If 3/4 of the number of women working at Company X is equal to 2/3 of

Question

If 3/4 of the number of women working at Company X is equal to 2/3 of the number of men, what fraction of the employees at Company X are women?

A) 5/12
B) 8/17
C) 1/2
D) 7/12
E) 8/9

acegmat123 · Accepted Answer

3w/4 = 2m/3

w/m = 8/9

w:m:T = 8:9:17

w/T = 8/17

B

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BrentGMATPrepNow · Answer

APPROACH #1  : Two variables
Let w = # of women
Let m = # of men

3/4 of the number of women working at Company X is equal to 2/3 of the number of men  
We can write: (3/4)w = (2/3)m
Rewrite as: 3w/4 = 2m/3
Cross multiply to get: 9w = 8m
Divide both sides of the equation by m to get: 9w/m = 8
Divide both sides of the equation by 9 to get: w/m = 8/9
This tells us that  the ratio of women to men is 8 to 9 .
In other words, for every 17 employees, 8 are women and 9 are men. 
In other words, 8/17 of the employees are women.

Answer: B

APPROACH #2  : One variable

Notice that the question does not ask us for the NUMBER of women; it asks us to determine the PROPORTION of women in the workforce. 
In these instances, we can assign a certain value to the number of women, and then see what this implies about the number of men and then go from there.

Let say there are  12  women     
 
  3/4 of the number of women working at Company X is equal to 2/3 of the number of men  
Let M = # of men
We can write: (3/4)( 12 ) = (2/3)(M)
Simplify: 9 = (2/3)(M)
Multiply both sides by 3/2 to get: (3/2)(9) = M
Evaluate:  27/2 = M 
Aside: Okay, so we get a fractional value for the number of men. No problem since we're supposed to answer the question....

What  fraction  of the employees at Company X are women?  
Total number of employees =  12  +  27/2  = 24/2 + 27/2 =   51/2  
So, the fraction of all employees who are women =  12 /(  51/2  )
= 24/51    
= 8/17    
Answer: B

Abhishek009 · Answer

\frac{3m}{4} = \frac{2w}{3} = 12

Or,  \frac{m}{4} = 4  and  \frac{w}{3} = 6

So,  m = 16  and  w = 18

Men : Women = 8 : 9

So, Fraction of Women in the firm is  \frac{8}{17}

Hence, answer will be (B)  \frac{8}{17}

lalania1 · Answer

thanks. The answer is B. The reason I uploaded this question is to find out whether smart numbers or algebraic approach get you the right answer faster. For me, I choose the algebraic approach for this type of question.

gopigmat · Answer

If 3/4 of the number of women working at Company X is equal to 2/3 of the number of men, what fraction of the employees at Company X are women?

A) 5/12
B) 8/17
C) 1/2
D) 7/12
E) 8/9

I approached it like this:

If W = total number of women employed in the Company X, and
if M = total number of men employed in the Company X, we are given

(3/4)W = (2/3)M
(or) in other words, 9W = 8M
(or) in other words, M = (9/8)W

Proportion of Women in the Total Employees of Company X = W / (W+M)

Substituting for M, we get

Proportion of Women = W / (W+9W/8) = W / (17W/8) =  8/17

Answer: B

generis · Answer

\frac{3}{4} W =  \frac{2}{3} M

W =  \frac{4}{3} * \frac{2}{3} M

W =  \frac{8}{9} M

\frac{W}{M}  =  \frac{8}{9} , so W = 8, M = 9

What fraction of the employees are women?

\frac{W}{W + M}  =  \frac{8}{17}

Answer B

ScottTargetTestPrep · Answer

We can let m = the number of men and w = the number of women. We need to determine the value of w/(w + m). We are given that:

(3/4)w = (2/3)m

w = (2/3)m x (4/3)

w = 8m/9

9w = 8m

We need to determine w/(w + m). Let’s multiply the numerator and the denominator by 8:

w/(w + m) = 8w/(8w + 8m) = 8w/(8w + 9w) = 8w/17w = 8/17

Answer: B

mimajit · Answer

This is how i solved

Assume the no of women to be 40
3/4 women = 3/4* 40 = 2/3* total men
3/4* 40 = 30 women 
therfore 2/3* Total men = 30
Total men = 45
Total staff = 40+45
Fraction of women / staff
40/85 = 8/17 = B

Pritishd · Answer

What is to be found? - women/(men+women)  
Given 3/4(women) = 2/3(men). Solving for the numerator of 1, we get women = 8/9(men)  
Solving for the denominator of 1, we get 8/9(men)+men = 17/9(men)

Combining the results of 2 and 3, we get:
8/9(men) / 17/9(men) = 8/17 (Option B)

PS. We can also assume men as M and women as W for simplicity.

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