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Managers

by Deepthi Subbu » Sun Mar 24, 2013 9:51 pm
Company A.s workforce consists of 10 percent managers and
90 percent software engineers. Company B.s workforce
consists of 30 percent managers, 10 percent software
engineers, and 60 percent support sta¤. The two companies
merge, every employee stays with the resulting company, and
no new employees are added. If the resulting company.s
workforce consists of 25 percent managers, what percent of
the workforce originated from Company A?
(A) 10%
(B) 20%
(C) 25%
(D) 50%
(E) 75%
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by Anju@Gurome » Sun Mar 24, 2013 9:56 pm
Deepthi Subbu wrote:Company A's workforce consists of 10 percent managers and 90 percent software engineers. Company B's workforce consists of 30 percent managers, 10 percent software engineers, and 60 percent support staff. The two companies merge, every employee stays with the resulting company, and no new employees are added. If the resulting company's workforce consists of 25 percent managers, what percent of the workforce originated from Company A?
Percentage of managers in A = 10
Percentage of managers in B = 30

We can view this as an weighted average problem where 25 is the weighted average of 10 and 30. We need to find the weight of 10.

<----10-----------25-----30---->

Weight of 10 = (30 - 25)/(30 - 10) = 5/20 = 1/4

Hence, required percentage = 100/4 = 25

The correct answer is C.
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by Deepthi Subbu » Mon Mar 25, 2013 12:09 am
Anju@Gurome : Can you please explain this line -

Weight of 10 = (30 - 25)/(30 - 10) ?
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by Anju@Gurome » Mon Mar 25, 2013 12:20 am
Deepthi Subbu wrote:Anju@Gurome : Can you please explain this line -

Weight of 10 = (30 - 25)/(30 - 10) ?
In an weighted average, if the average of A and B is C, and weights of A and B in the average are a and b respectively, then
  • aA + bB = C and (a + b) = 1
Now, b = (1 - a)

So, C = aA + (1 - a)B = B + a(A - B)
--> a = (C - B)/(A - B)

In other words, weight of A in the average = (Difference between the average and B)/(Difference between A and B)

In our case, weight of 10 = (Difference of average and 25)/(Difference between 10 and 30) = (30 - 25)/(30 - 10)

You can visualize the situation on the number line also.
<-----10-------------25-------30---->

The ratio of the weights of 10 and 30 in the average will be equal to the ratio of distances of 30 and 10 from 25, respectively.

So, (weight of 10)/(weight of 30) = (distance between 25 and 30)/(distance between 10 and 25)
--> (weight of 10)/(weight of 30) = 5/15 = 1/3
--> weight of 10 = (weight of 30)/3

Now, (weight of 10 + weight of 30) = 1

So, weight of 10 = 1/4

Hope that helps.
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by GMATGuruNY » Mon Mar 25, 2013 2:56 am
Deepthi Subbu wrote:Company A.s workforce consists of 10 percent managers and 90 percent software engineers. Company B.s workforce consists of 30 percent managers, 10 percent software
engineers, and 60 percent support staff. The two companies
merge, every employee stays with the resulting company, and
no new employees are added. If the resulting company's
workforce consists of 25 percent managers, what percent of
the workforce originated from Company A?
(A) 10%
(B) 20%
(C) 25%
(D) 50%
(E) 75%
Percentage of managers in A = 10%
Percentage of managers in B = 30%.
Percentage of managers in the MIXTURE of A and B = 25%.

Approach 1: ALLIGATION -- a very good way to handle MIXTURE PROBLEMS.

Step 1: Plot the 3 percentages on a number line, with the percentages for A and B (10% and 30%) on the ends and the percentage for the mixture (25%) in the middle.
A 40-------------25-----------30 B

Step 2: Calculate the distances between the percentages.
A 40-----15-----25-----5-----30 B

Step 3: Determine the ratio in the mixture.
The ratio of A to B in the mixture is the RECIPROCAL of the distances in red.
A : B = 5:15 = 1:3.

Thus, of every 4 managers in the mixture, 1 is from Company A, and 3 are from company B.
Thus:
A/total = 1/4 = 25%.

The correct answer is C.

For more alligation problems, check here:
https://www.beatthegmat.com/ratios-fract ... 15365.html

Approach 2: Plug in the answers

Answer choice C: 25% from Company A
Let A = 100 employees and B = 300 employees.
Managers in A = 10% of 100 = 10.
Managers in B = 30% of 300 = 90.
Total managers/total employees = (10+90)/(100+300) = 100/400 = 25%.
Success!
Last edited by GMATGuruNY on Mon Jun 03, 2013 3:38 pm, edited 1 time in total.
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by rintoo22 » Mon Mar 25, 2013 10:53 am
Hi,

The way I solved it is as follows.

x - no. of managers in company X
y - no. of managers in comapny y

(x*10 + y*30)/ (x+y) = 25
10x + 30y = 25x + 25y
5y = 15x
x/y = 1/3

Therefore x/(x+y) => 1/4 => Percentage would be 1/4 * 100 = 25%.
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