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# Company A's workforce consists of 10 percent managers and 90

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Company A's workforce consists of 10 percent managers and 90 [#permalink]  09 Sep 2012, 01:25
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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 companyís 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%

[Reveal] Spoiler:
EXPL: The question gives you two equations. First, the percents of the managers, where A and B stand for the total number of employees in each companyís workforce:
1/10 (A) + 3/10 B = 1 /4 (A + B)
Since A and B are fractions (or percents) of the total resulting workforce:
A+B=1
To combine the equations, rewrite the second equation: A=1- B
Then plug in to the first equation

I am not clear that how can A and B be treated as fractions when they represent the number of employees in firms A and B respectively. How is A+B =1?
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Sep 2012, 03:27, edited 3 times in total.
Renamed the topic and edited the question.
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Re: mixtures problem [#permalink]  09 Sep 2012, 01:53
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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 companyís 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%

[Reveal] Spoiler:
EXPL: The question gives you two equations. First, the percents of the managers, where A and B stand for the total number of employees in each companyís workforce:
1/10 (A) + 3/10 B = 1 /4 (A + B)
Since A and B are fractions (or percents) of the total resulting workforce:
A+B=1
To combine the equations, rewrite the second equation: A=1- B
Then plug in to the first equation

I am not clear that how can A and B be treated as fractions when they represent the number of employees in firms A and B respectively. How is A+B =1?

Let say Company A has x employes and B has y employees. Now they merge and total no of employees = x+y employees.

Per the question 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. We translate it into equation as follows:

.1x + .3y = .25 (x+y)
=> x + 3y =2.5 (x+y)
=> .5y = 1.5x
=> y=3x.
Now we know total employee = x+y. we need to find %age of x in total (x+y) ie x/(x+y) X100%
=> x/(3x+x) [substitute y=3x] => x/4x X 100%
=> .25 X 100 % => 25%.

Hence Answer C. Is it correct?
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Re: Company A's workforce consists of 10 percent managers and 90 [#permalink]  09 Sep 2012, 03:26
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Expert's post
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 companyís 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%

Say $$a$$ is the number of employees in company A and $$b$$ is the number of employees in company B.

The question is: "what percent of the workforce originated from Company A", so we should find the value of $$\frac{a}{a+b}$$.

We are told that 10% managers from A and 30% managers from B result in 25% managers in combined workforce, hence $$0.1a+0.3b=0.25(a+b)$$ --> $$b=3a$$ --> $$\frac{a}{a+b}=\frac{1}{4}=0.25$$.

Hope it's clear.

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Re: Company A's workforce consists of 10 percent managers and 90 [#permalink]  09 Sep 2012, 04:04
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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 companyís 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%

I love so solve such problem using algorithm.

Here-
-------------------M--------E-------SS
C1 --------------10 %---90%----0%
C2---------------30%----10%---60%

As, it is given that final % of managers is 25%, so we can say 10% of C1 and 30% of C2 constitute 25% of managers in merged company.
Now, let's arrange the algorithm-

---------------10--------------------------------------30
-------------------------------------25
----------------5 (=30-25)------------------------15 (=25-15) [Calculate difference diagonally; also this is the ratio of two companies]
----------------1--------------------------------------3 (Ratio remains same after dividing both 5, and 15 with 5)

This means, Company C1 has as share of $$1 / (1+3)$$ $$= 1/4$$$$= 25%$$

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Re: Company A's workforce consists of 10 percent managers and 90 [#permalink]  09 Sep 2012, 07:05
Thanks for the solutions guys.

I had a doubt regarding the solution i have supplied under the spoiler. In that A and B are considered as the number of employees in step one and in the next step as fractions/ratios, and we get the answer that way also. Can you please explain that?
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Re: Company A's workforce consists of 10 percent managers and 90 [#permalink]  10 Sep 2012, 02:35
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Expert's post
Thanks for the solutions guys.

I had a doubt regarding the solution i have supplied under the spoiler. In that A and B are considered as the number of employees in step one and in the next step as fractions/ratios, and we get the answer that way also. Can you please explain that?

Actually, they are assuming that A represents the fraction of workforce of A in the total workforce and B represents the fraction of workforce of B in the total workforce.

A and B do not stand for the number of employees.

