DS - GMAT PREP - practise test - Q2

[ata]

Each employee on a certain task force is either a clerk or an executive. wht % of employees on the task force are executives?

(1) Mean salary of clerks on the task force is 5000 less than the mean salary of all employees
(2) Mean salary of executives on the task force is 15000 more than the mean salary of all employees on the task force

ans: both together are sufficient

would really appreciate if someone can explain

[Joey Z.]

To fully understand this type of questions, it'll help if I can sit down with you and draw a little number line. However......

The easiest way to solve this particular question is to think this way:

Suppose an executive who has the mean salary of all executives (we're talking about averages here, so individual differences do not matter; it is safe to assume all executives earn the same and all clerks earn the same; if you have doubts about this, I can explain this in another post) just retired, how many clerks need to retire so that the mean salary of all employees remains the same? Three. Why? 15000/5000=3! The three poor guys wish that the executive would donate 5000 to each of them so that all four of them would earn the same.

This means for every executive there have to be three clerks, so 25% of employees on the task force are executives.

[RR]

Joey's approach is much faster.
But here is how you can do it mathematically.
Let us look at option C ie both together.

Let x be the mean salary of all employees
Let C be the total number of clerks
Let E be the total number of executives

Total number of employees = C + E
Mean salary of clerks = x - 5000
Total salary of all clerks = (x - 5000) C
Mean salary of executives = x + 15000
Total salary of all executives = (x + 15000) E
The mean salary of all employees can be written as a weighted average equation

(x - 5000) C + (x + 15000) E
----------------------------------- = x
C + E

x(C + E) - 5000C + 15000E
----------------------------------- = x
C + E

x - (5000C - 15000E)
--------------------- = x
C + E

15000E - 5000C
------------------- = 0
C + E

15000E - 5000C = 0

E 5000
-- = ------
C 15000

E/C = 1/3

ie Exectuives comprise 25 % of the workforce - SUFFICIENT

option i : Will tell us that salary of all clerks together is (x - 5000)C - insufficient

option ii : Will tell us that salary of all executives together is (x + 15000)E - insufficient

[RonPurewal]

huh, weird.

http://www.manhattangmat.com/forums/eac ... -t772.html

so are there really 2 different versions of this problem floating around, identical in all respects except for the replacement of "managers"/"directors" by "clerks"/"executives"?

[abedinbhuiyan]

x - (5000C - 15000E)
1) --------------------- = x
C + E

15000E - 5000C
2) ------------------- = 0
C + E

How did you derive the second line from the first line.

BR

Abedinbhuiyan

[RonPurewal]

x - (5000C - 15000E)
1) --------------------- = x
C + E

15000E - 5000C
2) ------------------- = 0
C + E

How did you derive the second line from the first line.

BR

Abedinbhuiyan

that x isn't supposed to be in the numerator -- it's x, minus the fraction.
therefore, the x's on both sides just cancel each other out (i.e., you can subtract x from both sides and it goes away).