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At Didymus Corporation, there are just two classes of employees: silve

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At Didymus Corporation, there are just two classes of employees: silve  [#permalink]

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New post 17 Mar 2015, 05:53
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At Didymus Corporation, there are just two classes of employees: silver and gold. The average salary of gold employees is $56,000 higher than that of silver employees. If there are 120 silver employees and 160 gold employees, then the average salary for the company is how much higher than the average salary for the silver employees?

A. $24,000
B. $28,000
C. $32,000
D. $36,000
E. $40,000

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At Didymus Corporation, there are just two classes of employees: silve  [#permalink]

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New post 17 Mar 2015, 22:25
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Answer = C = 32000

Let the average salary of 120 silver employees = 0, then

average salary of 160 gold employees = 56000

Total average of company \(= \frac{120 * 0 + 160*56000}{160+120} = 32000\)

Difference = 32000-0 = 32000
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Re: At Didymus Corporation, there are just two classes of employees: silve  [#permalink]

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New post 17 Mar 2015, 06:03
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Bunuel wrote:
At Didymus Corporation, there are just two classes of employees: silver and gold. The average salary of gold employees is $56,000 higher than that of silver employees. If there are 120 silver employees and 160 gold employees, then the average salary for the company is how much higher than the average salary for the silver employees?

A. $24,000
B. $28,000
C. $32,000
D. $36,000
E. $40,000

Kudos for a correct solution.


these questions are best done with weighted average method....
ratio of two types of employees S:G=120:160=3:4....
now the average will be 4 portions above avg salary of silver employees and 3 portions below that of gold ones, if we divide the difference in averages of two types in 7 portions..
7 portions of 56000=8000...
so the avg salary of silver is 4*8000 below the overall avg..
32000 ans C...
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Re: At Didymus Corporation, there are just two classes of employees: silve  [#permalink]

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New post 17 Mar 2015, 07:14
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Bunuel wrote:
At Didymus Corporation, there are just two classes of employees: silver and gold. The average salary of gold employees is $56,000 higher than that of silver employees. If there are 120 silver employees and 160 gold employees, then the average salary for the company is how much higher than the average salary for the silver employees?

A. $24,000
B. $28,000
C. $32,000
D. $36,000
E. $40,000

Kudos for a correct solution.


brute force method : (done within 2minutes)
G=S+56000

Company Average = \((120S + 160G)/(120+160)\)
substitute S= G- 56000
\((120G - 120*56000 +160G)/280 = G - 24000\)

so Company Average - Silver group Average
= G-24K-G+56K
=32K
=32000
Answer C
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Re: At Didymus Corporation, there are just two classes of employees: silve  [#permalink]

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New post 17 Mar 2015, 08:34
1
Bunuel wrote:
At Didymus Corporation, there are just two classes of employees: silver and gold. The average salary of gold employees is $56,000 higher than that of silver employees. If there are 120 silver employees and 160 gold employees, then the average salary for the company is how much higher than the average salary for the silver employees?

A. $24,000
B. $28,000
C. $32,000
D. $36,000
E. $40,000

Kudos for a correct solution.


IMO
The answer should be -> C. $32,000
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Re: At Didymus Corporation, there are just two classes of employees: silve  [#permalink]

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New post 23 Mar 2015, 04:05
2
Bunuel wrote:
At Didymus Corporation, there are just two classes of employees: silver and gold. The average salary of gold employees is $56,000 higher than that of silver employees. If there are 120 silver employees and 160 gold employees, then the average salary for the company is how much higher than the average salary for the silver employees?

A. $24,000
B. $28,000
C. $32,000
D. $36,000
E. $40,000

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

Method I: using sums

We can use this if we pick a value for the average salary for the silver employees. It actually doesn’t matter what value we pick, because averages will fall in the same relative places regardless of whether all the individual values are slid up and down the number line. The easiest value by far to pick is zero. Let’s pretend that the silver folks make $0, and the gold folks make $56. (I divided dollars by 1000 for simplicity).

Now, we also have to simplify the numbers of employees. We could reduce the number of employees as long as we preserve the relative ratio.

silver : gold = 120:160 = 12:16 = 3:4

So everything would be the same if we just had 3 silver employees and 4 gold employees. OK, now find the sums.

silver = 3*0 = 0

gold = 4*56

I am not even going to bother to multiply that out, because we know that the next step is to divide by 7, the total number of employees.

total average = 4*56/7 = 4*8 = 32

The average salary is $32,000, which is $32,000 higher than the average for the silver employees. Answer = (C)

Method II: proportional placement of the total average

The ratio of silver employees to gold employees is

silver : gold = 120:160 = 12:16 = 3:4

If we divide the distance between the two averages by 7, then silver will be “four parts” away from the total average, and gold will be “three parts” away.

Well, the difference is $56,000, so that divided by 7 is $8000. That’s one part. Four parts would be $32,000, which has to be the distance from the silver average to the total average.

Answer = (C)
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Re: At Didymus Corporation, there are just two classes of employees: silve  [#permalink]

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New post 04 Apr 2017, 16:19
1
Bunuel wrote:
At Didymus Corporation, there are just two classes of employees: silver and gold. The average salary of gold employees is $56,000 higher than that of silver employees. If there are 120 silver employees and 160 gold employees, then the average salary for the company is how much higher than the average salary for the silver employees?

A. $24,000
B. $28,000
C. $32,000
D. $36,000
E. $40,000


We can let the average salary of the silver employees = s, and so the average salary of the gold employees = s + 56,000.

Since there are 120 silver employees and 160 gold employees, the average salary for the whole company is (120s + 160(s + 56,000))/(120 + 160). Let’s simplify this expression:

(120s + 160(s + 56,000))/(120 + 160)

(120s + 160s + 160 x 56,000)/280

(280s + 160 x 56,000)/280

280s/280 + 160 x (56,000/280)

s + 160 x 200

s + 32,000

Thus, the company’s average salary is $32,000 more than the average salary of the silver employees.

Answer: C
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Re: At Didymus Corporation, there are just two classes of employees: silve  [#permalink]

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Re: At Didymus Corporation, there are just two classes of employees: silve   [#permalink] 26 May 2019, 18:53
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