The method they have used is not the most optimum. Use weighted avg formula instead. You know that company A has 10% managers and company B has 30% managers and together they have 25% managers.

wA/wB = (30 - 25)/(25 - 10) = 1/3

wA = 25% of total workforce

Check this for explanation on weighted average formula: http://www.veritasprep.com/blog/2011/03 ... -averages/
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Re: Company A's workforce consists of 10 percent managers and 90 [#permalink]  10 Sep 2012, 20:28
Bunuel 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 companyís 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%

Say $$a$$ is the number of employees in company A and $$b$$ is the number of employees in company B.

The question is: "what percent of the workforce originated from Company A", so we should find the value of $$\frac{a}{a+b}$$.

We are told that 10% managers from A and 30% managers from B result in 25% managers in combined workforce, hence $$0.1a+0.3b=0.25(a+b)$$ --> $$b=3a$$ --> $$\frac{a}{a+b}=\frac{1}{4}=0.25$$.

Hope it's clear.

It is clear thanks, and i have used the same method while solving this question, however i had a big doubt before chosing the answer. I started to look at the other part of the provided information. Eventhough i did not used it and i think it is not of much need here, but still i thought since it is given there should be some purpose.
My question, does the GMAT sometimes use information just to distract or i am missing something?
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Re: Company A's workforce consists of 10 percent managers and 90 [#permalink]  11 Sep 2012, 01:43
Expert's post
ziko wrote:
Bunuel 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 companyís 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%

Say $$a$$ is the number of employees in company A and $$b$$ is the number of employees in company B.

The question is: "what percent of the workforce originated from Company A", so we should find the value of $$\frac{a}{a+b}$$.

We are told that 10% managers from A and 30% managers from B result in 25% managers in combined workforce, hence $$0.1a+0.3b=0.25(a+b)$$ --> $$b=3a$$ --> $$\frac{a}{a+b}=\frac{1}{4}=0.25$$.

Hope it's clear.

It is clear thanks, and i have used the same method while solving this question, however i had a big doubt before chosing the answer. I started to look at the other part of the provided information. Eventhough i did not used it and i think it is not of much need here, but still i thought since it is given there should be some purpose.
My question, does the GMAT sometimes use information just to distract or i am missing something?

Yes, I've seen some questions from reliable sources which had redundant information just to confuse us.
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Re: Company As workforce consists of 10 percent managers and 90 [#permalink]  21 Mar 2013, 17:34
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See attached grid below.

We have to find $$\frac{X}{Z}$$: the number of workers that came from A over the total number of workers resulting from the merge.

Let's write the conditions for this problem:

(1) $$A + B + 25 = 100$$

(2) $$X+Y=Z$$

(3) $$A=\frac{(90X+10Y)}{Z}$$

(4) $$25=\frac{(10X+30Y)}{Z}$$

(5) $$B=\frac{60Y}{Z}$$

Very easily, we can see that using ONLY (4) and (2) we have: $$25=\frac{(10X+30Y)}{(X+Y)}$$ ---> $$25X+25Y=10X+30Y$$ --> $$3X=Y$$

Whit this, WE ALREADY HAVE THE SOLUTION as:

$$\frac{X}{Z}=\frac{X}{(X+Y)}=\frac{X}{(X+3X)}=\frac{X}{4X}=0.25$$

Solution: 25%

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Last edited by johnwesley on 22 Mar 2013, 15:44, edited 1 time in total.
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Re: Company As workforce consists of 10 percent managers and 90 [#permalink]  21 Mar 2013, 18:06
Expert's post
It's trueeeeeeeee

I'm always comfortable with these problems , even the most difficult but at 2.00 AM is not a big deal

0.1 X + 0.3 Y = 0.25 (X + Y )

Now 15 X = 5 Y ---> X / Y = 5/15 = 1/3 $$BUT$$ the ration 1 : 3 is = to 4 (the total) so the parts must be 1/4 and 3/4. We care about of X so 1/4 = 25.

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Re: Company As workforce consists of 10 percent managers and 90 [#permalink]  21 Mar 2013, 18:20
1. Let the total number of worforce of the resulting company be 100.
2. Let us say x number of the workforce originated from A.
3. 10 % of that number is the number of managers contributed by A which is$$x/10$$.
4. (100-x) of the workforce originated from B.
5. 30 % of that number is the number of managers contributed by B which is$$3(100-x)/10$$
6. We have the total number of managers in the resulting company as 25.
7. (3) + (5) =(6) i.e.,$$x/10 + 3(100-x)/10 = 25$$
x=25.

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Re: Company As workforce consists of 10 percent managers and 90 [#permalink]  21 Mar 2013, 20:30
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Expert's post
carcass 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 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%

I'm not fully convinced by OA.

