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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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35% (medium)

Question Stats:

69% (02:46) correct 30% (01:44) wrong based on 116 sessions
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: Company A's workforce consists of 10 percent managers and 90 [#permalink]  09 Sep 2012, 03:26
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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%

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]  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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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Senior Manager Joined: 15 Jun 2010 Posts: 363 Schools: IE'14, ISB'14, Kellogg'15 WE 1: 7 Yrs in Automobile (Commercial Vehicle industry) Followers: 5 Kudos [?]: 106 [1] , given: 50 Re: mixtures problem [#permalink] 09 Sep 2012, 01:53 1 This post received KUDOS adineo 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? _________________ Regards SD ----------------------------- Press Kudos if you like my post. Debrief 610-540-580-710(Long Journey): from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html Manager Joined: 24 Jul 2011 Posts: 77 Location: India Concentration: Strategy, General Management GMAT 1: 670 Q49 V33 WE: Asset Management (Manufacturing) Followers: 2 Kudos [?]: 46 [1] , given: 5 Re: Company A's workforce consists of 10 percent managers and 90 [#permalink] 09 Sep 2012, 04:04 1 This post received KUDOS adineo 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% 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% So, the answer is C _________________ My mantra for cracking GMAT: Everyone has inborn talent, however those who complement it with hard work we call them 'talented'. +1 Kudos = Thank You Dear Are you saying thank you? Manager Joined: 24 Jan 2013 Posts: 82 Followers: 3 Kudos [?]: 51 [1] , given: 6 Re: Company As workforce consists of 10 percent managers and 90 [#permalink] 21 Mar 2013, 17:34 1 This post received KUDOS 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% Answer: C Attachments Imagen1.jpg [ 10.41 KiB | Viewed 1382 times ] _________________ Does this post deserve KUDOS? Free Prep: Self-prepare GMAT for free and GMAT Math tips for free Free Flashcards: Free GMAT Flashcards More: "All I wish someone had told me about GMAT beforehand" There are many things you want to know before doing the GMAT exam (how is exam day, what to expect, how to think, to do's...), and you have them in this blog, in a simple way Last edited by johnwesley on 22 Mar 2013, 15:44, edited 1 time in total. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4032 Location: Pune, India Followers: 859 Kudos [?]: 3615 [1] , given: 144 Re: Company As workforce consists of 10 percent managers and 90 [#permalink] 21 Mar 2013, 20:30 1 This post received KUDOS 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% _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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Manager
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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, 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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Company As workforce consists of 10 percent managers and 90 [#permalink]  21 Mar 2013, 16:46
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 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
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KUDOS is the good manner to help the entire community.

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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 isx/10.
4. (100-x) of the workforce originated from B.
5. 30 % of that number is the number of managers contributed by B which is3(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]  22 Mar 2013, 01:46
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

Merging similar topics. Please refer to the solutions above.
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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
Cheers
J
Re: Company A's workforce consists of 10 percent managers and 90   [#permalink] 04 Feb 2014, 06:43
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