Bunuel wrote:
At a small company, 70 percent of the employees are women, and 60 percent of the employees are married. If 2/3 of the men are single, what fraction of the women are married?
A. 5/16
B. 1/3
C. 9/20
D. 7/10
E. 5/7
We can let the total number of employees = n, thus:
(7/10)n = women, (3/10)n = men, (6/10)n = (3/5)n = married, (4/10)n = (2/5)n = not married
Since 2/3 of the men are not married, (2/3) x (3/10)n = n/5 = not married men, thus:
2n/5 - n/5 = n/5 = not married women
Thus, the number of married women is 7n/10 - n/5 = 7n/10 - 2n/10 = 5n/10 and the fraction of the women are married is (5n/10)/(7n/10) = 5/7.
Alternate Solution:
Let’s assume there are 300 employees at the company. We know that 70% of them, or 0.7 x 300 = 210, are women, which means that there are 300 - 210 = 90 men employed at the company. We are also given that 2/3 of the 90 men, which is 2/3 x 90 = 60, are single. This means that there are 90- 60 = 30 married men.
We are also given that 60% of the employees are married, which is 0.6 x 300 = 180 employees. Subtracting the 30 married men from this total leaves us with 180 - 30 = 150 married women.
Thus, there are 150 married women out of 210 total women, giving us 150/210 = 15/21 = 5/7.
Answer: E
_________________
5-star rated online GMAT quant
self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.