Find all School-related info fast with the new School-Specific MBA Forum

It is currently 21 Oct 2014, 11:20

Close

GMAT Club Daily Prep

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Each employee of a certain task force is either a manager or

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4877
Location: Pune, India
Followers: 1152

Kudos [?]: 5350 [0], given: 165

Re: DS Weighted Average [#permalink] New post 24 Jan 2013, 03:48
Expert's post
kingston wrote:
In a work force, the employees are either managers or directors. What is the percentage of directors?
(1) the average salary for manager is $5,000 less than the total average salary.
(2) the average salary for directors is $15,000 more than the total average salary.


c


This is actually a direct application of weighted averages. If you recall the scale method (explained here: http://www.veritasprep.com/blog/2011/03 ... -averages/ ), this is what the number line will look like

AVG-5000 _____________ AVG _________________________AVG+15000

Number of managers/Number of directors = [(AVG+15000) - AVG]/[AVG - (AVG - 5000)] = 3/1

Percentage of directors = 1/(1+3) = 1/4 = 25%
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Veritas Prep GMAT Discount CodesKnewton GMAT Discount CodesKaplan GMAT Prep Discount Codes
Senior Manager
Senior Manager
User avatar
Joined: 28 Mar 2012
Posts: 286
Concentration: Entrepreneurship
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 15

Kudos [?]: 172 [0], given: 23

GMAT ToolKit User
Re: Each employee of a certain task force is either a manager or [#permalink] New post 18 Feb 2013, 09:09
I would prefer method of allegations in this problem.
achan wrote:
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 ( Arithemetic 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 ( Arithemetic mean) salary of the directors on the task force is 15000 greater than the average salary of all the employees on the task force.


Image Posted from GMAT ToolKit
_________________

My posts: Solving Inequalities, Solving Simultaneous equations, Divisibility Rules

My story: 640 What a blunder!

Vocabulary resource: EdPrep

Facebook page: fb.com/EdPrep

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1734
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 14

Kudos [?]: 191 [0], given: 294

GMAT ToolKit User
Re: Each employee of a certain task force is either a manager or [#permalink] New post 25 Jan 2014, 08:18
Or one can solve this by using differentials

(1) and (2) together

We have that M = X-5000, and D = X+15,000

X being the total average so

-5000M+15000D = 0

The weights M,D are in a relation 1:3

So we know that 25% of the employers are directors

Hope it helps!
Cheers!
J :)
Senior Manager
Senior Manager
avatar
Joined: 15 Aug 2013
Posts: 284
Followers: 0

Kudos [?]: 16 [0], given: 23

Re: Each employee of a certain task force is either a manager or [#permalink] New post 28 Aug 2014, 10:26
ConnectTheDots wrote:
This can be solved in allegations method.
The ratio of the components is inverse of the ratio of their differences from the average.

#Managers:#Directors = Difference between salary between combined avg and directors : Difference between salary between combined avg and managers

M:D = 15000:500 = 3:1

D:M = 1:3

D:(M+D) = 1: (1+3) = 1:4

this way you can solve under 30 secs.


Can you really do this here or was this pure luck? Doesn't the -5000 vs. +15,000 actually give us a ratio of 20,000 to 5,000, therefore, D/M=1/4?
Senior Manager
Senior Manager
avatar
Joined: 15 Aug 2013
Posts: 284
Followers: 0

Kudos [?]: 16 [0], given: 23

Re: Each employee of a certain task force is either a manager or [#permalink] New post 30 Aug 2014, 08:58
Bunuel wrote:
achan wrote:
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 ( Arithemetic 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 ( Arithemetic mean) salary of the directors on the task force is 15000 greater than the average salary of all the employees on the task force.


S_a - Average salary of all employees
S_m - Average salary for manager
S_d - Average salary of directors
d - # of directors;
m - # of managers.
Question \frac{d}{m+d}=?

(1) S_m=S_a-5000 --> Not sufficient to calculate ratio.
(2) S_d=S_a+15000 --> Not sufficient to calculate ratio.

