Aug 20 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Aug 20 09:00 PM PDT  10:00 PM PDT Take 20% off the plan of your choice, now through midnight on Tuesday, 8/20 Aug 22 09:00 PM PDT  10:00 PM PDT What you'll gain: Strategies and techniques for approaching featured GMAT topics, and much more. Thursday, August 22nd at 9 PM EDT Aug 24 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Aug 25 09:00 AM PDT  12:00 PM PDT Join a FREE 1day verbal workshop and learn how to ace the Verbal section with the best tips and strategies. Limited for the first 99 registrants. Register today! Aug 25 08:00 PM PDT  11:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 30 Apr 2010
Posts: 55

Each employee of a certain task force is either a manager or a directo
[#permalink]
Show Tags
Updated on: 13 Jun 2019, 03:22
Question Stats:
55% (02:11) correct 45% (02:19) wrong based on 965 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, 08:01.
Last edited by Bunuel on 13 Jun 2019, 03:22, edited 3 times in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 57155

Each employee of a certain task force is either a manager or a directo
[#permalink]
Show Tags
18 May 2010, 08:21
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 (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. \(S_a\)  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 \((1x)\) (\(1x=\frac{m}{d+m}\)) > \(S_a=x(S_a+15000)+(1x)(S_a5000)\) > \(S_a=x*S_a+15000x+S_a5000x*S_a+5000x\) > \(x=\frac{1}{4}\).
_________________




Kaplan GMAT Instructor
Joined: 21 Jun 2010
Posts: 69
Location: Toronto

Re: Each employee of a certain task force is either a manager or a directo
[#permalink]
Show Tags
04 Jul 2010, 00:46
[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: 1841
Concentration: General Management, Nonprofit

Re: Each employee of a certain task force is either a manager or a directo
[#permalink]
Show Tags
03 Jul 2010, 22:54
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.



Retired Moderator
Joined: 02 Sep 2010
Posts: 755
Location: London

Re: Each employee of a certain task force is either a manager or a directo
[#permalink]
Show Tags
06 Jan 2011, 00:37
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)
_________________



Manager
Joined: 17 Dec 2010
Posts: 89
Location: Australia
GPA: 3.37
WE: Engineering (Consulting)

Re: Each employee of a certain task force is either a manager or a directo
[#permalink]
Show Tags
06 Jan 2011, 02:34
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: 57155

Re: Each employee of a certain task force is either a manager or a directo
[#permalink]
Show Tags
06 Jan 2011, 03:31
MackyCee wrote: 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? Generally you can stop solving a DS question at the point you realize a statement is sufficient to get the answer. Note that for this question we don't need to solve for unknowns, we need to get the ratio of directors to total employees. I don't know what 3 equations are you talking about but the statements together are indeed sufficient to get the desired ratio and one can get this even not calculating its exact value.
_________________



Manager
Joined: 29 Jul 2011
Posts: 80
Location: United States

Re: Each employee of a certain task force is either a manager or a directo
[#permalink]
Show Tags
08 Jan 2012, 18:03
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: 121

Re: Each employee of a certain task force is either a manager or a directo
[#permalink]
Show Tags
10 Jan 2012, 02:26
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.



Senior Manager
Joined: 28 Apr 2012
Posts: 273
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 a directo
[#permalink]
Show Tags
26 Aug 2012, 06:35
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: 598
WE: Science (Education)

Re: Each employee of a certain task force is either a manager or a directo
[#permalink]
Show Tags
26 Aug 2012, 08:56
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: Each employee of a certain task force is either a manager or a directo
[#permalink]
Show Tags
17 Jan 2013, 02:07
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: 9541
Location: Pune, India

Re: Each employee of a certain task force is either a manager or a directo
[#permalink]
Show Tags
24 Jan 2013, 04:48
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 >



