Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178

A factory has 500 workers, 15 percent of whom are women. If
[#permalink]
Show Tags
17 Dec 2012, 07:00
Question Stats:
86% (01:08) correct 14% (01:03) wrong based on 882 sessions
HideShow timer Statistics
A factory has 500 workers, 15 percent of whom are women. If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent? (A) 3 (B) 10 (C) 25 (D) 30 (E) 35
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 47920

Re: A factory has 500 workers, 15 percent of whom are women. If
[#permalink]
Show Tags
17 Dec 2012, 07:04



Senior Manager
Joined: 23 Oct 2010
Posts: 362
Location: Azerbaijan
Concentration: Finance

Re: A factory has 500 workers, 15 percent of whom are women. If
[#permalink]
Show Tags
03 Jul 2013, 10:08
We also can use mixture method Say we add to 15% females of 550 ppl x % females of 50 ppl to get 20% females So we have (x20)/5=500/50 X=70% 70%of 50=35
_________________
Happy are those who dream dreams and are ready to pay the price to make them come true
I am still on all gmat forums. msg me if you want to ask me smth



Senior Manager
Joined: 23 Oct 2010
Posts: 362
Location: Azerbaijan
Concentration: Finance

Re: A factory has 500 workers, 15 percent of whom are women. If
[#permalink]
Show Tags
03 Jul 2013, 10:22
Or (75+x)/550=20% X =35
_________________
Happy are those who dream dreams and are ready to pay the price to make them come true
I am still on all gmat forums. msg me if you want to ask me smth



Intern
Joined: 06 Jan 2013
Posts: 11
Location: United States
Concentration: Finance, Economics
GMAT Date: 11152013
GPA: 3.5
WE: Education (Education)

Re: A factory has 500 workers, 15 percent of whom are women. If
[#permalink]
Show Tags
22 Aug 2014, 20:24
I also solved this as a mixture problem (see image attached) where w denotes the number of new women hired. Once I had the table set up I solved (75+w) / 550 = 0.20 => 75+w = 110 => w=35. Therefore, 35 of the 50 workers hired need to be women.
Attachments
Mixture.png [ 2.83 KiB  Viewed 11958 times ]



Intern
Joined: 22 Oct 2014
Posts: 27

A factory has 500 workers, 15 percent of whom are women. If
[#permalink]
Show Tags
Updated on: 31 Oct 2014, 00:34
LalaB wrote: We also can use mixture method
Say we add to 15% females of 550 ppl x % females of 50 ppl to get 20% females So we have (x20)/5=500/50 X=70% 70%of 50=35 Hello, could anyone please explain how we came into that equation from the first line? I am clear up to this: 15% of 500 + x% of 50 = 20% of 550 [correction: 15% of 500, not 550] * Then how can I come to the highlighted equation. Am I missing anything?
Originally posted by appleid on 31 Oct 2014, 00:26.
Last edited by appleid on 31 Oct 2014, 00:34, edited 1 time in total.



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1835
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: A factory has 500 workers, 15 percent of whom are women. If
[#permalink]
Show Tags
04 Nov 2014, 01:12
appleid wrote: LalaB wrote: We also can use mixture method
Say we add to 15% females of 550 ppl x % females of 50 ppl to get 20% females So we have (x20)/5=500/50 X=70% 70%of 50=35 Hello, could anyone please explain how we came into that equation from the first line? I am clear up to this: 15% of 500 + x% of 50 = 20% of 550 [correction: 15% of 500, not 550] * Then how can I come to the highlighted equation. Am I missing anything? Its called allegation method: 15% .................. x% ............. 20% ............... ( 2015)% .............. (x 20)% \(\frac{x20}{5} = \frac{500}{50}\) x = 70% \(\frac{70}{100} * 50 = 35\) Answer = E
_________________
Kindly press "+1 Kudos" to appreciate