(1)+(2) S_a=\frac{S_m*m+S_d*d}{d+m} --> substitute S_m and S_d --> S_a=\frac{(S_a-5000)*m+(S_a+15000)*d}{d+m} --> S_a*d+S_a*m=S_a*m-5000*m+S_a*d+15000*d --> S_a*d and S_a*m cancel out --> m=3d --> \frac{d}{m+d}=\frac{d}{3d+d}=\frac{1}{4}. Sufficient.

Answer: C.

Or for (1)+(2): if we say that the fraction of the directors is x (x=\frac{d}{d+m}) then the fraction of the managers will be (1-x) (1-x=\frac{m}{d+m}) --> S_a=x(S_a+15000)+(1-x)(S_a-5000) --> S_a=x*S_a+15000x+S_a-5000-x*S_a+5000x --> x=\frac{1}{4}.


Hi Bunuel,

I utilized a similar approach but ended up getting the wrong answer. I set up the two equations just like you have but instead of Setting up the weighted average formula, I plugged the two equated directly into d/(d+m) = which made (Sa) to be 5,000 == when I plugged this back in, I got SM = 0 which made everything screwy.

What did I do wrong here? Was it wrong because I plugged the two equations directly into d/(d+m)? Why is that wrong?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23355
Followers: 3604

Kudos [?]: 28717 [0], given: 2821

Re: Each employee of a certain task force is either a manager or [#permalink] New post 31 Aug 2014, 23:37
Expert's post
russ9 wrote:
Bunuel wrote:
achan wrote:
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 ( Arithemetic 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 ( Arithemetic mean) salary of the directors on the task force is 15000 greater than the average salary of all the employees on the task force.


S_a - Average salary of all employees
S_m - Average salary for manager
S_d - Average salary of directors
d - # of directors;
m - # of managers.
Question \frac{d}{m+d}=?

(1) S_m=S_a-5000 --> Not sufficient to calculate ratio.
(2) S_d=S_a+15000 --> Not sufficient to calculate ratio.

(1)+(2) S_a=\frac{S_m*m+S_d*d}{d+m} --> substitute S_m and S_d --> S_a=\frac{(S_a-5000)*m+(S_a+15000)*d}{d+m} --> S_a*d+S_a*m=S_a*m-5000*m+S_a*d+15000*d --> S_a*d and S_a*m cancel out --> m=3d --> \frac{d}{m+d}=\frac{d}{3d+d}=\frac{1}{4}. Sufficient.

Answer: C.

Or for (1)+(2): if we say that the fraction of the directors is x (x=\frac{d}{d+m}) then the fraction of the managers will be (1-x) (1-x=\frac{m}{d+m}) --> S_a=x(S_a+15000)+(1-x)(S_a-5000) --> S_a=x*S_a+15000x+S_a-5000-x*S_a+5000x --> x=\frac{1}{4}.


Hi Bunuel,

I utilized a similar approach but ended up getting the wrong answer. I set up the two equations just like you have but instead of Setting up the weighted average formula, I plugged the two equated directly into d/(d+m) = which made (Sa) to be 5,000 == when I plugged this back in, I got SM = 0 which made everything screwy.

What did I do wrong here? Was it wrong because I plugged the two equations directly into d/(d+m)? Why is that wrong?


Please show your work with proper formatting.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: Each employee of a certain task force is either a manager or   [#permalink] 31 Aug 2014, 23:37
    Similar topics Author Replies Last post
Similar
Topics:
Each employee on a certain task force is either a manager or baileyf16 1 27 Oct 2007, 10:33
Each employee on a certain task force is either a manager or briks123 6 23 Jul 2007, 07:22
Each employee on a certain task force is either a manager or amd08 2 08 Apr 2007, 08:45
Each employee on a certain task force is either a manager or tank 7 20 Nov 2005, 00:23
Each employee on a certain task force is either a manager or Dan 8 22 Jul 2005, 22:07
Display posts from previous: Sort by

Each employee of a certain task force is either a manager or

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page   Previous    1   2   [ 26 posts ] 



GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.