It take 6 days for 3 women and 2 men working together...

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

It take 6 days for 3 women and 2 men working together...

by swerve » Fri Feb 02, 2018 6:05 am

It take 6 days for 3 women and 2 men working together to complete a work. 3 men would do the same work 5 days sooner than 9 women. How many times does the output of a man exceed that of a woman?

A. 3 times
B. 4 times
C. 5 times
D. 6 times
E. 7 times

The OA is D.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

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Source: Beat The GMAT — Problem Solving | Fri Feb 02, 2018 6:05 am

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 » Fri Feb 02, 2018 8:13 am

swerve wrote:It take 6 days for 3 women and 2 men working together to complete a work. 3 men would do the same work 5 days sooner than 9 women. How many times does the output of a man exceed that of a woman?

A. 3 times
B. 4 times
C. 5 times
D. 6 times
E. 7 times

We can PLUG IN THE ANSWERS.
When the correct answer is plugged in, 3 men will take 5 fewer days than 9 women to complete the job.
Since the time for 3 men is much less than the time for 9 women, the men must work MUCH FASTER than the women.
Thus, the correct answer is probably D or E.

D: 6 times
Let the rate for each woman = 1 widget per day, implying that the rate for each man = 6*1 = 6 widgets per day.
In 6 days, the amount of work produced by 3 women and 2 men = (combined rate for 3 women and 2 men)(number of days) = (3*1 + 2*6)(6) = 90 widgets.
Time for 9 women to produce 90 widgets = (work)/(rate for 9 women) = 90/(9*1) = 10 days.
Time for 3 men to produce 90 widgets = (work)/(rate for 3 men) = 90/(3*6) = 5 days.
Success!
The time for 3 men is 5 days less than the time for 9 women.

The correct answer is D.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Jul 12, 2019 5:56 pm

swerve wrote:It take 6 days for 3 women and 2 men working together to complete a work. 3 men would do the same work 5 days sooner than 9 women. How many times does the output of a man exceed that of a woman?

A. 3 times
B. 4 times
C. 5 times
D. 6 times
E. 7 times

We can let m = the number of days a man can complete the work by himself and w = the number of days a woman can complete the work by herself. Thus, 1/m = the rate of a man, and 1/w = the rate of a woman.

We can create the equations

6(3 x 1/w + 2 x 1/m) = 1

and

1/(3 x 1/m) = 1/(9 x 1/w) - 5

Simplifying the first equation, we have:

3/w + 2/m = 1/6

Multiplying the equation by 6wm, we have:

18m + 12w = mw

Simplifying the second equation, we have:

m/3 = w/9 - 5

Multiplying the equation by 9, we have:

3m = w - 45

3m + 45 = w

Substituting this in 18m + 12w = mw, we have:

18m + 12(3m + 45) = m(3m + 45)

18m + 36m + 540 = 3m^2 + 45m

3m^2 - 9m - 540 = 0

m^2 - 3m - 180 = 0

(m - 15)(m + 12) = 0

m = 15 or m = -12

Since m can't be negative, m = 15. Hence, w = 3(15) + 45 = 90. We see that a man's rate is 6 times that of a woman's rate since the number of days a man can complete the job is only 1/6 of the number of days a woman can complete the job.

Answer: D

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