Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Each employee of a certain task force is either a manager or [#permalink]

Show Tags

25 Mar 2009, 10:07

7

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

53% (01:56) correct
47% (01:21) wrong based on 213 sessions

HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Each 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.

it is a weighted average type problem, we know that Director income is 15000 more than the avg and we know that manager income is 5000 less than the avg..

so if you look at it, the avg is closer to the manager salary than it is to the director salary clearly there are more managers than directors!

it is a weighted average type problem, we know that Director income is 15000 more than the avg and we know that manager income is 5000 less than the avg..

so if you look at it, the avg is closer to the manager salary than it is to the director salary clearly there are more managers than directors!

Well that still doesn't give the percentage of directors in the group. I'm still not convinced. Sure there are more managers than directors - but to find the percentage of directors, won't we need the number of directors ? I may be missing something very basic here. Any help will be appreciated.

- pradeep
_________________

In the land of the night, the chariot of the sun is drawn by the grateful dead

I tried this way and agree that A & B are not the answers...

Total avg of Manager and Director = x

For Managers , Salary Avg = m = (x-5000) Managers Count = M

For Directors , Salary Avg = d = (x+15000) Directors Count = D

We have a clue in stmt that they are talking abt averages so lets substitute in the formula

Avg (x) = {M(x-5000) + D(x+15000) } / (M+D) After solving the above eqn you will get a relationship between M and D and it is M/D =1/3 and hence the answer is C.

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

1) Average salary for manager is $5,000 less than average of all employees. 2) Average salary of directors is $15,000 greater than average salary of all employees

Please explain your answers.

Suppose: no. of managers = m managers' avg. salary = s1 no. of directors = d directors avg salary = s2

From st 1: s1 + 5000 = (s1 m + s2 d) / (m+d) s1 (m+d) + 5000 (m+d) = (s1 m + s2 d) s1 m + s1 d + 5000m + 5000d = s1 m + s2 d s1 d + 5000m + 5000d = s2 d s2 d - s1 d = 5000 (m + d) d (s2 - s1) = 5000 (m + d) s2 - s1 = 5000 (m + d)/d

From st 2: s2 - 15000 = (s1 m + s2 d) / (m+d) s2 - s1 = 15000 (m+d)/m

From 1 and 2: 5000 (m+d)/d = 15000 (m+d)/m m = 3d d/(m+d) = d/(3d+d) = 1/4

Let m = no of managers and M be the avg salaray of a manager d = no of directors and D be the avg salary of the director. T be the avg salary of the total group.

We can say that Mm + Dd = T(m + d) ----> Eq 1

Question asked is what is the Percentage of directors ie (d / (m+d)) = ?

For simplicity lets consider 5 and 15 instead of 5000 or 15000.

From stmt1, avg salary of managers is 5 less than total avg

==> Mm = (T-5)m. ---> Eq 2. We don't know any thing abt d or D. Cannot simplfy this further to find out what is d / (m+d). Hence Insufficient.

From stmt2, avg salary of directors is 15 more than total avg

==> Dd = Td + 15d. --> Eq 3. We don't know anything abt M or m. Cannot simplfy this further to find out what is d / (m+d). Hence Insufficient.

Combine stmt 1 and 2 for Mm and Dd in Eq 1, we get,

Tm - 5m + Td + 15d = Tm + Td. ==> 3d = m.

Now we can solve for d / (m+d) which is d / 4d = 1/4. Hence sufficient.

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

1) Average salary for manager is $5,000 less than average of all employees. 2) Average salary of directors is $15,000 greater than average salary of all employees

Please explain your answers.

This question is testing weighted average. D - % of Directors M- % of Managers D+M=1 D? ____________ Let "a" be total average Stmt1. a-5k=m (i.e. average salary for manager)

Stmt2. a+15k=d (i.e. average salary for director)

None is suff by itself.

Stmt 1 &2. Formula for weighted average: M*m+D*d=a M(a-5k)+D(a+15k)=a Ma-M5k+Da+D15k=a a(M+D)+D15k-M5k=a As M+D=1, we are left with D15k-M5k=0 Also, M=1-D => D15k-5k+D5k=0 D=1/4 or 25%

Yes this probelm is a bit time consuming. I liked GMAT tigers equation approach. It was more understandable to me.

Have seen this problem in some other forum some time back and i remember they put the below explaination. It will be good if someone can expalin. Just wanted to share with u all.

Concept of weighted averages

5000-------- Av ------------------150000

salarys are the ratio M/D = 5000 / 15000 = 1/3

the number of mangers and directors will be in the inverse ratio M / D = 3/1 .

Solving this ques. by equations will take a lot of time.

Alternative approach.

Manager manager manager............x managers ................Average..............director director director.....y director instaed of 5000 and 15000 lets deal with 5 and 15.

So managers are trying to bring down the average and directors are trying to bring up the average. however the average is fixed.

