Night reader 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%

This is a weighted average question. Company A is 10% managers. Company B is 30% managers. We want to combine the two companies so that the resulting combination is 25% managers. A great method for solving is called alligation.

To combine a 10% entity with a 30% entity to get a combined entity that is 25%:

The proportion needed of each starting percentage is the positive difference between the other 2 percentages.

Proportion needed of the 10% entity = 30-25 = 5.
Proportion needed of the 30% entity = 25-10 = 15.

Thus, Company A: Company B = 5:15 = 1:3.

Thus, 1/4 = 25% of the combined entity must come from Company A.

The correct answer is C.

Another approach would be to plug in the answer choices, which represent the percentage of the merged company that must come from company A.

Answer choice C: 25% from Company A
Plug in A = 100 employees.
Plug in B = 300 employees.
10% of A = 10 managers.
30% of B = 90 managers.
Total managers = 10+90 = 100.
Total employees = 100+300 = 400.
Managers/employees = 100/400 = 25%. Success!

it's interesting - allegation method; never used this, but it works with all problems I solved with lengthy equations so far.
Thanks Mitch

I think the simplest way to solve this problem is to eliminate the %.
Company A has 10 managers and 90 employees
Company B has 30 manager and 70 (10 + 60)
After the merger, the new company has 40 managers. 10 of the the 40 managers were from Company A. So, 25%(10/40) of the workforce originated from Company A.
Answer: C

vpmba wrote:I think the simplest way to solve this problem is to eliminate the %.
Company A has 10 managers and 90 employees
Company B has 30 manager and 70 (10 + 60)
After the merger, the new company has 40 managers. 10 of the the 40 managers were from Company A. So, 25%(10/40) of the workforce originated from Company A.
Answer: C

First, we can not put 10+30 into such expression. % are not numbers, there can be 1,000,000 employees of Company A and 15 employees of company B (theoretically) - you can not (!) say 10+30=40 (this is just ridiculous...)

That your answer is the same as OA is because the weighted average is equal to 25% in the new company after it had merged.

See the correct solution from GMATGuruNY.

Night reader 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%

Let A and B be the number of people in the corresponding workforce.

We are looking for the value of A/(A+B).

From the managers info, A/10 + (3B)/10 = (A+B)/4 ;

multiplying both sides by 20 we get 2A + 6B = 5A + 5B,

therefore B = 3A.

Answer: A/(A+B) = A/(A+3A) = 1/4 = 25%

Regards,
Fabio.