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 percents 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 correct answer is E. ---------- I believe the right answer should be 4/7 and not 5/7. Am I right or not? thank you
I believe the right answer should be 4/7 and not 5/7. Am I right or not? thank you
Plug in each answer to check if it is correct.
4/7 of women are married Let's pick the number of married women as 40. Then there are 70 women overall. Women make 70% of the employees, so there are 100 employees overall. Men make 30% of the employees, so there are 30 men overall. 2/3 of the men are single, so there are 20 single men and 10 married men. It looks like everything is fine, but let's check the percentage of employees that are married. There are 40 women and 10 men married, which results in 50. 50 makes 50% of the employees (100). This contradicts the original question statement ("… and 60 percent of the employees are married. …"), so 4/7 does NOT fit and therefore it is NOT a solution.
5/7 of women are married Take a look at the table, where the numbers perfectly comply with the question statement. Think of the numbers as percentages to see that this works fine for any number of employees (which do not yield fractional numbers of pers.).
Numbers given or implied by the question statement are written in black.
To practice: Make such table on your own and fill in the empty cells starting with the information in the question statement.
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