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

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
At a small company, 70 percent of the employees are women, and 60 perc  [#permalink]

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09 Jul 2015, 04:04
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5% (low)

Question Stats:

93% (01:51) correct 7% (02:55) wrong based on 146 sessions

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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

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Re: At a small company, 70 percent of the employees are women, and 60 perc  [#permalink]

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09 Jul 2015, 04:55
3
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

Kudos for a correct solution.

Make a Double Matrix and Solve as mentioned below

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Re: At a small company, 70 percent of the employees are women, and 60 perc  [#permalink]

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09 Jul 2015, 05:57
2
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

Kudos for a correct solution.

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
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Re: At a small company, 70 percent of the employees are women, and 60 perc  [#permalink]

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09 Jul 2015, 18:58
1
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?
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At a small company, 70 percent of the employees are women, and 60 perc  [#permalink]

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09 Jul 2015, 19:02
1
xLUCAJx wrote:
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?

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).
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Re: At a small company, 70 percent of the employees are women, and 60 perc  [#permalink]

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11 Jul 2015, 11:12
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

Kudos for a correct solution.

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
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Posts: 58427
Re: At a small company, 70 percent of the employees are women, and 60 perc  [#permalink]

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13 Jul 2015, 02:58
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

Kudos for a correct solution.

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).
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Re: At a small company, 70 percent of the employees are women, and 60 perc  [#permalink]

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26 Feb 2018, 11:18
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.

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Re: At a small company, 70 percent of the employees are women, and 60 perc   [#permalink] 26 Feb 2018, 11:18
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