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Joined: 16 May 2014
Posts: 592
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GRE 1: Q165 V161
GRE Math Challenge #5-number of women working at Company X
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Updated on: 29 Nov 2017, 12:26
Updated on: 29 Nov 2017, 12:26
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If \(\frac{3}{4}\) of the number of women working at Company X is equal to \(\frac{2}{3}\) of the number of men, what fraction of the employees at Company X are women?
A) \(\frac{5}{12}\)
B) \(\frac{8}{17}\)
C) \(\frac{1}{2}\)
D) \(\frac{7}{12}\)
E) \(\frac{8}{9}\)
A) \(\frac{5}{12}\)
B) \(\frac{8}{17}\)
C) \(\frac{1}{2}\)
D) \(\frac{7}{12}\)
E) \(\frac{8}{9}\)
Originally posted by soumya1989 on 02 Sep 2014, 03:21.
Last edited by Carcass on 29 Nov 2017, 12:26, edited 1 time in total.
Last edited by Carcass on 29 Nov 2017, 12:26, edited 1 time in total.
Edited by Carcass
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Re: GRE Math Challenge #5-number of women working at Company X
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10 Apr 2020, 15:58
10 Apr 2020, 15:58
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]
Answer:
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]
Answer:
Show: ::
B
Re: GRE Math Challenge #5-number of women working at Company X
[#permalink]
10 Apr 2020, 15:58
10 Apr 2020, 15:58
Expert Reply
Great explanation Sir
