Sep 22 08:00 PM PDT  09:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE Sep 23 08:00 AM PDT  09:00 AM PDT Join a free 1hour webinar and learn how to create the ultimate study plan, and be accepted to the upcoming Round 2 deadlines. Save your spot today! Monday, September 23rd at 8 AM PST Sep 28 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn two proprietary ways to PreThink assumptions and ace GMAT CR in 10 days.
Author 
Message 
TAGS:

Hide Tags

Manager
Status: faciendo quod indiget fieri
Joined: 13 Mar 2012
Posts: 70

Company A's workforce consists of 10 percent managers and 90
[#permalink]
Show Tags
Updated on: 09 Sep 2012, 04:27
Question Stats:
72% (02:17) correct 28% (02:28) wrong based on 287 sessions
HideShow timer Statistics
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% 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?
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by adineo on 09 Sep 2012, 02:25.
Last edited by Bunuel on 09 Sep 2012, 04:27, edited 3 times in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 58133

Re: Company A's workforce consists of 10 percent managers and 90
[#permalink]
Show Tags
09 Sep 2012, 04:26
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 \(0.1a+0.3b=0.25(a+b)\) > \(b=3a\) > \(\frac{a}{a+b}=\frac{1}{4}=0.25\). Answer: C. Hope it's clear. P.S. Please read and follow: rulesforpostingpleasereadthisbeforeposting133935.html (rule #3)
_________________




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9645
Location: Pune, India

Re: Company A's workforce consists of 10 percent managers and 90
[#permalink]
Show Tags
10 Sep 2012, 03:35
adineo wrote: 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/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Senior Manager
Joined: 15 Jun 2010
Posts: 280
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)

Re: mixtures problem
[#permalink]
Show Tags
09 Sep 2012, 02:53
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% 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 610540580710(Long Journey): http://gmatclub.com/forum/from600540580710finallyachievedin4thattempt142456.html



Manager
Joined: 24 Jul 2011
Posts: 63
Location: India
Concentration: Strategy, General Management
WE: Asset Management (Manufacturing)

Re: Company A's workforce consists of 10 percent managers and 90
[#permalink]
Show Tags
09 Sep 2012, 05:04
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 MESS C1 10 %90%0% C230%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 1030 25 5 (=3025)15 (=2515) [Calculate difference diagonally; also this is the ratio of two companies] 13 (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: 66

Re: Company As workforce consists of 10 percent managers and 90
[#permalink]
Show Tags
Updated on: 22 Mar 2013, 16:44
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 9853 times ]
Originally posted by johnwesley on 21 Mar 2013, 18:34.
Last edited by johnwesley on 22 Mar 2013, 16:44, edited 1 time in total.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9645
Location: Pune, India

Re: Company As workforce consists of 10 percent managers and 90
[#permalink]
Show Tags
21 Mar 2013, 21:30
carcass wrote: Company As workforce consists of 10 percent managers and 90 percent software engineers. Company Bs 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 companys 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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2818

Re: Company A's workforce consists of 10 percent managers and 90
[#permalink]
Show Tags
29 Mar 2017, 10:07
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% We can let the number of people from Company A = A and the number of people from Company B = B. Thus, 0.1A = the number of managers from Company A and 0.3B = the number of managers from Company B. When the two companies merged, because the workforce was 25% managers, we can create the following equation and determine the relationship between A and B: 0.1A + 0.3B = 0.25(A + B) 10A + 30B = 25A + 25B 5B = 15A B = 3A The percentage of the workforce from A is: A/(A + B) = A/(A + 3A) = A/4A = 1/4 = 25%. Answer: C
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Intern
Joined: 13 Mar 2019
Posts: 27

Re: Company A's workforce consists of 10 percent managers and 90
[#permalink]
Show Tags
10 Aug 2019, 10:30
Assume the weightage ratio given to Company B Workforce is x.So the weightage ratio of Company A will be 1x. Now (1x)10% + x* 30% = 25 % 1010x+30x = 25 20x = 15 x =15/20 x= 3/4
So Company A weightage ratio will be 1/4 And hence the contribution will be 25%.



