In Dives Corporation, 75% of the employees are customer

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by AAPL » Wed Sep 26, 2018 6:32 am

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Magoosh

In Dives Corporation, 75% of the employees are customer service representatives, 15% are programmers, and 10% are managers. The customer service representatives have an average salary of $60,000, and the programmers have an average salary of $100,000. If the average salary of all employees is also $100,000, what is the average salary of the managers?

A. $140,000
B. $180,000
C. $260,000
D. $400,000
E. $560,000

OA D.

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Source: Beat The GMAT — Problem Solving | Wed Sep 26, 2018 6:32 am

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by [email protected] » Wed Sep 26, 2018 8:45 am

Hi All,

We're told that in the Dives Corporation, 75% of the employees are customer service representatives, 15% are programmers, and 10% are managers, the customer service representatives have an average salary of $60,000, and the programmers have an average salary of $100,000. We're asked if the average salary of ALL employees is also $100,000, what is the average salary of the managers. This question can be approached in a variety of different ways - using some variation on the Average Formula. Here's how you can use the concept of a 'Weighted Average' against this prompt.

Since the average salary of ALL employees is $100,000, we can ignore the programmers (since they have an average salary of $100,000 already). This allows us to focus on the customer service representatives and the managers. 75% of the employees are customer service representatives and 10% are managers, so that is a ratio of 7.5 to 1 (meaning for every 1 manager, there are 7.5 customer service reps).

Customer service reps have an average salary of $60,000, so each rep is essentially $40,000 BELOW the average. This difference has to be 'made up' by the managers. For every 7.5 customer service reps, we'll be (7.5)($40,000) = $300,000 total below what the average is supposed to be, so the 1 manager will have to 'make up' that $300,000 AND have a $100,000 salary to match the average. This means that each manager would need to earn $300,000 + $100,000 = $400,000 to balance out the average.

Final Answer: D

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Rich

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Wed Sep 26, 2018 11:11 am

AAPL wrote:Magoosh

In Dives Corporation, 75% of the employees are customer service representatives, 15% are programmers, and 10% are managers. The customer service representatives have an average salary of $60,000, and the programmers have an average salary of $100,000. If the average salary of all employees is also $100,000, what is the average salary of the managers?

A. $140,000
B. $180,000
C. $260,000
D. $400,000
E. $560,000

All numbers related to salaries will be presented in thousands (of dollars).

(*) Homogeneity nature of the average

\[{\text{(say)}}\,\,100\,\,{\text{employees}}\,\,\,\left\{ \begin{gathered}
\,75\,\,{\text{representatives}}\,\,\,\, \to \,\,\,\,\$ {\text{60}}\,\,\,{\text{each}}\,\,{\text{ }}\,\,\left( * \right) \hfill \\
\,15\,\,{\text{programmers}}\,\,\,\, \to \,\,\,\,\$ {\text{100}}\,\,\,{\text{each}}\,\,\,\,\left( * \right) \hfill \\
\,10\,\,{\text{managers}}\,\,\,\, \to \,\,\,\,\$ \,{\text{x}}\,\,\,{\text{each}}\,\,\,\,\left( * \right) \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\]
\[? = x\]
\[\left( * \right)\,\,\,\, \Rightarrow \,\,\,\,\left\{ \begin{gathered}
\,\,\sum\nolimits_{75} = \,\,\,75 \cdot \$ 60\,\, \hfill \\
\,\,\sum\nolimits_{15} = \,\,\,15 \cdot \$ 100 \hfill \\
\,\,\sum\nolimits_{10} = \,\,\,10 \cdot \$ x \hfill \\
\,\,\sum\nolimits_{100} = \,\,\,100 \cdot \$ 100\,\,\,\,\,\,\,\left( {\$ 100\,\,{\text{average}}\,\,{\text{in}}\,\,{\text{total}}} \right) \hfill \\
\end{gathered} \right.\]
\[75 \cdot 60 + 15 \cdot 100 + 10x = 10000\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = x = \frac{{10\left( {1000 - 3 \cdot 150 - 150} \right)}}{{10}} = \underleftrightarrow {1000 - 4 \cdot 150} = 400\,\,\,\,\left[ {{{10}^3}\,\,{\text{dollars}}} \right]\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Wed Sep 26, 2018 11:18 am

AAPL wrote:Magoosh

In Dives Corporation, 75% of the employees are customer service representatives, 15% are programmers, and 10% are managers. The customer service representatives have an average salary of $60,000, and the programmers have an average salary of $100,000. If the average salary of all employees is also $100,000, what is the average salary of the managers?

A. $140,000
B. $180,000
C. $260,000
D. $400,000
E. $560,000

Alternate Solution (using Addends):

The average salary is equal to the programmers (average) salary, hence the "minus 40" per representative must be balanced by "plus y" per manager, so that we get "zero balance":
\[75 \cdot \left( { - 40} \right) + 10 \cdot \left( y \right) = 0\,\,\, \Rightarrow \,\,\,y = 75 \cdot 4 = 300\]
\[? = 100 + 300 = 400\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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by Scott@TargetTestPrep » Tue Oct 09, 2018 9:44 am

AAPL wrote:Magoosh

In Dives Corporation, 75% of the employees are customer service representatives, 15% are programmers, and 10% are managers. The customer service representatives have an average salary of $60,000, and the programmers have an average salary of $100,000. If the average salary of all employees is also $100,000, what is the average salary of the managers?

A. $140,000
B. $180,000
C. $260,000
D. $400,000
E. $560,000

We can let n = the average salary of the managers and create the weighted average equation:

0.75(60,000) + 0.15(100,000) + 0.1n = 100,000

45,000 + 15,000 + 0.1n = 100,000

0.1n = 40,000

n = 400,000

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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