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

It is currently 22 Feb 2019, 02:27

Close

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
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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT RC Webinar

     February 23, 2019

     February 23, 2019

     07:00 AM PST

     09:00 AM PST

    Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
  • FREE Quant Workshop by e-GMAT!

     February 24, 2019

     February 24, 2019

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53066
Re: Time n Work Problem  [#permalink]

Show Tags

New post 07 Feb 2014, 03:57
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 \(w=90\). \(\frac{w}{m}=6\).

Answer: D.


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
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
avatar
S
Joined: 04 Aug 2010
Posts: 352
Schools: Dartmouth College
It takes 6 days  [#permalink]

Show Tags

New post 16 Jul 2018, 02:46
An alternate approach for a problem in a locked thread:

Quote:
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
b. 4
c. 5
d. 6
e. 7


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
Click here to learn more
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.
For more information, please email me at GMATGuruNY@gmail.com.

Senior Manager
Senior Manager
avatar
S
Joined: 04 Aug 2010
Posts: 352
Schools: Dartmouth College
Re: It takes 6 days for 3 women and 2 men working together to  [#permalink]

Show Tags

New post 17 Jul 2018, 03:15
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
Click here to learn more
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.
For more information, please email me at GMATGuruNY@gmail.com.

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4955
Location: United States (CA)
Re: It takes 6 days for 3 women and 2 men working together to  [#permalink]

Show Tags

New post 19 Jul 2018, 11:42
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.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

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

CEO
CEO
User avatar
P
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2798
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: It takes 6 days for 3 women and 2 men working together to  [#permalink]

Show Tags

New post 07 Nov 2018, 22:55
1
1
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


Please find attached the solution
Attachments

File comment: www.GMATinsight.com
Screenshot 2018-11-08 at 12.23.23 PM.png
Screenshot 2018-11-08 at 12.23.23 PM.png [ 759.01 KiB | Viewed 521 times ]


_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

VP
VP
User avatar
D
Joined: 09 Mar 2016
Posts: 1284
Re: It takes 6 days for 3 women and 2 men working together to  [#permalink]

Show Tags

New post 26 Nov 2018, 09:10
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



3w+2m= 1/6 (in one day )

NEXT: 3 men would do the same work 5 days sooner than 9 women , SO let X be the job done by woman and let x-5 be the work done by men


HENCE: \(\frac{1}{x}- \frac{1}{(x-5)} = \frac{x-5-x}{x(x-5)}\) i.e \(\frac{-5}{x(x-5)}\) (i know i got negative in numerator but still continued solving further :lol: )


\(\frac{-5}{x(x-5)}\) = \(\frac{1}{6}\) cross multiply

\(x(x-5)=-30\)

\(x\) = \(\frac{-30}{x(x-5)}\) now if i divide -30 by -5 i get 6. this was my solution to correct answer :grin:


Bunuel, pushpitkc generis do you think my solution is correct ? :)
Intern
Intern
avatar
B
Joined: 12 Aug 2018
Posts: 3
Re: It takes 6 days for 3 women and 2 men working together to  [#permalink]

Show Tags

New post 11 Jan 2019, 00:05
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



Hello all,

I couldn't solve this question within time. But i did attempt it the following manner and got the answer right. Can someone tell me if this approach is correct/incorrect?

Let the work be W.

Now, based on the data provided
- one man can do 1/3 of W
- one woman can do 1/9 of W

Here i am now assuming a number for W - let's say the work needed to be done is eating 27 pies. i.e. W=27

So one man can eat 9 pies and one woman can eat 3 pies.

Because the question asks How many times does the output of a man exceed that of a woman?, I have understood this as Output of a man (9 pies) is x more than output of a woman (3 pies).
so 9 = 3+x therefore, X=6.

Let me know if this makes sense or I was just lucky to get the answer right (won't work all the time)
GMAT Club Bot
Re: It takes 6 days for 3 women and 2 men working together to   [#permalink] 11 Jan 2019, 00:05

Go to page   Previous    1   2   [ 27 posts ] 

Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.