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Manager  Joined: 17 Nov 2013
Posts: 81
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Difficulty:   35% (medium)

Question Stats: 73% (01:51) correct 27% (01:45) wrong based on 289 sessions

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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
Manager  B
Joined: 28 Jun 2016
Posts: 216
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Re: If 3/4 of the number of women working at Company X is equal to 2/3 of  [#permalink]

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lalania1 wrote:
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

3w/4 = 2m/3

w/m = 8/9

w:m:T = 8:9:17

w/T = 8/17

B

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Re: If 3/4 of the number of women working at Company X is equal to 2/3 of  [#permalink]

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lalania1 wrote:
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

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

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) $$\frac{8}{17}$$
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Re: If 3/4 of the number of women working at Company X is equal to 2/3 of  [#permalink]

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lalania1 wrote:
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

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 [12 is a nice value since it works with many of the values in the two given fractions]

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 [multiplied top and bottom by 2]
= 8/17 [divided top and bottom by 3]

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Manager  Joined: 17 Nov 2013
Posts: 81
Re: If 3/4 of the number of women working at Company X is equal to 2/3 of  [#permalink]

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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.
Intern  Joined: 02 Jul 2017
Posts: 2
Re: If 3/4 of the number of women working at Company X is equal to 2/3 of  [#permalink]

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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

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Joined: 22 May 2016
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If 3/4 of the number of women working at Company X is equal to 2/3 of  [#permalink]

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lalania1 wrote:
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

$$\frac{3}{4}$$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?

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

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Re: If 3/4 of the number of women working at Company X is equal to 2/3 of  [#permalink]

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lalania1 wrote:
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

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

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Intern  B
Joined: 03 Aug 2017
Posts: 30
Re: If 3/4 of the number of women working at Company X is equal to 2/3 of  [#permalink]

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lalania1 wrote:
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

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
Manager  B
Joined: 18 Jul 2015
Posts: 50
GMAT 1: 530 Q43 V20 WE: Analyst (Consumer Products)
Re: If 3/4 of the number of women working at Company X is equal to 2/3 of  [#permalink]

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

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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Press +1 if my explanation helps. Thanks! Re: If 3/4 of the number of women working at Company X is equal to 2/3 of   [#permalink] 28 Jan 2019, 01:34
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