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

It is currently 25 Sep 2018, 06:14

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

Twenty workers can finish a piece of work in 30 days

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

Hide Tags

Retired Moderator
avatar
V
Joined: 28 May 2014
Posts: 528
GMAT 1: 730 Q49 V41
GMAT ToolKit User Premium Member
Twenty workers can finish a piece of work in 30 days  [#permalink]

Show Tags

New post 09 Feb 2017, 00:02
5
13
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

68% (02:57) correct 32% (02:36) wrong based on 184 sessions

HideShow timer Statistics

Twenty workers can finish a piece of work in 30 days. After how many days should 5 workers leave the job so that the work is completed in 35 days?
(A) 5 days
(B) 10 days
(C) 12 days
(D) 15 days
(E) 20 days

_________________

440 to 730: If I Can, You Can Too

Senior Manager
Senior Manager
avatar
B
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: Twenty workers can finish a piece of work in 30 days  [#permalink]

Show Tags

New post 09 Feb 2017, 00:32
1
2
saswata4s wrote:
Twenty workers can finish a piece of work in 30 days. After how many days should 5 workers leave the job so that the work is completed in 35 days?
(A) 5 days
(B) 10 days
(C) 12 days
(D) 15 days
(E) 20 days


Hi

\(\frac{20}{x} = \frac{1}{30}\)

x=600 (600 days for one worker to finish the job)

Now 20 workers will work x days, after 5 leave 15 workers will work 35-x days.

\(\frac{20}{600} * x + \frac{15}{600} * (35 - x) = 1\)

20x + 75 - 15x = 600

x = 15

Answer D
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1090
Twenty workers can finish a piece of work in 30 days  [#permalink]

Show Tags

New post Updated on: 11 Feb 2017, 14:17
saswata4s wrote:
Twenty workers can finish a piece of work in 30 days. After how many days should 5 workers leave the job so that the work is completed in 35 days?
(A) 5 days
(B) 10 days
(C) 12 days
(D) 15 days
(E) 20 days


rate of 1 man per day=1/(20*30)=1/600
let d=number of days with 20 workers
20d/600+[15(35-d)]/600=1
d=15 days
D

Originally posted by gracie on 09 Feb 2017, 15:52.
Last edited by gracie on 11 Feb 2017, 14:17, edited 1 time in total.
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8298
Location: Pune, India
Re: Twenty workers can finish a piece of work in 30 days  [#permalink]

Show Tags

New post 10 Feb 2017, 00:01
2
saswata4s wrote:
Twenty workers can finish a piece of work in 30 days. After how many days should 5 workers leave the job so that the work is completed in 35 days?
(A) 5 days
(B) 10 days
(C) 12 days
(D) 15 days
(E) 20 days


Weighted Average Method:

20 workers do 1/30th of the work per day.
15 workers will do (1/30)*(15/20) = (1/40)th of the work per day.

We want the average work to be 1/35 per day.

w1/w2 = (1/40 - 1/35) / (1/35 - 1/30) = (5/40*35) / (5/35*30) = 3/4

So 20 people should work for (3/7) * 35 = 15 days.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: Twenty workers can finish a piece of work in 30 days  [#permalink]

Show Tags

New post 15 Feb 2017, 10:51
3
1
saswata4s wrote:
Twenty workers can finish a piece of work in 30 days. After how many days should 5 workers leave the job so that the work is completed in 35 days?
(A) 5 days
(B) 10 days
(C) 12 days
(D) 15 days
(E) 20 days


We are given that 20 workers can complete a job in 30 days. Since rate = work/time, the rate of the 20 workers is 1/30. We can let x be the number of days it would take 5 fewer workers (i.e., 15 workers) to complete the job (from beginning to end); thus the rate of the 15 workers would be 1/x. Let’s determine x using the following proportion:

20/(1/30) = (15)/(1/x)

600 = 15x

40 = x

Thus, the number of days it takes for the 15 workers to complete the job (from beginning to end) is 15 and their rate is 1/40.