1 director can raise the average by 15 so to nullify it we need 3managers. so total employees = 4.Hence ratio of manager to director = 1/4.

Yes this probelm is a bit time consuming. I liked GMAT tigers equation approach. It was more understandable to me.

Have seen this problem in some other forum some time back and i remember they put the below explaination. It will be good if someone can expalin. Just wanted to share with u all.

Concept of weighted averages

5000-------- Av ------------------150000

salarys are the ratio M/D = 5000 / 15000 = 1/3

the number of mangers and directors will be in the inverse ratio M / D = 3/1 .

This is the best approach I've ever seen for averages. I might never have figured this out myself had i not seen this.

Actually the above diagram can be better represented as

Avg M-----(5000)-----Avg Tot-----------------(15000)--------------Avg D

ie, Avg of managers is at distance of 5000 from total avg, and avg of directors is at a distance for 15000 from tot avg.

Now concept of weighted avg is that The total avg will be most affected by the heaviest weight, ie, more the number of managers, closer will be tot avg to their avg salary, more the number of directors, closer will be the tot avg to their avg.

Now Avg tot is most affected by avg M, that means managers are more. How many more relative to directors?

Avg D is 3 times as far from tot avg as is Avg M.

that implies that weight of AvgM is 3 times greater than weight of AvgD. weight here is nothing but number of managers.

Using pen and paper, it takes arround 2-3 minuets.

reply2spg wrote:

btw....How much time will it take to answer the question?????

GMAT TIGER wrote:

Accountant wrote:

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

1) Average salary for manager is $5,000 less than average of all employees. 2) Average salary of directors is $15,000 greater than average salary of all employees

Please explain your answers.

Suppose: no. of managers = m managers' avg. salary = s1 no. of directors = d directors avg salary = s2

From st 1: s1 + 5000 = (s1 m + s2 d) / (m+d) s1 (m+d) + 5000 (m+d) = (s1 m + s2 d) s1 m + s1 d + 5000m + 5000d = s1 m + s2 d s1 d + 5000m + 5000d = s2 d s2 d - s1 d = 5000 (m + d) d (s2 - s1) = 5000 (m + d) s2 - s1 = 5000 (m + d)/d

From st 2: s2 - 15000 = (s1 m + s2 d) / (m+d) s2 - s1 = 15000 (m+d)/m

From 1 and 2: 5000 (m+d)/d = 15000 (m+d)/m m = 3d d/(m+d) = d/(3d+d) = 1/4

since the distance from the average should sum to zero, then the distance from the total average of one group plus the distance from the average of the second group should be equal to zero! So, a quick formula would be: (-5000)x(number of managers) + (15000)(number of directors) = 0 So: number of managers/number of directors = 15000/5000 = 3/1

Out of the total number, the managers would be 3 times the number of directors.

as this is DS problem and understanding the problem's concept and what is solution for this is important though, it does not need actual solution. As above mentioned in various post, weight average concept should yield percentage of director as relation 1) between manager Avg and total avg is available 2) between director avg and total avg is available Hence answer is C.

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

1) Average salary for manager is $5,000 less than average of all employees. 2) Average salary of directors is $15,000 greater than average salary of all employees

Statement 1 Let average of all employees be x. Avg salary for manager: x - 5000 Insufficient.

Statement 2 Avg salary of directors (D): x + 15000 Insufficient.

Statement 1 + 2

\(\frac{M(x-5000)+D(x+15000)}{M+D}= x\)

\(\frac{Mx-5000M+Dx+15000D}{M+D} = x\)

\(\frac{x(M+D)+15000D-5000M}{M+D} = x\)

\(\frac{15000D-5000M}{M+D}=0\)

\(5000(3D-M)=0\)

\(3D=M\) (from here you can actually derive the required percentage)

Sufficient!

Answer: C

The below by karimsafi is a really quick method though! +1 Kudos!

Quote:

Concept of weighted averages

(-5000)............x............................(+15000) M-------- Average ------------------D

since the distance from the average should sum to zero, then the distance from the total average of one group plus the distance from the average of the second group should be equal to zero! So, a quick formula would be: (-5000)x(number of managers) + (15000)(number of directors) = 0 So: number of managers/number of directors = 15000/5000 = 3/1

Out of the total number, the managers would be 3 times the number of directors.

so, D = 1/4 of total and M = 3/4 of total

_________________

"The best day of your life is the one on which you decide your life is your own. No apologies or excuses. No one to lean on, rely on, or blame. The gift is yours - it is an amazing journey - and you alone are responsible for the quality of it. This is the day your life really begins." - Bob Moawab

Re: Each employee on a certain task force is either a manager or [#permalink]

Show Tags

31 Oct 2013, 21:19

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...

The words of John O’Donohue ring in my head every time I reflect on the transformative, euphoric, life-changing, demanding, emotional, and great year that 2016 was! The fourth to...