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In a certain company, the ratio of the number of manager to

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by swerve » Tue Oct 23, 2018 11:57 am

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In a certain company, the ratio of the number of manager to the number of production-line workers is 5 to 72. If 8 additional production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

A. 5
B. 10
C. 15
D. 20
E. 25

The OA is D.

Source: Official Guide
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by Brent@GMATPrepNow » Tue Oct 23, 2018 12:26 pm
swerve wrote:In a certain company, the ratio of the number of manager to the number of production-line workers is 5 to 72. If 8 additional production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

A. 5
B. 10
C. 15
D. 20
E. 25

The OA is D.

Source: Official Guide
One option is to use TWO VARIABLES

Let M = CURRENT # of managers
Let W = CURRENT # of production-line workers

The ratio of the number of managers to the number of production-line workers is 5 to 72.
So, we can write: M/W = 5/72
Cross multiply to get: 5W = 72M

If 8 additional production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74
If 8 workers are hired then:
W + 8 = NEW number of workers
Also, M = number of managers (since nothing changes with the managers).
We can now write: M/(W + 8) = 5/74
Cross multiply to get: 74M = 5(W + 8)
Expand: 74M = 5W + 40
Rearrange to get: 74M - 40 = 5W

So, we now have two equations: 5W = 72M and 74M - 40 = 5W

Since BOTH equations are set equal to 5W, we can conclude that 72M = 74M - 40
Subtract 74M from both sides to get: -2M = -40
Solve to get M = 20

So, there are 20 managers.

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by fskilnik@GMATH » Tue Oct 23, 2018 2:37 pm
swerve wrote:In a certain company, the ratio of the number of manager to the number of production-line workers is 5 to 72. If 8 additional production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

A. 5
B. 10
C. 15
D. 20
E. 25

Source: Official Guide
Excellent opportunity for the k technique:
$$\left\{ \matrix{
\,{\rm{managers}} = 5k \hfill \cr
\,{\rm{workers}}\, = \,\,72k \hfill \cr} \right.\,\,\,\,\,\left( {k > 0} \right)\,\,\,\,\,\,\,;\,\,\,\,\,\,\,\,\,? = 5k$$
$${{5k} \over {72k + 8}} = {5 \over {74}}\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits_{{\rm{and}}\,\,{\rm{cross - multiply}}}^{:\,\,5} \,\,\,\,\,\,74k = 72k + 8\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,k = 4\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,? = 20$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by [email protected] » Tue Oct 23, 2018 2:43 pm
Hi swerve,

We're told that the ratio of the number of manager to the number of production-line workers is 5 to 72 - and IF 8 additional production-line workers were to be hired, then the ratio of the number of managers to the number of production-line workers would be 5 to 74. We're asked for the number of managers that the company has. This question can be approached in a number of different ways, including by TESTing THE ANSWERS. Let's TEST Answer B first:

Answer B: 10 manages

Since we have a ratio of 5 managers to 72 workers, we would have
10 managers & 144 workers
After adding 8 more workers, we would have...
10 managers & 152 workers
This ratios is...5:76, which is NOT a match for what we're looking for (we want 5:74, so we'll need more managers)

Answer D: 20 managers

Since we have a ratio of 5 managers to 72 workers, we would have
20 managers & 288 workers
After adding 8 more workers, we would have...
20 managers & 296 workers
This ratio is 5:74, which is a MATCH for what we're looking for, so this must be the answer.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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by Scott@TargetTestPrep » Thu Oct 25, 2018 8:22 am
swerve wrote:In a certain company, the ratio of the number of manager to the number of production-line workers is 5 to 72. If 8 additional production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

A. 5
B. 10
C. 15
D. 20
E. 25
We are given that the ratio of managers to production-line workers is 5 to 72, or 5x to 72x. We can create the following equation:

(5x)/(72x + 8) = 5/74

74(5x) = (72x + 8)(5)

370x = 360x + 40

10x = 40

x = 4

The company has 4*5 = 20 managers.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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