, there's a definite symmetry between the two answer choices: they're essentially the same type of information (they both tell you that ONE of the groups' average salary is X more/less than the average). Because they provide exactly the same kind of information, if one of them works by itself, then the other should too. Therefore, it's unlikely that A or B will be the answer.
Anyway:
Important fact: If you have a weighted average of TWO groups, then the average of the BIGGER group will be closer to the overall average than will the average of the smaller group.
(1) itself: Consider a couple of different cases:
* Average salary of the managers is 5000 less than the average, but the average salary of the directors is, say, only 1000 greater. By the above principle, there are a lot more directors.
* Average salary of the managers is 5000 less than the average, but the average salary of the directors is, say, 20,000 greater. By the above principle, there are a lot more managers.
* so (1) is insufficient by itself.
(2) Use exactly the same reasoning to deduce that (2) is insufficient by itself.
Taken together: Let P stand for the proportion of managers, and let A stand for the average salary. Then each of the managers makes A - 5000, and each of the directors makes A + 15000. Also, if the proportion of managers is P, then the proportion of directors is 1 - P.
Using the equation for weighted averages,
P(A - 5000) + (1 - P)(A + 15000) = A
PA - 5000P + A - PA + 15000 - 15000P = A
15000 - 20000P = 0
P = 3/4
Three-fourths of the group consists of managers. Answer = C
Anyway:
Important fact: If you have a weighted average of TWO groups, then the average of the BIGGER group will be closer to the overall average than will the average of the smaller group.
(1) itself: Consider a couple of different cases:
* Average salary of the managers is 5000 less than the average, but the average salary of the directors is, say, only 1000 greater. By the above principle, there are a lot more directors.
* Average salary of the managers is 5000 less than the average, but the average salary of the directors is, say, 20,000 greater. By the above principle, there are a lot more managers.
* so (1) is insufficient by itself.
(2) Use exactly the same reasoning to deduce that (2) is insufficient by itself.
Taken together: Let P stand for the proportion of managers, and let A stand for the average salary. Then each of the managers makes A - 5000, and each of the directors makes A + 15000. Also, if the proportion of managers is P, then the proportion of directors is 1 - P.
Using the equation for weighted averages,
P(A - 5000) + (1 - P)(A + 15000) = A
PA - 5000P + A - PA + 15000 - 15000P = A
15000 - 20000P = 0
P = 3/4
Three-fourths of the group consists of managers. Answer = C
2 posts Page 1 of 1