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vaibhav101: Master | Next Rank: 500 Posts; Posts: 138; Joined: Mon May 01, 2017 11:56 pm; Thanked: 4 times

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by vaibhav101 » Sun Jun 03, 2018 9:51 am

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3 men, 4 women and 6 children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days?

A 7
B 8
C 12
D 15
E none of these

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Source: Beat The GMAT — Problem Solving | Sun Jun 03, 2018 9:51 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

by Vincen » Mon Jun 11, 2018 12:59 am

Hello.

We know that the job can be completed in 7 days when there are working

- 3 M (men)
- 4 W (women)
- 6 C (children)

Also, we know that "a woman does double the work a man does", hence $$W=2M\ \ \ \Rightarrow\ \ \ \ M=\frac{W}{2}$$ and "a child does half the work a man does", hence $$C=\frac{M}{2}\ \ \ \Rightarrow\ \ \ \ C=\frac{\frac{W}{2}}{2}=\frac{W}{4}.$$ Then, the job can be completed in 7 days when there are working

- 3M =(3/2)W.
- 4W
- 6C= (6/4)W=(3/2)W

If we sum these quantities we will get that there are needed 7 women to complete the job in 7 days.

Therefore, the correct answer is the option A.

I hope it is clear enough.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Mon Jun 11, 2018 2:16 am

vaibhav101 wrote:3 men, 4 women and 6 children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days?

A 7
B 8
C 12
D 15
E none of these

Let the rate for each child = 1 unit per day.
Since each child does half the work of a man, the rate for each man = 2 units per day.
Since each woman does double the work of a man, the rate for each woman = 4 units per day.

Combined rate for 3 men, 4 women and 6 children = (3*2) + (4*4) + (6*1) = 28 units per day.
Over 7 days, the amount of work produced by 3 men, 4 women and 6 children = rt = 7*28 units.

To complete the job in 7 days, the required rate = w/t = (7*28)/7 = 28 units per day.
Since each woman produces 4 units per day, the number of women required to produce 28 units per day = 28/4 = 7.

The correct answer is A.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Mon Jun 11, 2018 4:38 am

vaibhav101 wrote:3 men, 4 women and 6 children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days?

A 7
B 8
C 12
D 15
E none of these

Starting point: 3 men, 4 women and 6 children

A child does half the work a man does.
In other words, 1 child = 1/2 a man
This means 6 children = 3 men
So, let's just REPLACE the 6 children with 3 men to get: 6 men and 4 women

A woman does double the work a man does
In other words, 1 man = 1/2 a woman
This means 6 men = 3 women
So, let's just REPLACE the 6 men with 3 women to get: 7 women

Answer: A

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Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Wed Jun 13, 2018 3:37 pm

vaibhav101 wrote:3 men, 4 women and 6 children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days?

A 7
B 8
C 12
D 15
E none of these

We can let the rate of a man = m, the rate of a woman = 2m, and the rate of a child = (1/2)m, thus:

3m + 4(2m) + 6[(1/2)m] = 1/7

3m + 8m + 3m = 1/7

14m = 1/7

m = 1/98

So the rate of a woman = 2/98 = 1/49 of the job per day.

Thus, in 7 days, a woman can complete 7 x 1/49 = 1/7 of the job. So if there are 7 women, they can complete 7 x 1/7 = 1 entire job.

Alternate Solution:

Since a child does half the work a man does, the work done by 3 men, 4 women and 6 children is equivalent to the work done by 3 + 6/2 = 6 men and 4 women. Since a woman does twice the work a man does, the work done by 6 men and 4 women is equivalent to the work done by 6/2 + 4 = 7 women. So, 7 women can complete the job in 7 days.

Answer: A

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