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GMAT Club Around The World!!! In an office, there are three types of e 31 Dec 2021, 15:00
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In an office, there are three types of employees - clerks, managers, and executives. The average salary of the clerks is $3,000, the average salary of the managers is $6,000, and the average salary of the executives is $10,000. If the average salary of clerks and managers is $4,000 and the average salary of clerks and executives is $5,000, what is the ratio of clerks : managers : executives in the office?

A. 5:2:1
B. 5:2:3
C. 10:4:3
D. 10:5:2
E. 10:5:4

 


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GMAT Club Around The World!!! In an office, there are three types of e 02 Jan 2022, 22:00
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Bunuel
In an office, there are three types of employees - clerks, managers, and executives. The average salary of the clerks is $3,000, the average salary of the managers is $6,000, and the average salary of the executives is $10,000. If the average salary of clerks and managers is $4,000 and the average salary of clerks and executives is $5,000, what is the ratio of clerks : managers : executives in the office?

A. 5:2:1
B. 5:2:3
C. 10:4:3
D. 10:5:2
E. 10:5:4



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Bunuel
In an office, there are three types of employees - clerks, managers, and executives. The average salary of the clerks is $3,000, the average salary of the managers is $6,000, and the average salary of the executives is $10,000. If the average salary of clerks and managers is $4,000 and the average salary of clerks and executives is $5,000, what is the ratio of clerks : managers : executives in the office?

A. 5:2:1
B. 5:2:3
C. 10:4:3
D. 10:5:2
E. 10:5:4



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Let there be X clerks
Y managers
& Z executives
Avg salary of clerks = sum/X = 3000
Sum = 3000x
Same for Managers it would be = 6000Y
& for Executives it would be = 10000Z

average salary of clerks and managers = sum of salaries of clerks and managers / X+Y
3000x+6000Y/X+Y = 4000
3000x +6000y = 4000x +4000y
2000Y = 1000X
2Y = X
Y = X/2
average salary of clerks and executives = sum of salaries of clerks and executives/X+Z
3000X+10000Z/X+Z = 5000
3000X +10000Z = 5000X + 5000Z
5000Z = 2000X
5Z = 2X
Z = 2/5X
ratio of clerks : managers : executives = X:Y:Z =?
Only [b]E[/b] satisfies these conditions.
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Average salary of

clerks - $ 3,000
managers - $6,000
executives - $ 10,000

We can use weighted average to find the ratio

\(\frac{Clerks }{ Manager }\) = \(\frac{Managers - Average }{ Average - Clerks }\)

\(\frac{Clerks }{ Manager }\) = \(\frac{ 6000 - 4000}{ 4000 - 3000 }\)

\(\frac{Clerks }{ Manager }\) = \(\frac{ 2 }{ 1 }\)

Similarly,

\(\frac{Clerks }{ Executives }\) = \(\frac{Executives - Average }{ Average - Clerks }\)

\(\frac{Clerks }{ Executives }\) = \(\frac{ 10000 - 5000}{ 5000 - 3000 }\)

\(\frac{Clerks }{ Executives }\) = \(\frac{ 5 }{ 2 }\)

Combined Ratio =

\(\frac{Clerks }{ Manager }\) = \(\frac{ 2 }{ 1 }\)

\(\frac{Clerks }{ Executives }\) = \(\frac{ 5 }{ 2 }\)

Clerks : Managers : Executives = 10 : 5 : 4
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Correct answer is E.

You can also use the easy Plug-In method:

You want to find out c:m:e and have the terms

I) (3000c+6000m/(c+m)) = 4000
II) (3000c + 10000e/(c+e)) = 5000

Now, start with C. 10:4:3

Plug in 10 and 4 for c and m, respectively, into the first term I).

3000*10 + 6000*4 / (10 + 4) = 54,000 / 14.

You should see, that this does not equal 4000. Cross out C.

However, the answer was quite close (4000*14 = 56,000), so let´s move on with D, since there are similar numbers.

3000*10 + 6000*5 / (10 + 5) = 60,000 / 15 = 4000

Nice! This one fits. Now, we only have to try out whether the answer also fits into the second term II):

3000 * 10 + 10000*2 / (10 + 2) = 50,000 / 12 =/= 5000

--> Cross out D.

Now, since E is similar to D (c:m is the same), let´s try out E:

3000 * 10 + 10000 * 4 / (10 + 4) = 70,000 / 14 = 5,000

This is it! You have found the right answer: E.
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