NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 00:10 It is currently 26 Apr 2024, 00:10
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Three men and eight machines can finish a job in half the time taken

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92916
Own Kudos [?]: 619079 [14]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Three men and eight machines can finish a job in half the time taken [#permalink] New post   31 Mar 2020, 03:27
14
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

70% (02:55) correct 30% (03:09) wrong based on 114 sessions
Hide Show timer Statistics
Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days?

A. 10
B. 11
C. 12
D. 13
E. 14

Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS



Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
D
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8019
Own Kudos [?]: 4098 [3]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User CAT Tests
Re: Three men and eight machines can finish a job in half the time taken [#permalink] New post   31 Mar 2020, 03:49
2
Kudos
1
Bookmarks
rate of one machine ; 13*2 ; 26 days
and rate of man ; x
3/x+8/26 = 2*(8/x+3/26)
solve for x
we get x= 169
so in 13 days ; 169/13 ; 13 men would be required
IMO D


Bunuel wrote:
Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days?

A. 10
B. 11
C. 12
D. 13
E. 14

Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS



Are You Up For the Challenge: 700 Level Questions
User avatar
D
eakabuah
Retired Moderator
Joined: 18 May 2019
Posts: 785
Own Kudos [?]: 1040 [1]
Given Kudos: 101
Send PM
GMAT ToolKit User
Three men and eight machines can finish a job in half the time taken [#permalink] New post   31 Mar 2020, 03:50
1
Kudos
time taken by 3Men + 8 Machines = half * time taken by 3 machines + 8 men
In other words time taken by 3 men + 8 machines = time taken by 6 machines + 16 men
Two machines can finish the work in 13 days means that one machine can finish the work in 26 days.

let the time take for a man to finish the work be x, then

3/x + 8/26 = 6/26 + 16/x
2/26 = 13/x
x = 13*13
Hence 13 men will take 13*13/13 = 13 days.

The answer is D.
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5960
Own Kudos [?]: 13388 [2]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: Three men and eight machines can finish a job in half the time taken [#permalink] New post   31 Mar 2020, 04:01
2
Kudos
Expert Reply
Bunuel wrote:
Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days?

A. 10
B. 11
C. 12
D. 13
E. 14



Find Video Solution With CONCEPT EXPLAINED and DERIVED


Answer: Option D

User avatar
L
GMATWhizTeam
GMATWhiz Representative
Joined: 07 May 2019
Posts: 3409
Own Kudos [?]: 1800 [1]
Given Kudos: 68
Location: India
GMAT 1: 740 Q50 V41
GMAT 2: 760 Q51 V40
Send PM
Re: Three men and eight machines can finish a job in half the time taken [#permalink] New post   31 Mar 2020, 04:33
1
Kudos
Expert Reply
Bunuel wrote:
Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days?

A. 10
B. 11
C. 12
D. 13
E. 14

Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS



Are You Up For the Challenge: 700 Level Questions


Solution:


Let A and B be the per day work of one man and one machine respectively
    • Work done by 3 men and 8 machines in one day = 3A + 8B
    • Work done by 8 men and 3 machines in one day = 8A + 3B
      o Time taken to complete the work by 3 men and 8 machines is half time by 8 men and 3 machines
      o Work done by 3 men and 8 machines in one day is twice of the work done by 8 men and 3 machines in one day
      o \(3A + 8B = 2(8A + 3B)\)
      o \(3A +8B = 16A + 6B\)
      o \(8B-6B = 16A – 3A\)
      o \(2B = 13A\)
    • Work done by 2 machines in one day is equal to the work done by 13 men in one day.
    • 2 machines can complete the job in 13 days
      o 13 men can complete the job in 13 days
Hence, the correct answer is Option D.
avatar
B
MAMUN790
Intern
Intern
Joined: 27 Feb 2018
Posts: 3
Own Kudos [?]: 2 [1]
Given Kudos: 15
Location: Bangladesh
Schools: Neeley '22
GMAT 1: 560 Q45 V23
GPA: 3.05
Send PM
GMAT ToolKit User
Re: Three men and eight machines can finish a job in half the time taken [#permalink] New post   31 Mar 2020, 05:17
1
Kudos
Since, TEAM-1 (3 men and 8 machines) can finish a job in half the time taken by TEAM-2 (3 machines and 8 men) to finish the same job, we can express the TWO TEAM'S CAPACITY through the following equation:
3 MEN+ 8 MACHINES= 2 (3 MACHINES+ 8 MEN)
=> 3 MEN+8 MACHINES= 6 MACHINES+16 MEN
=>8 MACHINES- 6 MACHINES= 16 MEN- 3 MEN
=> 2 MACHINES=13 MEN
Therefore, we can infer that THE CAPACITY OF TWO MACHINES IS EQUIVALENT TO THAT OF 13 MEN.
Hence, it requires 13 men to complete what can be done by 2 machines in the same amount of time.

The answer is D.

Bunuel, please convey me whether my approach is efficient.
User avatar
L
CareerGeek
VP
VP
Joined: 20 Jul 2017
Posts: 1300
Own Kudos [?]: 3450 [3]
Given Kudos: 162
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 690 Q51 V30
WE:Education (Education)
Send PM
Re: Three men and eight machines can finish a job in half the time taken [#permalink] New post   31 Mar 2020, 10:20
2
Kudos
1
Bookmarks
Bunuel wrote:
Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days?

A. 10
B. 11
C. 12
D. 13
E. 14


two machines can finish the job in 13 days
--> 1 machine can complete a job in 26 days
Let 1 man complete a job in '\(m\)' days

Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job
--> \(\frac{3}{m} + \frac{8}{26} = 2(\frac{3}{26} + \frac{8}{m})\)
--> \(\frac{8}{26} - \frac{6}{26} = \frac{16}{m} - \frac{3}{m}\)
--> \(\frac{1}{13} = \frac{13}{m}\)
--> \(m = 169\) days

Number of men required to finish the job in 13 days = \(\frac{169}{13} = 13\) men

Option D
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32680
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: Three men and eight machines can finish a job in half the time taken [#permalink] New post   10 Feb 2023, 10:56
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.
GMAT Club Bot
gmatclubot
Re: Three men and eight machines can finish a job in half the time taken [#permalink]
10 Feb 2023, 10:56
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions