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
In a certain company, the ratio of the number of manager to
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One option is to use TWO VARIABLESswerve 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
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
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Brent
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Excellent opportunity for the k technique: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
$$\left\{ \matrix{
\,{\rm{managers}} = 5k \hfill \cr
\,{\rm{workers}}\, = \,\,72k \hfill \cr} \right.\,\,\,\,\,\left( {k > 0} \right)\,\,\,\,\,\,\,;\,\,\,\,\,\,\,\,\,? = 5k$$
$${{5k} \over {72k + 8}} = {5 \over {74}}\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits_{{\rm{and}}\,\,{\rm{cross - multiply}}}^{:\,\,5} \,\,\,\,\,\,74k = 72k + 8\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,k = 4\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,? = 20$$
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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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
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
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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: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
(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
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