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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: If 12 men and 16 women can do a piece of work in 5 days and [#permalink]

Show Tags

17 Aug 2004, 18:18

Wow, this is an insane problem. I wonder if someone can come up with a quick solution but it took me a long time to figure it out. Too much calculation. I came up with 1452/175 days or about 8.3 days.

1) M/12 + W/16 = 5
2) M/13 + W/24 = 4

Multiply second line by -3/2 to eliminate variable W:
2) -3M/26 - W/16 = -6

Add up line 1 and 2:
M/12 - 3M/26 = 5 - 6
(-18 + 13)M/156 = -1
-5M = -156
M = 156/5

Now plug in second equation to get W:
156/65 + W/24 = 4
12/5 + W/24 = 20/5
W/24 = 8/5
W = 192/5

Plug in back to the question asked:
M/7 + W/10 = X
156/(5*7) + 192/(5*10) = X
156/35 + 96/25 = X
(672+780)/175 = X
X = 1452/175 = approx 8.3 days

Will certainly not be on the GMAT. _________________

Re: If 12 men and 16 women can do a piece of work in 5 days and [#permalink]

Show Tags

17 Aug 2004, 18:35

These are some the toughest problems that I have. I do have the solutions, but I am throwing them out in the hope that somebody can come up with a simpler solution as well as to challenge people.

Re: If 12 men and 16 women can do a piece of work in 5 days and [#permalink]

Show Tags

16 Jan 2014, 00:24

Here is how I solved it:

Create two equations based on the information given. Start from the basics. Each man can do 1/x work per day and each woman can to 1/y work per day. If we have 12 men and 16 women, then in total they can do 12/x work per day and 16/y work per day together. We also know that they can do the work together in 5 days. So in 1 day, how much of the job did they finish? 1/5 or 20%. Repeat this logic to create the second formula. 12/x + 16/y = 1/5 13/x + 24/y = 1/4

Solve for common denominators in each formula: 12y+16x=((xy)^2)/5 13y+24x=((xy)^2)/4

Multiply by denominator of fraction in each formula to get nice numbers. Since both would equal the same variable, make them equal to each other: 60y+80x=52y+96x 8y=16x y=2x

Plug y=2x into the first equation to get: 12/x+16/2x=1/5 12/x+8/x=1/5 20/x=1/5 x=100

If x=100 and y=2x, y=200

Now in the original equation, it asks us how long 7 men and 10 women can do the work. We can create the following formula, similar to what we did in the first step. This formula tells us that in one day 7 men and 10 women can do X% of the job. We can simply take the reciprocal of the fraction to get the number of days the job will be completed in: 7/x+10/y=1/z (we want to solve for z) 7/100+10/200=1/z 7/100+5/100=1/z 12/100=1/z z=100/12 or 8.33

Last edited by psal on 16 Jan 2014, 13:36, edited 1 time in total.

Using equations (I) and (II) we need to find the sum of 7M and 10W. We can get a multiple of 7M in various ways: (3M + 4W = 1/20) * 5 gives 15M + 20W = 1/4 Adding this to equation II, we get 28M + 44W = 1/2 7M + 11W = 1/8

7 men and 11 women complete the work in 8 days. 7 men and 10 women will take a little more than 8 days to complete the work. If you do get such a question in GMAT, you will easily be able to manipulate the equations to get the desired equation. Finding the values of M and W is way too painful to interest GMAT. _________________

Re: If 12 men and 16 women can do a piece of work in 5 days and [#permalink]

Show Tags

18 May 2015, 01:39

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: If 12 men and 16 women can do a piece of work in 5 days and [#permalink]

Show Tags

17 Jul 2016, 21:31

let d=number of days needed let m=rate of 1 man per 1 day w=rate of 1 woman per 1 day 5(12m+16w)=4(13m+24w) m=2w substituting, d(7m+5m)=5(12m+8m) d=8.3 days

gmatclubot

Re: If 12 men and 16 women can do a piece of work in 5 days and
[#permalink]
17 Jul 2016, 21:31

This is the kickoff for my 2016-2017 application season. After a summer of introspect and debate I have decided to relaunch my b-school application journey. Why would anyone want...

Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...

Time is a weird concept. It can stretch for seemingly forever (like when you are watching the “Time to destination” clock mid-flight) and it can compress and...