January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 29 Apr 2010
Posts: 60

Each employee of a certain task force is either a manager or
[#permalink]
Show Tags
Updated on: 01 Nov 2013, 00:13
Question Stats:
55% (02:14) correct 45% (02:21) wrong based on 1432 sessions
HideShow timer Statistics
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.
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by achan on 18 May 2010, 07:01.
Last edited by Bunuel on 01 Nov 2013, 00:13, edited 2 times in total.
OA added.




Math Expert
Joined: 02 Sep 2009
Posts: 52231

Re: Each employee..
[#permalink]
Show Tags
18 May 2010, 07:21
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) \(S_m=S_a5000\) > 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 \(S_d\) > \(S_a=\frac{(S_a5000)*m+(S_a+15000)*d}{d+m}\) > \(S_a*d+S_a*m=S_a*m5000*m+S_a*d+15000*d\) > \(S_a*d\) 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 \((1x)\) (\(1x=\frac{m}{d+m}\)) > \(S_a=x(S_a+15000)+(1x)(S_a5000)\) > \(S_a=x*S_a+15000x+S_a5000x*S_a+5000x\) > \(x=\frac{1}{4}\).
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics




Kaplan GMAT Instructor
Joined: 21 Jun 2010
Posts: 70
Location: Toronto

Re: NEED HELP  2 DATA SUFFICIENCY PROBLEMS
[#permalink]
Show Tags
03 Jul 2010, 23:46
[quote2raulmaldonadomtz]I don't understand how can you get the number of employees from an average salary. Can someone explain this problem. For me neither of the 2 statements answer the question.[/quote2] We can't get the number. We can get the ratio of director to total though. This is a weighted average problem. From (1) and (2) together, we know that the managers are 5,000 smaller than the grand average, and that the directors are 15,000 greater than the grand average, or: 5000grand average15000 (mgrs)(dirctrs) The managers are way closer to the grand average than are the directors. So, there must be way more managers than directors. In fact, there are 15000/5000 or 3 times as many managers as directors. So, the manager to director ratio is 3:1. Thus, the director to total ratio is 1:4, or 25%. I discuss weighted average strategy in more detail here: mixtures96284.html(For question 2, whiplash's explanation was simply superb).




SVP
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1855
Concentration: General Management, Nonprofit

Re: NEED HELP  2 DATA SUFFICIENCY PROBLEMS
[#permalink]
Show Tags
03 Jul 2010, 21:54
Question 1:
Okay, let us assume the number of managers are M and the number of directors are D. So the total number of employees = M +D
Average Salary of Manager = x Average Salary of Director = y
So, we have: Total salary of all employees = Mx + Dy Average salary of employee = Total salary/Total employees = \(\frac{Mx+Dy}{M+D}\)
Statement 1:
Average salary of manager = Average salary of employee  5000
\(x = \frac{Mx+Dy}{M+D}  5000\)
Cross multiplying to the other side we get:
\(x(M+D) = Mx + Dy  5000\)
Cancelling Mx on both sides and rearranging like terms together we get:
\(D(yx) = 5000\)  (1)
However, this doesn't say anything specific to us. So we move on to the second statement.
Statement 1:
Average salary of director = Average salary of employee + 15000
\(y = \frac{Mx+Dy}{M+D} + 15000\)
Cross multiplying to the other side we get:
\(y(M+D) = Mx + Dy + 15000\)
Cancelling Mx on both sides and rearranging like terms together we get:
\(M(yx) = 15000\)  (2)
This doesn't say anything by itself either. But when we put the results of the two statements [(1) and (2)] together, we get:
\(D(yx) = 5000\) \(M(yx) = 15000\)
Dividing statement 1 by 2 we get
\(\frac{D}{M} = \frac{5000}{15000} = \frac{1}{3}\)
M = 3D
Total = M+D = 4D
From here, we can say percentage of directors = \(\frac{D}{4D}*100 = 25%\).
Hence answer is C.



Intern
Joined: 03 Mar 2010
Posts: 37

Re: Each employee..
[#permalink]
Show Tags
27 Jul 2010, 04:01
Let's call all employee A, manager M, and director D, so A=M+D. Their average salary is Sa, Sm, and Sd for A, M, and D respectively. The percentage of M and D are x% and y% respectively, so x+y=100%. We have the following equation: Sa=\frac{x*Sm+y*Sd}{x+y} or Sa=\frac{x*Sm+y*Sd}{100} Now consider the statement 1, it can be written as Sm=Sa5000, not sufficient to determine x and y. The same for statement 2, it leads to Sd=Sa+15000, not sufficient to determine x and y. Nevertheless, using both statement, by eliminating the constant as follows: 3Sm+Sd=3*(Sa5000)+(Sa+15000) 3Sm+Sd=4Sa Sa=\frac{3Sm+Sd}{4}=Sa=\frac{75Sm+25Sd}{100} Answer is C.
_________________
Hardworkingly, you like my post, so kudos me.