Manager
Joined: 27 Aug 2015
Posts: 86

Re: Each employee of a certain task force is either a manager or a directo
[#permalink]
Show Tags
11 Sep 2016, 05:07
VeritasPrepKarishma wrote: kumarpritam wrote: Each employee on a certain task force is either a manager or director. What percent of the employees on the task force are director? 1. The average (Arithmetic Mean) salary of the mangers on the task force is $5,000 less than the average salary of all employees on the task force. 2. The average (Arithmetic Mean) salary of the directors on the task force is $15,000 greater than the average salary of all employees on the task force. As Rich said, the right forum for this question is the DS forum. The employees are a mix of managers and directors. We need to find the percentage of directors. No statement alone gives you information on both managers and directors. We need to find whether both statements together are sufficient. Use the scale method of weighted averages here. w1/w2 = (A2  Aavg)/(Aavg  A1) = 15000/5000 = 3:1 So for every 3 managers, there is one director. Hence, directors are 25% of the employees task force. Answer (C) Check this post for details of the scale method: http://www.veritasprep.com/blog/2011/03 ... averages/Hi Karishma, I also tried the same method for this but the ratio of 3:1 s the ration of average salary. How can we say that it would be the ratio of Managers and Directors? Thanks



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9541
Location: Pune, India

Re: Each employee of a certain task force is either a manager or a directo
[#permalink]
Show Tags
11 Sep 2016, 22:49
rakaisraka wrote: VeritasPrepKarishma wrote: kumarpritam wrote: Each employee on a certain task force is either a manager or director. What percent of the employees on the task force are director? 1. The average (Arithmetic Mean) salary of the mangers on the task force is $5,000 less than the average salary of all employees on the task force. 2. The average (Arithmetic Mean) salary of the directors on the task force is $15,000 greater than the average salary of all employees on the task force. As Rich said, the right forum for this question is the DS forum. The employees are a mix of managers and directors. We need to find the percentage of directors. No statement alone gives you information on both managers and directors. We need to find whether both statements together are sufficient. Use the scale method of weighted averages here. w1/w2 = (A2  Aavg)/(Aavg  A1) = 15000/5000 = 3:1 So for every 3 managers, there is one director. Hence, directors are 25% of the employees task force. Answer (C) Check this post for details of the scale method: http://www.veritasprep.com/blog/2011/03 ... averages/Hi Karishma, I also tried the same method for this but the ratio of 3:1 s the ration of average salary. How can we say that it would be the ratio of Managers and Directors? Thanks How would you find the average salary of both  Managers + Directors Average salary of group = (Avg sal of Managers * No of managers + Avg sal of Directors * No of Directors) / (No of Managers + No of Directors) So note that the weights in weighted average formula are 'no of managers' and 'no of directors'. The formula w1/w2 = (A2  Aavg)/(Aavg  A1) is just an arrangement of the above formula. w1 and w2 are the weights. A2 is the average salary of Directors, Aavg is the average salary of the group and A1 is the average salary of Managers. Stmt. 1. The average (Arithmetic Mean) salary of the mangers on the task force is $5,000 less than the average salary of all employees on the task force. This means Aavg  A1 = 5,000 Stmt 2. The average (Arithmetic Mean) salary of the directors on the task force is $15,000 greater than the average salary of all employees on the task force. This means A2  Aavg = 15,000
_________________
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 >



Director
Joined: 26 Oct 2016
Posts: 624
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: Each employee of a certain task force is either a manager or a directo
[#permalink]
Show Tags
30 Jan 2017, 18:03
Apply weighted Average formula: N1/N2 = (M2M)/(MM1) Let N1 = Managers N2 = Directors Statement 1: MM1 = 5000 NOT SUFFICIENT Statement 2: M2M = 15000 NOT SUFFICIENT Combining... N1/N2 = 15000/5000 = 3:1 SUFFICIENT, SO [C]
_________________
Thanks & Regards, Anaira Mitch



NonHuman User
Joined: 09 Sep 2013
Posts: 12053

Re: Each employee of a certain task force is either a manager or a directo
[#permalink]
Show Tags
13 Jun 2019, 03:26
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.
_________________




Re: Each employee of a certain task force is either a manager or a directo
[#permalink]
13 Jun 2019, 03:26