However, we need to determine at what point in time 5 of the 20 workers should leave the job so that the work is completed in 35 days. We can let this be t, and note that the work done by the 20 workers in these t days plus the work done by the 15 workers after these t days (i.e., in 35 - t days) will be the complete job. Recall that work = rate x time, so we have:

(1/30)t + (1/40)(35 - t) = 1

t/30 + (35 - t)/40 = 1

Multiplying the equation by 120, we have:

4t + 3(35 - t) = 120

4t + 105 - 3t = 120

t + 105 = 120

t = 15

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

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

Intern
Intern
avatar
Joined: 28 Jun 2016
Posts: 6
Re: Twenty workers can finish a piece of work in 30 days  [#permalink]

Show Tags

New post 24 Feb 2017, 09:36
2
1
20 workers finish the job in 30 days. i.e total work = 20*30 = 600 worker days

Not suppose after x days 5 workers left the job. i.e 20 workers worked for x days and 15 workers worked for (35 -x) days to finish the job.

600 = 20*x + 15*(35-x)

x = 15

Ans 15 days i.e option D
Intern
Intern
avatar
B
Joined: 29 Dec 2015
Posts: 4
GMAT 1: 600 Q41 V32
Re: Twenty workers can finish a piece of work in 30 days  [#permalink]

Show Tags

New post 16 Mar 2017, 16:06
1 worker takes 600 days to finish the job. So rate for each worker is 1/600 per day.
rate of 15 workers is 15/600. Job done by 15 workers in 5 days is 75/600.
How many days would it have taken 5 workers to do 75/600 units of the job?
time taken by 5 workers to complete 75/600 of the job = 75/600 / rate of 5 workers= (75/600)/(5/600) = 75/5 = 15
workers left after 30-15=15 days

ans = 15 days
Senior Manager
Senior Manager
User avatar
B
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 457
Location: India
Premium Member
Re: Twenty workers can finish a piece of work in 30 days  [#permalink]

Show Tags

New post 17 Mar 2017, 02:22
let the rate of work done by each worker be x and the total work be T. Also the no of days after 5 workers leave be d
20*30*x = T
20*d*x + 15*(35-d)*x = T = 20*30*x

solving for d we get d = 15 days
_________________

GMAT Mentors
Image

Intern
Intern
User avatar
B
Joined: 05 Dec 2017
Posts: 21
GPA: 3.35
Re: Twenty workers can finish a piece of work in 30 days  [#permalink]

Show Tags

New post 06 Feb 2018, 08:30
saswata4s wrote:
Twenty workers can finish a piece of work in 30 days. After how many days should 5 workers leave the job so that the work is completed in 35 days?
(A) 5 days
(B) 10 days
(C) 12 days
(D) 15 days
(E) 20 days


Let, assume 5 workers will leave after X days in 30 days,
basically, the x days are the time spent by all the workers from estimated 30 days dead line.

so, 30+5-x= \(\frac{20*(30-X)}{(20-5)}\)

>35- x= \(\frac{20*(30-X)}{15}\)

>20x-15x= 600 - 525

>X= 15 days
so, the ans is (D) 15 days.
Manager
Manager
User avatar
B
Joined: 28 Jan 2018
Posts: 54
Location: Netherlands
Concentration: Finance
GMAT 1: 710 Q50 V36
GPA: 3
Re: Twenty workers can finish a piece of work in 30 days  [#permalink]

Show Tags

New post 06 Feb 2018, 09:31
20 workers worked for 30 days, so there are 600 units worked in total

After x days, there will be 5 worker left, therefore total amount of units worked up to that point = 20*x

Time allocated to the remaining 15 workers is (35- x) (since the work need to be completed in 35 days)

Together we have the following equation: 20*x + (35-x)*15 = 600 (still work the same units)

Solve for x we got x = 15 => Answers D
Intern
Intern
avatar
B
Joined: 11 Dec 2016
Posts: 33
Re: Twenty workers can finish a piece of work in 30 days  [#permalink]

Show Tags

New post 05 Apr 2018, 09:02
1. 20 workers in 30 days do 600 units of work (20*30=600). And each worker does 600/20= 30 units of work every day.
2. If 20 workers do work for 35 days they'll finish 35*20=1050 units of work.
3. Extra work is 1050-600=450 units of of work.
4. Hence 450/(30units of work per day)= 15 days

Bunuel
@veristasprepkarishma
Is this approach correct?
GMAT Club Bot
Re: Twenty workers can finish a piece of work in 30 days &nbs [#permalink] 05 Apr 2018, 09:02
Display posts from previous: Sort by

Twenty workers can finish a piece of work in 30 days

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

Events & Promotions

PREV
NEXT


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®.