Senior Manager
Status: Math is psychological
Joined: 07 Apr 2014
Posts: 421
Location: Netherlands
GMAT Date: 02112015
WE: Psychology and Counseling (Other)

Re: A factory has 500 workers, 15 percent of whom are women. If
[#permalink]
Show Tags
19 Jan 2015, 02:14
Or, setting up an equation:
First, find how many women we have: 500*0.15 = 75 women now. We need the number of women to be 20% of the total number of employees.
We will have 50 new employees, making the total # 500+50=550. We need to know how many of the additional workers need to be women in order for the women to be 0.20(550).
In other words: 75+x=0.20(550). This means how many women should we add to the 75 we already have so that the total # of women is 20% of the total # of workers (550).
Solving the equation we get: 75 + x = 0.20(550) 75 + x = 110 x = 11075 x = 35 ANS E



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3161
Location: United States (CA)

Re: A factory has 500 workers, 15 percent of whom are women. If
[#permalink]
Show Tags
09 May 2016, 07:35
Walkabout wrote: A factory has 500 workers, 15 percent of whom are women. If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent?
(A) 3 (B) 10 (C) 25 (D) 30 (E) 35 To solve this problem we first need to determine the number of women. We know that there are 500 people and 15% of them are women. Thus we know: 500 x 0.15 = 75 women We are asked, if 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent? To translate this idea to a mathematical statement we have: (Number of woman after hire)/(total workers after hire) = 20% To solve this statement, we can set up the actual equation with the numbers given in the question stem, and we let w be the number of additional women hired: (75 +w)/(500 + 50) = 20% (75 +w)/550 = 0.2 75 + w = 550 x 0.2 75 + w = 110 w = 35 Answer E.
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 1166
Location: India
WE: Engineering (Other)

Re: A factory has 500 workers, 15 percent of whom are women. If
[#permalink]
Show Tags
27 Dec 2017, 21:23
Bunuel, niks18Quote: After 50 additional workers are hired, there will be total of 550 workers and we need 0.2*550=110 of them to be women, so we need 11075=35 more women. I miscalculated 20% of female workers as 1.2x of 75 since in Q we are given: If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent If earlier no of female workers is 75 then do we not need to perform 1.2*75?
_________________
It's the journey that brings us happiness not the destination.



PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1201
Location: India
GPA: 3.82

Re: A factory has 500 workers, 15 percent of whom are women. If
[#permalink]
Show Tags
29 Dec 2017, 11:25
adkikani wrote: Bunuel, niks18Quote: After 50 additional workers are hired, there will be total of 550 workers and we need 0.2*550=110 of them to be women, so we need 11075=35 more women. I miscalculated 20% of female workers as 1.2x of 75 since in Q we are given: If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent If earlier no of female workers is 75 then do we not need to perform 1.2*75? Hi adkikani, Why are you increasing 75 by 20%? If you read the language of the question carefully it implies that in the new population the composition of women increased to 20%. the question does not say that women population increased by 20% of the original women population after addition of 50 people. in % problems read carefully what is being increased/decreased



eGMAT Representative
Joined: 04 Jan 2015
Posts: 1891

Re: A factory has 500 workers, 15 percent of whom are women. If
[#permalink]
Show Tags
31 Dec 2017, 11:45
Walkabout wrote: A factory has 500 workers, 15 percent of whom are women. If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent?
(A) 3 (B) 10 (C) 25 (D) 30 (E) 35 Current Ratio of Men: Women \(85: 15 = 17: 3\) Thus, Initial number of Women \(= \frac{3}{(17+3)} * 500 = 75\) Required Ratio of Men: Women \(80: 20 = 4: 1\) Thus, final number of Women \(= \frac{1}{(4+1)} * (500+50) = 110\) Therefore, additional women required \(= 110  75 = 35\) Correct answer is Option E. Regards, Saquib eGMATQuant Expert
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com




Re: A factory has 500 workers, 15 percent of whom are women. If &nbs
[#permalink]
31 Dec 2017, 11:45