Manager
Joined: 21 Feb 2010
Posts: 183

Re: Each employee..
[#permalink]
Show Tags
15 Aug 2010, 11:14
thanks a lot bunuel!! i wonder how you know that someone posted the same question before. i did try to do a search, but couldn't find any...



Manager
Joined: 17 Dec 2010
Posts: 91
Location: Australia
GPA: 3.37
WE: Engineering (Consulting)

Re: Percentage of salary of directors.
[#permalink]
Show Tags
05 Jan 2011, 18:58
From the given, avg salary = (D(X%) + M(100X%))/100 Statement 1 doesn't provide any info on D. Not Sufficient Statement 2 doesn't provide any info on M. Not Sufficient Now we have 3 unknowns  with 2 equations... Statement 1 & Statement 2 can come together to provide us with our 3rd equation, which is, on avg, M = D  20,000 With 3 equations and 3 unknowns  u can find M, D & X. Sufficient Answer: C
_________________
Kudos always appreciated if my post helped you



Retired Moderator
Joined: 02 Sep 2010
Posts: 765
Location: London

Re: Percentage of salary of directors.
[#permalink]
Show Tags
05 Jan 2011, 23:37
shan123 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. (1) : Tells us nothing about how many directors or managers (2) : Again tells us nothing about how many (1+2) : Say average salary is x and there be m fraction of managers and hence (1m) directors m(x5000) + (1m)(x+15000) = x mx  5000m + x + 15000 mx  15000m = x 15000  20000m = 0 m = (3/4) Hence fraction of directors = (1/4) Sufficient ! Answer is (c)
_________________
Math writeups 1) Algebra101 2) Sequences 3) Set combinatorics 4) 3D geometry
My GMAT story
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 17 Dec 2010
Posts: 91
Location: Australia
GPA: 3.37
WE: Engineering (Consulting)

Re: Each employee..
[#permalink]
Show Tags
06 Jan 2011, 01:34
Bunuel  is my minimalist solution of just identifying 3 equations satisfactory? Or do you recommend fully solving it out to see if I net a result?
_________________
Kudos always appreciated if my post helped you



Math Expert
Joined: 02 Sep 2009
Posts: 52231

Re: Each employee..
[#permalink]
Show Tags
06 Jan 2011, 02:31



Intern
Status: "You never fail until you stop trying." ~Albert Einstein~
Joined: 16 May 2010
Posts: 22

Re: Each employee..
[#permalink]
Show Tags
06 Jan 2011, 09:56
Good question. While you can not figure out the number of manager and directors available, you still can manipulate the two equations to get a ratio or percentage. I didn't do any calculations but knowing that there where two statements that are relative to one another and that has factors that do not cancel one another out when setting up the equation to solve for the ratio is enough to conclude that C is the answer.



Manager
Status: what we want to do, do it as soon as possible
Joined: 24 May 2010
Posts: 77
Location: Vietnam
WE 1: 5.0

Re: Each employee..
[#permalink]
Show Tags
15 Mar 2011, 22:31
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) \(S_m=S_a5000\) > 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 \(S_d\) > \(S_a=\frac{(S_a5000)*m+(S_a+15000)*d}{d+m}\) > \(S_a*d+S_a*m=S_a*m5000*m+S_a*d+15000*d\) > \(S_a*d\) 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 \((1x)\) (\(1x=\frac{m}{d+m}\)) > \(S_a=x(S_a+15000)+(1x)(S_a5000)\) > \(S_a=x*S_a+15000x+S_a5000x*S_a+5000x\) > \(x=\frac{1}{4}\). GREAT EXPLANATION.
_________________
Consider giving me kudos if you find my explanations helpful so i can learn how to express ideas to people more understandable.



Manager
Joined: 29 Jul 2011
Posts: 89
Location: United States

Re: Statistics
[#permalink]
Show Tags
08 Jan 2012, 17:03
Good one. To solve it under 2 minutes, I had to guess this one as C. You are provided two relationships: managersall and directorsall. That should be likely enough to determine the number of managers and directors as note that the differences in average numbers are specific to the number of managers and directors. To calculate, you can solve two equations such as: 1. Sm/m = (Sm+Sd)/(m+d)  5000. 2. Sd/d = (Sm+Sd)/(m+d) + 15000. You need to solve for d/m+d.
_________________
I am the master of my fate. I am the captain of my soul. Please consider giving +1 Kudos if deserved!
DS  If negative answer only, still sufficient. No need to find exact solution. PS  Always look at the answers first CR  Read the question stem first, hunt for conclusion SC  Meaning first, Grammar second RC  Mentally connect paragraphs as you proceed. Short = 2min, Long = 34 min



