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

Question

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

(A) 3
(B) 10
(C) 25
(D) 30
(E) 35

Bunuel · Accepted Answer

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.

Answer: E.

LalaB · Answer

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

LalaB · Answer

Or

(75+x)/550=20%
X =35

imperfectdark · Answer

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.

appleid · Answer

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

* Then how can I come to the highlighted equation. Am I missing anything?

PareshGmat · Answer

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

Answer = E

pacifist85 · Answer

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

ScottTargetTestPrep · Answer

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.

adkikani · Answer

Bunuel ,  niks18

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?

niks18 · Answer

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

EgmatQuantExpert · Answer

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
e-GMAT
Quant Expert

BrentGMATPrepNow · Answer

A factory has 500 workers, 15 percent of whom are women  
15% of 500 =  75 
So, there are presently  75  women at the factory

Once the  additional  50 workers are hired, there will be  550  workers. 
We want 20% of those  550  workers to be women.
20% of 550 = 110, so we need there to be  110  women altogether.

So, we need to increase the number of female workers from  75  to  110 . 
 110  -  75  = 35

So, 35 of the additional workers must be women.

Answer: E

Cheers,
Brent

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