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# In Dives Corporation, 75% of the employees are customer service repres

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Math Expert
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Posts: 52971
In Dives Corporation, 75% of the employees are customer service repres  [#permalink]

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04 Dec 2017, 03:08
00:00

Difficulty:

15% (low)

Question Stats:

84% (02:14) correct 16% (02:13) wrong based on 74 sessions

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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

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Re: In Dives Corporation, 75% of the employees are customer service repres  [#permalink]

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04 Dec 2017, 03:20
1
imo D
let total # of employees be 100 & the average salary of the managers be x
sum of salaries = average salary* number of employees
$$10^7$$= (60,000*75) +($$10^5$$ *15) + 10x
$$10^7$$= 45*$$10^5$$ + 15*$$10^5$$ +10x
$$10^5$$(100-60)=10x
x= 400,000
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Re: In Dives Corporation, 75% of the employees are customer service repres  [#permalink]

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04 Dec 2017, 03:21
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Bunuel wrote:
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

40....100....x (Distance from Mean)

75 * 40 = x * 10
x = 30
Salary of manager = 30 + 10 = 40
D
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In Dives Corporation, 75% of the employees are customer service repres  [#permalink]

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11 Dec 2017, 09:30
Bunuel wrote:
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

Weighted average approach.* For easier calculation, remove three zeros from salaries (divide all by 1,000). Obviously, put them back for the answer.

Percentages sum to 100, in decimal form, = 1. They are the weight.
Salaries are the average for each group.
Let $x = managers' average salary Customer service: .75($60)
Programmers: .15($100) Managers: .10($x)
Total weight: (.75 + .15 + .10 = 1)
Overall average salary: $100 .75($60) + .15($100) + .10($x) = (1)($100)$45 + $15 + .10x =$100
.10x = $40 $$x = \frac{40}{.10}=400$$ (put three zeros back, i.e.,$400 * 1,000)
x = $400,000 Answer D *$$(W_1)(A_1) + (W_2)(A_2) + (W_3)(A_3) = (W{1+2+3})(A_{overall})$$ _________________ To live is the rarest thing in the world. Most people just exist. Oscar Wilde Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 4933 Location: United States (CA) Re: In Dives Corporation, 75% of the employees are customer service repres [#permalink] ### Show Tags 12 Jan 2018, 06:29 Bunuel wrote: 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 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 GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13553 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: In Dives Corporation, 75% of the employees are customer service repres [#permalink] ### Show Tags 26 Sep 2018, 21:58 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, then 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: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: In Dives Corporation, 75% of the employees are customer service repres   [#permalink] 26 Sep 2018, 21:58
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