Manager
Status: faciendo quod indiget fieri
Joined: 13 Mar 2012
Posts: 70

Re: Company A's workforce consists of 10 percent managers and 90
[#permalink]
Show Tags
09 Sep 2012, 08:05
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?



Manager
Joined: 28 Feb 2012
Posts: 104
Concentration: Strategy, International Business
GPA: 3.9
WE: Marketing (Other)

Re: Company A's workforce consists of 10 percent managers and 90
[#permalink]
Show Tags
10 Sep 2012, 21:28
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 \(0.1a+0.3b=0.25(a+b)\) > \(b=3a\) > \(\frac{a}{a+b}=\frac{1}{4}=0.25\). Answer: C. Hope it's clear. P.S. Please read and follow: rulesforpostingpleasereadthisbeforeposting133935.html (rule #3) 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?
_________________
If you found my post useful and/or interesting  you are welcome to give kudos!



Math Expert
Joined: 02 Sep 2009
Posts: 58133

Re: Company A's workforce consists of 10 percent managers and 90
[#permalink]
Show Tags
11 Sep 2012, 02:43
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 \(0.1a+0.3b=0.25(a+b)\) > \(b=3a\) > \(\frac{a}{a+b}=\frac{1}{4}=0.25\). Answer: C. Hope it's clear. P.S. Please read and follow: rulesforpostingpleasereadthisbeforeposting133935.html (rule #3) 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.
_________________



Board of Directors
Joined: 01 Sep 2010
Posts: 3402

Re: Company As workforce consists of 10 percent managers and 90
[#permalink]
Show Tags
21 Mar 2013, 19:06
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.
_________________



Director
Joined: 17 Dec 2012
Posts: 628
Location: India

Re: Company As workforce consists of 10 percent managers and 90
[#permalink]
Show Tags
21 Mar 2013, 19:20
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. (100x) of the workforce originated from B. 5. 30 % of that number is the number of managers contributed by B which is\(3(100x)/10\) 6. We have the total number of managers in the resulting company as 25. 7. (3) + (5) =(6) i.e.,\(x/10 + 3(100x)/10 = 25\) x=25. Answer is choice C.
_________________
Srinivasan Vaidyaraman Sravna Test Prep http://www.sravnatestprep.comHolistic and Systematic Approach



SVP
Joined: 06 Sep 2013
Posts: 1598
Concentration: Finance

Re: Company A's workforce consists of 10 percent managers and 90
[#permalink]
Show Tags
04 Feb 2014, 07:43
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



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1768
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: mixtures problem
[#permalink]
Show Tags
11 Mar 2014, 00:27
SOURH7WK wrote: 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% 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%
_________________
Kindly press "+1 Kudos" to appreciate



Director
Joined: 17 Dec 2012
Posts: 628
Location: India

Re: Company A's workforce consists of 10 percent managers and 90
[#permalink]
Show Tags
11 Mar 2014, 01:31
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 The answer is therefore 25%
_________________
Srinivasan Vaidyaraman Sravna Test Prep http://www.sravnatestprep.comHolistic and Systematic Approach



Retired Moderator
Joined: 20 Dec 2013
Posts: 169
Location: United States (NY)
GMAT 1: 640 Q44 V34 GMAT 2: 710 Q48 V40 GMAT 3: 720 Q49 V40
GPA: 3.16
WE: Consulting (Venture Capital)

Re: Company A's workforce consists of 10 percent managers and 90
[#permalink]
Show Tags
15 Mar 2014, 20:46
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[(100x)/100]]/[[100(x/100)]+[100[(100x)/100]]] = 1/4 [(150x)/5]/100=1/4 150x=500/4 x=25
_________________



Director
Joined: 23 Jan 2013
Posts: 529

Re: Company A's workforce consists of 10 percent managers and 90
[#permalink]
Show Tags
03 Aug 2015, 03:54
10%25%30%
if ratio of A/B was equal than A portion would be 50% and managers would be 20%. But result is shifted to B, so we can eliminate D and E. The true ratio is 1/3, so A=25%
C




Re: Company A's workforce consists of 10 percent managers and 90
[#permalink]
03 Aug 2015, 03:54