Manager
Joined: 20 Aug 2011
Posts: 128

Re: Statistics
[#permalink]
Show Tags
10 Jan 2012, 01:26
Supergmatgirl wrote: Can you please elaborate? One has to understand the concept of weighted averages pretty well to understand my solution. The point of a weighted average is to know how much weight to give these two individual groups, the managers and the directors. Statement 1 tells how the managers' salaries relate to employee average but there is no information about how the directors' salaries relate to the employee average. Insufficient Eliminate A & D Statement 2 tells how the directors' salaries relate to employee average but there is no information about how the managers' salaries relate to the employee average. Insufficient Eliminate B Statements 1 and 2 together: The manager average is 5000 less than the combined average. The director average is 15000 greater than the combined average. The difference between the manager average and the director average is 20000. If there were an equal number of managers and directors they would each be 10000 off of the combined average  that would be a 50/50 weighting. But the combined average is closer to the manager average, so there are more managers than directors. Use the above three numbers to know how much: the difference is 20000, and the combined average is threequarters of the way towards the manager average. Hence, 3/4 of the employees are managers & 1/4 are directors. Sufficient. Hence C.
_________________
Hit kudos if my post helps you. You may send me a PM if you have any doubts about my solution or GMAT problems in general.



Intern
Joined: 28 Dec 2010
Posts: 19

Re: Statistics
[#permalink]
Show Tags
10 Jan 2012, 04:25
There should be a minor correction in the above equations  as the salaries are not same. 1. S1m/m = (S1m+S2d)/(m+d)  5000. 2. S2d/d = (S1m+S2d)/(m+d) + 15000.
Going back to the weighted average method. I would think in this way, say if the average of all employee’s salary is 10K then that of Manager is(105) = 5K and of Directors is (10+15) = 25 k . So for each new directors, we need 3 managers to offset the total average from increasing. That’s it  meaning for every 4 employees  3 are manager and 1 is director.



Manager
Joined: 12 Feb 2012
Posts: 125

Re: Each employee of a certain task force is either a manager or
[#permalink]
Show Tags
12 May 2012, 18:19
Hey Bunuel,
What clue told you that "average salary of all the employees", your S_alpha was a weighted average?I tried solving the problem thinking it was an arithmetic average. Was the clue that the question did not specify that it was an arithmetic? Just puzzled. I mean it makes sense that its a weighted average but the question did not specify that info.



Senior Manager
Joined: 28 Apr 2012
Posts: 278
Location: India
Concentration: Finance, Technology
GMAT 1: 650 Q48 V31 GMAT 2: 770 Q50 V47
WE: Information Technology (Computer Software)

Re: Each employee of a certain task force is either a manager or
[#permalink]
Show Tags
26 Aug 2012, 05:35
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.
_________________
"Appreciation is a wonderful thing. It makes what is excellent in others belong to us as well." ― Voltaire
Press Kudos, if I have helped. Thanks!



Director
Joined: 22 Mar 2011
Posts: 600
WE: Science (Education)

Re: Each employee of a certain task force is either a manager or
[#permalink]
Show Tags
26 Aug 2012, 07:56
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. This is a question involving weighted average. Having two quantities \(Q_1\) and \(Q_2\) with averages \(a_1\) and \(a_2\) respectively, if the combined average is \(a\), and let assume that \(a_1>a>a_2,\) then we can write: \(\frac{a_1Q_1+a_2Q_2}{Q_1+Q_2}=a\) from which \(a_1Q_1+a_2Q_2=aQ_1+aQ_2\) or \((a_1a)Q_1=(aa_2)Q_2,\) which means that the distances from the combined average are inversely proportional to the quantities. This equality we can also be written as \(\frac{a_1a}{aa_2}=\frac{Q_2}{Q_1}.\) To answer the question it is enough to know the ratio between the two types of employees. In our case we have a certain number of managers \(Q_1\) and a certain number of directors \(Q_2.\) From the above, if we know the two differences between the combined average (average salary of all employees) and each type of average, then in fact we have the ratio between \(Q_1\) and \(Q_2.\) Sufficient Answer C
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



SDA Bocconi Thread Master
Joined: 27 Dec 2012
Posts: 32
Location: India
Concentration: Technology, Entrepreneurship
GMAT 1: 660 Q48 V33 GMAT 2: 730 Q49 V40
WE: Engineering (Energy and Utilities)

Re: DS Weighted Average
[#permalink]
Show Tags
17 Jan 2013, 01:07
Let T be the total average salary. M be the no of Managers D be no of Directors.
1st Statement: Aveg salary of Managers is T5000. 2nd Statement: Avg salary of Directors is T+15000
1st things first. None of the statements provide sufficient information when taken one at a time. So the answer is either C or E Combine two statements and you get one equation:
(T5000)*M + (T+15000)*D = T*(M+D) (Average Salary of M * no of Managers + Average salary of D* no of directors = Total Average Salary T * (M+D)
solving this we get M=3D
So ratio of Directors = D/(D+M) = D/(D + 3D) = 1/4 = 0.25
Hence 25%. So the answer is C
DJ



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8789
Location: Pune, India

Re: DS Weighted Average
[#permalink]
Show Tags
24 Jan 2013, 03:48
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 AVG5000 _____________ 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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Re: DS Weighted Average &nbs
[#permalink]
24 Jan 2013, 03:48



Go to page
1 2
Next
[ 28 posts ]



