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At Didymus Corporation there are just two classes of employe

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rajlal

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Joined: 22 Aug 2018

Posts: 29

At Didymus Corporation there are just two classes of employe [#permalink]

Updated on: 12 Jan 2019, 06:28

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Question Stats:

81% (01:48) correct

18% (03:35) wrong

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At Didymus Corporation there are just two classes of employees: Silver and Gold. The average salary of Gold is $56000 higher than that of silver employees. If there are 120 silver employees and 160 gold employees then the average salary for the company is higher than the average salary for the silver by

A) 8000
B) 15000
C) 25000
D) 32000
E) 36000

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Originally posted by rajlal on 20 Sep 2018, 07:33.
Last edited by chetan2u on 12 Jan 2019, 06:28, edited 1 time in total.

Formatted the question

Carcass

Verbal Expert

Joined: 18 Apr 2015

Posts: 16945

GRE 1: Q160 V160

Re: At Didymus Corporation there are just two classes of employe [#permalink]

20 Sep 2018, 07:50

Expert Reply

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.

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.

C
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rajlal

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Joined: 22 Aug 2018

Posts: 29

Re: At Didymus Corporation there are just two classes of employe [#permalink]

20 Sep 2018, 11:32

Carcass wrote:

How can we take the algebraic approach?

Carcass

Verbal Expert

Joined: 18 Apr 2015

Posts: 16945

GRE 1: Q160 V160

Re: At Didymus Corporation there are just two classes of employe [#permalink]

20 Sep 2018, 11:33

Expert Reply

it is cumbersome. You should always try to use the fastest approach.

Regards
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sandy

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GRE 1: Q167 V156

WE:Business Development (Energy and Utilities)

Re: At Didymus Corporation there are just two classes of employe [#permalink]

20 Sep 2018, 15:53

Expert Reply

rajlal wrote:

How can we take the algebraic approach?

Assume a salary for Silver employees=x

Now then salary of gold employees = x + $56,000.

Average salary of of comapny is = $\frac{160 (x+56000)+ 120x}{160+120}$

Difference between comapany average and silver =$\frac{160 (x+56000)+ 120x}{160+120}-x$=$\frac{160 (x+56000)+ 120x -(160+120)x}{160+120}$= $\frac{160 (56000)}{160+120}=32000$
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Director

Joined: 09 Nov 2018

Posts: 505

Re: At Didymus Corporation there are just two classes of employe [#permalink]

10 Jan 2019, 21:02

rajlal wrote:

Please fix typo
should be then the average salary for the company is how much higher than the average salary for the silver employees

Director

Joined: 09 Nov 2018

Posts: 505

Re: At Didymus Corporation there are just two classes of employe [#permalink]

10 Jan 2019, 21:21

MAGOOSH OFFICIAL SOLUTION wrote:

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)

rajlal

Intern

Joined: 22 Aug 2018

Posts: 29

Re: At Didymus Corporation there are just two classes of employe [#permalink]

12 Jan 2019, 04:03

AE wrote:

rajlal wrote:

Please fix typo
should be then the average salary for the company is how much higher than the average salary for the silver employees

The question is correct from the source. If you have any problem I expect you to take it with Magoosh team and not bicker it with me.

Bye bye

Carcass

Verbal Expert

Joined: 18 Apr 2015

Posts: 16945

GRE 1: Q160 V160

Re: At Didymus Corporation there are just two classes of employe [#permalink]

12 Jan 2019, 04:35

Expert Reply

Guys no need to pick some wasteful dull fights.

Often the questions from NON-official resources have typos.

As well, those from OFFICIAL resources.

As such, it is just a question. Wed o have on the board countless questions more. Move on.

Thank you
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chetan2u

Supreme Moderator

Joined: 01 Nov 2017

Posts: 371

Re: At Didymus Corporation there are just two classes of employe [#permalink]

12 Jan 2019, 06:27

Expert Reply

rajlal wrote:

you can use weighted average method too...

........gold.............silver
average..x............x+56000...
weights... 160.............120..

so company'S AVERAGE = $x+56000*\frac{120}{120+160}=x+56000*\frac{120}{280}=x+200*120=x+24000$

difference in silver and company's average = (x+56000)-(x+24000)=x+56000-x-24000=32000
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2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
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