GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 13 Nov 2018, 12:23

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### Essential GMAT Time-Management Hacks

November 14, 2018

November 14, 2018

07:00 PM PST

08:00 PM PST

Join the webinar and learn time-management tactics that will guarantee you answer all questions, in all sections, on time. Save your spot today! Nov. 14th at 7 PM PST

# A factory has 500 workers, 15 percent of whom are women. If

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 177
A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

### Show Tags

17 Dec 2012, 06:00
2
8
00:00

Difficulty:

5% (low)

Question Stats:

90% (01:28) correct 10% (01:52) wrong based on 909 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
Math Expert
Joined: 02 Sep 2009
Posts: 50572
Re: A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

### Show Tags

17 Dec 2012, 06:04
2
2
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

Currently the factory has 0.15*500=75 women.

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 110-75=35 more women.

_________________
Senior Manager
Joined: 23 Oct 2010
Posts: 353
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Re: A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

### Show Tags

03 Jul 2013, 09:08
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 (x-20)/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: 353
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Re: A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

### Show Tags

03 Jul 2013, 09:22
1
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: 11-15-2013
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, 19:24
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 12830 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: 30 Oct 2014, 23:34
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 (x-20)/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 30 Oct 2014, 23:26.
Last edited by appleid on 30 Oct 2014, 23:34, edited 1 time in total.
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1827
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, 00:12
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 (x-20)/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% ...............

(20-15)% .............. (x-20)%

$$\frac{x-20}{5} = \frac{500}{50}$$

x = 70%

$$\frac{70}{100} * 50 = 35$$

_________________

Kindly press "+1 Kudos" to appreciate

Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 422
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

### Show Tags

19 Jan 2015, 01:14
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 = 110-75
x = 35 ANS E
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4154
Location: United States (CA)
Re: A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

### Show Tags

09 May 2016, 06:35
1
1
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

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 1247
Location: India
WE: Engineering (Other)
Re: A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

### Show Tags

27 Dec 2017, 20:23
Bunuel, niks18

Quote:
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 110-75=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: 1217
Location: India
GPA: 3.82
Re: A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

### Show Tags

29 Dec 2017, 10:25
1
Bunuel, niks18

Quote:
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 110-75=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?

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
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2181
Re: A factory has 500 workers, 15 percent of whom are women. If  [#permalink]

### Show Tags

31 Dec 2017, 10:45
1
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 $$= 110 - 75 = 35$$

Regards,
Saquib
e-GMAT
Quant Expert
_________________

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

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
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 | Inequalities

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.e-gmat.com

Re: A factory has 500 workers, 15 percent of whom are women. If &nbs [#permalink] 31 Dec 2017, 10:45
Display posts from previous: Sort by