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 Post subject: GMAT Overlapping SetsPosted: Thu Aug 05, 2010 4:50 am

Joined: Sun May 30, 2010 3:15 am
Posts: 424
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

(E) A good strategy when asked to find fractions or percentages of populations of unspecified size is to assume that the whole population is composed of 100 members. This makes it easier to handle. Therefore, suppose that there are 100 employees in the company. If 70% are women, then 30% are men. We then have 70 women and 30 men. If 2/3 of the men are single, then 1/3 of 30 (10 men) are married. 60% of 100 (or 60) employees are married. If 10 are men, then 50 are women. Therefore, the fraction of women who are married is 50/70, or 5/7. The right answer is choice (E).

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 Post subject: Re: math: Venn diagram, percentagesPosted: Thu Aug 05, 2010 5:45 am

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Let us analyze this question using graphics.

We know that there are 70% women and 30% men in a company:

60% of all employees are married (some of them are women and some are men):

There are 30% of the men in a company overall so if 2/3 of the men are single then 20% of employees in a company are single men. Obviously, 10% of employees in a company are married men:

Considering that overall 60% of employees are married we now know that 50% of employees are married women:

Since women are 70% of employees and married women are 50% of employees we can easily find what fraction of the women are married:

50% / 70% = 5/7.

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