Manager / Director - averages

[susan.meng]

Each employee on a certain task force is either a manager or director. What percent of the employees on the task force are directors?

1. 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.
2. The average salary of the directors on the task force is $15,000 greater than the salary of all employees on the task force.

[supratims]

I think its E. as we cannot find the number of employees from their average salaries.
At least one of the total salaries has to be provided.

[jayachandran.b]

1 is clearly insufficient because we have no information regarding directors here..
2 is clearly insufficient because we have no information regarding managers here..

lets take both together..

say,
d = number of directors.
m = number of managers.
D is the average salary of directors.
M is the average salary of managers.
S is the total average salary.

M = S - 5000 (from 1) .... (1)
D = S + 15000 (from 2) .... (2)

Total salary = (d+m)S .. total number of task force members (m + d) times the total average salary
Total salary = mM + dD .. total salary of Managers + total salary of Directors

(d+m)S = mM + dD .. (I)

(1).m ==>
mM = mS - m5000 ..(3)
(2).d ==>
dD = dS + d15000 ..(4)

(3) + (4) ==>
mM + dD = (m+d)S + d15000 - m5000 .. (II)


I and II ==>

d15000 - m5000 = 0

d/m = 1/3

d/d+m = 1/4

So both of them together are sufficient. Thus C.

Of course we don't have to calculate the answer. We can quit after we form I and II.

[Ben Ku]

Thanks Jay, for your approach to this problem. Here's a more direct algebra approach. We're looking for some relationship between d and m.

Let me start at your equations (1), (2), and (I)
(1) M = S - 5000
(2) D = S + 15000
(I) (d+m)S = mM + dD .. (I)

(d+m)S = m(S - 5000) + d(S + 15000) = mS - 5000m + dS + 15000d
dS + mS = dS + mS - 5000m + 15000d
5000m = 15000d
m / d = 3

If there are three times as many managers as directors, then 25% of employees on the task force are directors.

[tuheroe]

Is this considered as a "difficult problem" on the GMAT?

[anoo.anand]

after seeing the solution it seems very easy...ist time i was unable to solve it :)

[abhasjha]

Try solving this by method of mixtures and alligation .......

the basic behind all mixture and alligation problem is that we mix two quantities to produce a third quantity ..

Let one of the quantity be called cheaper quantity (say C) and the other quantity be called a dearer quantity (Say D )

Then In all such cases the ratio in which the two quantities were mixed can be derived by the formula ......

C .................. D

X (mean )

D-X .............. X- C

here ratio in which the two quantities are mixed is given by D-X and X- C respectively ......


applying this to the above problem .....

Let the avg salary of all the employee be X (mean )
Avg salary of manger = X- 5000

Avg salary of directors = x+15000

in order to know the ratio of managers to directors we apply the formula

x-5000 ............. x+15000

X

15000 ........... 5000


Therefore the ratio of directors to managers is 5000 /15000 = 1: 3

So percentage of employees who are directors is (1/4) x 100 = 25 %

Hence the answer is C

One of the advantages of using the method of mixture and alligation is that it will reduce your time considerably ....... This would be a big plus since in a lot a debreif we read that test takers felt shortage of time in the quant section .....

you can solve other questions from the grpep by using method of mixture and alligation .... i am pasting those proplems for the convinience of all the users ...

Q1. During a sale, a clothing store sold each shirt at a price of $15 and each sweater at a price of $25. Did the store sell more sweaters than shirts during the sale?

(1) The average (aritmetic mean) of the prices of all the shirts and sweaters that the store sold during the sale was $21.

(2) The total of the prices of all the shirts and sweaters that the store sold during the sale was $420


Q2 . 11In a certain senior class, 72 percent of the male students and 80 percent of the female students have applied to college. What fraction of the students in the senior class are male?

(1) There are 840 students in the senior class
(2) 75 percent of the students in the senior class have applied to college.


Og 12 - Question 223 - PS section ........

[RonPurewal]

Thanks Jay, for your approach to this problem. Here's a more direct algebra approach. We're looking for some relationship between d and m.

Let me start at your equations (1), (2), and (I)
(1) M = S - 5000
(2) D = S + 15000
(I) (d+m)S = mM + dD .. (I)

(d+m)S = m(S - 5000) + d(S + 15000) = mS - 5000m + dS + 15000d
dS + mS = dS + mS - 5000m + 15000d
5000m = 15000d
m / d = 3

If there are three times as many managers as directors, then 25% of employees on the task force are directors.

this is nicely done.

just to add, you could shorten this work quite a bit by eliminating all the thousands (i.e., just write 5 instead of 5000, 15 instead of 15,000, etc.). this would be not unlike working a problem in, say, kilograms instead of grams - everything would still work out the same.

here's another post on the same thread.

post2398.html#p2398