Managers to Workers - Ratios

[EricKryk]

In a certain company, the ratio of the number of managers 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

[Patrick_GMATFix]

The easiest way to deal with ratios algebraically is to express all values within the same ratio in terms of the same variable. For instance, a ratio of 5 to 72 means that there are 5x managers and 72x production workers.

An alternative approach would be to work backwards and figure out which answer choice fits the data in the prompt. I go through the question in detail in the full solution below (taken from the GMATFix App).



-Patrick

[Brent@GMATPrepNow]

In a certain company, the ratio of the number of managers 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

Another 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

[GMATGuruNY]

In a certain company, the ratio of the number of managers 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

In the original ratio -- M:W = 5:72 -- the workers are represented by a value of 72.
In the new ratio -- M:W = 5:74 -- the workers are represented by a value of 74.
74-72 = 2.
The ACTUAL increase in the number of workers -- 8 -- is 4 TIMES AS GREAT.
Implication:
All of the values in the two ratios -- including the value for M -- must be increased by a FACTOR OF 4.
Thus, M = 4*5 = 20.

The correct answer is D.

When all of the values in the two ratios are increased by a factor of 4, we get:
Original M:W = (4*5) : (4*72) = 20:288.
New M:W = (4*5) : (4*74) = 20:296.
Increase in the number of workers = 296-288 = 8.

[[email protected]]

Hi EricKryk,

Since the other explanations have focused more on the algebra behind this prompt, here's another approach: TEST THE ANSWERS:

We'll start with answer B, which is 10 managers...

To start, we have a ratio of 5 managers to 72 workers, so....
10 managers & 144 workers
Then we're told to +8 workers

Now we 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)

Next, try answer D, which is 20 managers....

20 managers & 288 workers
Now +8 workers gives us....

20 managers & 296 workers
This ratio is 5:74 which is a MATCH for what we're looking for.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[Abhishek009]

In a certain company, the ratio of the number of managers 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

All the methods posted above are great , so would not repeat it , I like solving Problems with minimum paperwork so suggesting my method through a diagram...

Once you get the concept right this will seem like a cakewalk -

[Scott@TargetTestPrep]

In a certain company, the ratio of the number of managers 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 x 5 = 20 managers.

Answer: D