At a small company, 70 percent of the employees are women, and 60 perc

Question

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

Kudos for a correct  solution .

GMATinsight · Accepted Answer

Make a Double Matrix and Solve as mentioned below

Answer: Option E

balamoon · Answer

Solution -

Lets take total employees are 100.

Given that,  Total Women  = 70 and Total Married = 60.

Total Men = 100 - 70 = 30 and Single men = 2/3*30 = 20.

Married men = total men - single men = 30 - 20 = 10.
 Married women  = Total married - Married men = 60 - 10 = 50.

Fraction of women are married = Married women / Total Women = 50 / 70 = 5/7. ANS E

xLUCAJx · Answer

I got the right answer but only by partially guessing since the only answer I recognized after the matrix was 5/7.

But the question stem had me confused because I was thinking Married Women/total employees. Am I reading something wrong?

ENGRTOMBA2018 · Answer

Yes, the question asks you to provide a ratio of married women / total women (=5/7) and not married women/ total employees (this will incorrectly give you 1/2). The question stem asks about "what fraction  of the women  are married?". It does not say "what fraction of total employees are the women married?" (or a similar language).

KS15 · Answer

Let no of employees=100
No of women=70
No of men=30
Married employees=60
2/3 of men i.e 20 are single
Married men=10
Married women=60-10=50
Single women=20
Single men=10
Reqd fraction=50/70=5/7
Answer E

Bunuel · Answer

800score Official Solution:

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).

JeffTargetTestPrep · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

At a small company, 70 percent of the employees are women, and 60 perc

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

At a small company, 70 percent of the employees are women, and 60 perc

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards