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

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SVP
Joined: 06 Sep 2013
Posts: 1705
Concentration: Finance
Re: Each employee of a certain task force is either a manager or  [#permalink]

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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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8805
Location: Pune, India
Each employee of a certain task force is either a manager or  [#permalink]

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19 Oct 2015, 21:12
1
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.

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.

Check this post for details of the scale method: http://www.veritasprep.com/blog/2011/03 ... -averages/
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Karishma
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Posts: 11
Re: Data Sufficiency Question from GMAT Prep  [#permalink]

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19 Oct 2015, 21:24
Hi Kumarpritam,

Let the average salary of all the employees be \$x.
Statement 1. the avg salary of the employees is \$(x-5000) {Insufficient}
Statement 2. the avg salary of the directors is \$(x+15000) {Insufficient}

Lets take S1 and S2 together. We can see that whatever may be the value of x, three employees salary would average out the salary of 1 director to have the average as x. [3*-5000 + 1*15000 = 0]
Hence, we can say that 25% are directors [1/(3+1)*100=1/4*100=25%] and rest 75% will be employees.

Let me know for any further clarification. Thanks.

P.S. Be kind and give Kudos. :D
Intern
Joined: 07 Sep 2015
Posts: 11
Re: Each employee of a certain task force is either a manager or  [#permalink]

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19 Oct 2015, 21:24
Instead of going for such long calculations, I think the best way to get on with this question is as follows:

Let the average salary of all the employees be \$x.
Statement 1. the avg salary of the employees is \$(x-5000) {Insufficient}
Statement 2. the avg salary of the directors is \$(x+15000) {Insufficient}

Lets take S1 and S2 together. We can see that whatever may be the value of x, three employees salary would average out the salary of 1 director to have the average as x. [3*-5000 + 1*15000 = 0]
Hence, we can say that 25% are directors [1/(3+1)*100=1/4*100=25%] and rest 75% will be employees.

Let me know for any further clarification. Thanks.

P.S. Be kind and give Kudos. :D
Manager
Joined: 27 Aug 2015
Posts: 85
Re: Each employee of a certain task force is either a manager or  [#permalink]

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11 Sep 2016, 04:07
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.

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: 8805
Location: Pune, India
Re: Each employee of a certain task force is either a manager or  [#permalink]

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11 Sep 2016, 21:49
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.

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
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Karishma
Veritas Prep GMAT Instructor

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Joined: 26 Oct 2016
Posts: 636
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Re: Each employee of a certain task force is either a manager or  [#permalink]

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30 Jan 2017, 17:03
1
Apply weighted Average formula:

N1/N2 = (M2-M)/(M-M1)

Let N1 = Managers
N2 = Directors

Statement 1: M-M1 = 5000
NOT SUFFICIENT

Statement 2: M2-M = 15000
NOT SUFFICIENT

Combining...

N1/N2 = 15000/5000 = 3:1

SUFFICIENT, SO [C]
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Anaira Mitch

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Joined: 09 Sep 2013
Posts: 9463
Re: Each employee of a certain task force is either a manager or  [#permalink]

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02 Feb 2018, 23:17
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