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

_________________

Jeffery Miller

Head of GMAT Instruction

GMAT Quant Self-Study Course

500+ lessons 3000+ practice problems 800+ HD solutions