GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Aug 2018, 19:02

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

It takes 6 days for 3 women and 2 men working together to

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 48110
Re: Time n Work Problem  [#permalink]

Show Tags

07 Feb 2014, 04:57
mrwells2 wrote:
Bunuel wrote:
nonameee wrote:
Guys, even if you know the solution right away, it takes several minutes (definitely more than 3) to just write it down to find the answer. Is it a real GMAT question? Can something like that be expected on the real test?

Below is another solution which is a little bit faster.

It takes 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

Let one woman complete the job in $$w$$ days and one man in $$m$$ days. So the rate of 1 woman is $$\frac{1}{w}$$ job/day and the rate of 1 man is $$\frac{1}{m}$$ job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}$$.

3 men would do the same work 5 days sooner than 9 women --> $$\frac{m}{3}+5=\frac{w}{9}$$.

Solving: $$m=15$$ and $$w=90$$. $$\frac{w}{m}=6$$.

I stumbled on this answer and think it's worth clarifying:

In the second equation: 3 men would do the same work 5 days sooner than 9 women --> $$\frac{m}{3}+5=\frac{w}{9}$$.

m and w are representing TOTAL work done by men and women.

Whereas in the first equation: Let one woman complete the job in $$w$$ days and one man in $$m$$ days. So the rate of 1 woman is $$\frac{1}{w}$$ job/day and the rate of 1 man is $$\frac{1}{m}$$ job/day.

m and w are representing the RATE of work done by men and women.

I hope this is correct (Bunuel can you confirm?) and has helped some grasp the concept.

No, that's not correct.

m and w in both equations represent the same thing: time.

w is the number of days (time) one woman needs complete the job.
m is the number of days (time) one man needs complete the job.

The following posts might help:
it-takes-6-days-for-3-women-and-2-men-working-together-to-82718.html#p751436
it-takes-6-days-for-3-women-and-2-men-working-together-to-82718-20.html#p1272526
it-takes-6-days-for-3-women-and-2-men-working-together-to-82718-40.html#p1295389
_________________
Manager
Joined: 04 Aug 2010
Posts: 243
Schools: Dartmouth College
Re: It takes 6 days for 3 women and 2 men working together to  [#permalink]

Show Tags

17 Jul 2018, 04:15
2
virtualanimosity wrote:
It takes 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, which represent how many times a man's output exceeds that of a woman.
When the correct answer is plugged in, 3 men will take 5 fewer days to complete the job than 9 women.

B: 4
Let the rate for each woman = 1 unit per day and the rate for each man = 4 units per day.
Since it takes 6 days for 3 women and 2 men to complete the job, the job = (rate for 3 women and 2 men)(6 days) = (3*1 + 2*4)(6) = 66 units.
Time for 9 women to complete the job = $$\frac{work}{rate-for-9-women} = \frac{66}{(9*1)} = \frac{22}{3} ≈ 7$$ days.
Time for 3 men to complete the job = $$\frac{work}{rate-for-3-men} = \frac{66}{(3*4)} = \frac{66}{12} = \frac{11}{2} ≈ 5$$ days.
Doesn't work:
Here, 3 men take only about 2 fewer days than 9 women.
Eliminate B.
For 3 men to take 5 fewer days, the rate for each man must INCREASE.
Eliminate A.

D: 6
Let the rate for each woman = 1 unit per day and the rate for each man = 6 units per day.
Since it takes 6 days for 3 women and 2 men to complete the job, the job = (rate for 3 women and 2 men)(6 days) = (3*1 + 2*6)(6) = 90 units.
Time for 9 women to complete the job = $$\frac{work}{rate-for-9-women} = \frac{90}{(9*1)} = \frac{90}{9} = 10$$ days.
Time for 3 men to complete the job = $$\frac{work}{rate-for-3-men} = \frac{90}{(3*6)} = \frac{90}{18} = 5$$ days.
Success!
Here, 3 men take 5 fewer days than 9 women.

_________________

GMAT and GRE Tutor
Over 1800 followers
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3197
Location: United States (CA)
Re: It takes 6 days for 3 women and 2 men working together to  [#permalink]

Show Tags

19 Jul 2018, 12:42
virtualanimosity wrote:
It takes 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 the number of days for 1 man to finish the work = m and that for 1 woman = w. Thus, the rate of 1 man = 1/m and the rate of 1 woman = 1/w.

Since it takes 6 days for 3 women and 2 men working together to complete the work, we have:

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

Since 3 men would do the same work 5 days sooner than 9 women, we have:

1/(3/m) + 5 = 1/(9/w)

m/3 + 5 = w/9

Multiplying the above by 9, we have:

3m + 45 = w

Substituting this into 6(3/w + 2/m) = 1, we have:

6(3/(3m + 45) + 2/m) = 1

6(1/(m + 15) + 2/m) = 1

Multiplying the above by m(m + 15), we have:

6m + 12(m + 15) = m(m + 15)

6m + 12m + 180 = m^2 + 15m

m^2 - 3m - 180 = 0

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

m = 15 or m = -12

Since m can’t be negative, m = 15. So w = 3(15) + 45 = 90. We see that it takes a man 15 days to complete the work but 90 days for a woman to complete the same work. So a man’s output is 6 times the output of a woman.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: It takes 6 days for 3 women and 2 men working together to &nbs [#permalink] 19 Jul 2018, 12:42

Go to page   Previous    1   2   [ 24 posts ]

Display posts from previous: Sort by

Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.