In Dives Corporation, 75% of the employees are customer

Question

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.

Rich.C@EMPOWERgmat.com · Answer

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

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

fskilnik@GMATH · Answer

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.

fskilnik@GMATH · Answer

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.

Scott@TargetTestPrep · Answer

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

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