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A company employs 20 workers for every 3 managers, and 5

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A company employs 20 workers for every 3 managers, and 5 [#permalink] New post 15 Aug 2017, 01:35
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A company employs 20 workers for every 3 managers, and 5 managers for every director. If the total number of employees at the company is between 300 and 400, what is the number of managers who work at the company?

enter your value

[Reveal] Spoiler: OA
45

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Re: A company employs 20 workers for every 3 managers, and 5 [#permalink] New post 17 Aug 2017, 14:00
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Carcass wrote:
A company employs 20 workers for every 3 managers, and 5 managers for every director. If the total number of employees at the company is between 300 and 400, what is the number of managers who work at the company?

enter your value

[Reveal] Spoiler: OA
45


Let W = # of workers
Let M = # of managers
Let D = # of directors

Company employs 20 workers for every 3 managers
So, W : M = 20 : 3

Company employs 5 managers for every 1 director
So, M: D = 5: 1

The common value is the number of managers. So, let's create some EQUIVALENT ratios so that both ratios have the same number of managers.

Take 20 : 3 and multiply both values by 5 to get: 100 : 15
Take 5: 1 and multiply both values by 3 to get: 15: 3

We can now COMBINE the ratios to get: W : M : D = 100 : 15 : 3

So, one POSSIBLE scenario is that there are 100 workers, 15 managers, and 3 directors for a TOTAL of 118 people.

Another POSSIBLE scenario is that there are 200 workers, 30 managers, and 6 directors for a TOTAL of 236 people.

Another POSSIBLE scenario is that there are 300 workers, 45 managers, and 9 directors for a TOTAL of 354 people. PERFECT!!

We're told that the total number of employees at the company is between 300 and 400.
So, the last scenario meets this condition.

So, there must be 45 managers

Answer:
[Reveal] Spoiler:
45


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Re: A company employs 20 workers for every 3 managers, and 5 [#permalink] New post 08 Jan 2019, 07:51
Expert's post
Carcass wrote:


A company employs 20 workers for every 3 managers, and 5 managers for every director. If the total number of employees at the company is between 300 and 400, what is the number of managers who work at the company?

enter your value

[Reveal] Spoiler: OA
45


1 director for 5 managers and 20 workers for 3 managers.... Let us take the number of managers as LCM of 3 and 5 or 15..
so 1 director for 5 managers means 1*3 director for 3*5 managers and 20 workers for 3 managers means 5*20 workers for 3*5 managers..
so the group is 3 director, 15 managers and 100 workers, thus a total of 3+15+100 = 118
Now multiple of 118 between 300 and 400 is 118*3..
Thus managers = 15*3=45
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1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
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Re: A company employs 20 workers for every 3 managers, and 5   [#permalink] 08 Jan 2019, 07:51
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