If the two companies are merged and supposed that we have 200 people, then 25 % of 200 is 50. So. 50 people are manager (if I understand correct).

Now the problem asks: what % of this 50 comes from company A................let me know. Thanks

Use weighted avgs here. Company A has 10% managers and company B has 30% managers. Overall, the merged company has 25% managers. So what is the ratio number of employees of company A to number of employees of company B?

number of employees of company A:number of employees of company B = (30 - 25):(25 - 10) = 1:3

What percent of the workforce originated from Company A? 1/4 = 25%
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Re: Company A's workforce consists of 10 percent managers and 90 [#permalink]  04 Feb 2014, 06:43
Alternative approach: Apply differentials

-15A +5B = 0, 15A = 5B, A/B = 1/3
Therefore 1/4 or 25% of the managers came from division A

Hope this helps
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Re: mixtures problem [#permalink]  10 Mar 2014, 23:27
SOURH7WK 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 companyís 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%

[Reveal] Spoiler:
EXPL: The question gives you two equations. First, the percents of the managers, where A and B stand for the total number of employees in each companyís workforce:
1/10 (A) + 3/10 B = 1 /4 (A + B)
Since A and B are fractions (or percents) of the total resulting workforce:
A+B=1
To combine the equations, rewrite the second equation: A=1- B
Then plug in to the first equation

I am not clear that how can A and B be treated as fractions when they represent the number of employees in firms A and B respectively. How is A+B =1?

Let say Company A has x employes and B has y employees. Now they merge and total no of employees = x+y employees.

Per the question 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. We translate it into equation as follows:

.1x + .3y = .25 (x+y)
=> x + 3y =2.5 (x+y)
=> .5y = 1.5x
=> y=3x.
Now we know total employee = x+y. we need to find %age of x in total (x+y) ie x/(x+y) X100%
=> x/(3x+x) [substitute y=3x] => x/4x X 100%
=> .25 X 100 % => 25%.

Hence Answer C. Is it correct?

Did the same way till we get y = 3x

So, $$\frac{y}{x} =\frac{3}{1} = \frac{75}{25}$$

Contribution from x = 25%
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Re: Company A's workforce consists of 10 percent managers and 90 [#permalink]  11 Mar 2014, 00:31
General solution for mixture problems.

In this type of problems S1 consisting of some components and S2 consisting of one or more of the same components are mixed

Steps:

1.Identify the S1 and S2 and their components. For simplicity let us assume S1 and S2 are solutions. They may also be solids such as bars.

2.S1 and S2 are identified as follows:

(i)S1 and S2 are explicitly mentioned as two different solutions.
(ii)S1 is the original solution. S2 is the same type of solution but added to S1. The elements become added in the proportion they are present
(iii)S1 is the original solution and S2 is a different type of solution and may contain only one element ,such as water. This element will be present in S1 also.
(iv)S1 is the original solution and S2 is the same type of solution got from removing some quantity from S1. The elements are removed in the same proportion they are present.
(v)S1 is the original solution and S2 is that which is got by removing only one element from S1.
(vi)S1 and S2 are two solutions and they contain only one element or only one element is mentioned.

3.The general formula is:

re1/re2 = s1 *e1/(e1+e2) + s2* e1/(e1+e2) / s1*e2/(e1+e2) + s2* e2/(e1+e2)

where re1/re2 is the ratio of the elements in the result after s1 and s2 are mixed, s1 and s2 are the quantity of the solutions . The elements in each solution are normally given in ratios.

In this problem,

re1/re2 = 10/100 * s1 + 30/100*s2 / 90/100 *s1 + 70/100 * s2
re1/re2 = 0.1*s1 + 0.3 *s2 / 0.9*s1 + 0.7*s2
25/75= 0.1*s1 + 0.3 *s2 / 0.9*s1 + 0.7*s2
=> s1/s2 = 1/3 or s1/(s1+s2) = 1/4

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Re: Company A's workforce consists of 10 percent managers and 90 [#permalink]  15 Mar 2014, 19:46
Expert's post
easy to make this question a lot harder than it needs to be (see below lol)

Total Employees:
A=100
B=100

Managers:
A (100)(.1) = 10
B (100(.3) = 30

[10(x/100)+30[(100-x)/100]]/[[100(x/100)]+[100[(100-x)/100]]] = 1/4
[(150-x)/5]/100=1/4
150-x=500/4
x=25
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Re: Company A's workforce consists of 10 percent managers and 90   [#permalink] 15 Mar 2014, 19:46
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