It is currently 19 Apr 2018, 14:32

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Dwight and Mose decide to build a new barn on their farm, and they beg

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44566
Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]

### Show Tags

21 Mar 2017, 04:59
Expert's post
12
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

67% (03:00) correct 33% (03:09) wrong based on 181 sessions

### HideShow timer Statistics

Dwight and Mose decide to build a new barn on their farm, and they begin to work in alternating shifts, with Dwight taking the first shift. During each of his shifts, Dwight does 1/4 of the remaining work. During each of his shifts, Mose does 1/6 of the remaining work. How much of the barn is left to finish when Mose begins his third shift?

A. 1/24
B. 5/36
C. 25/72
D. 75/256
E. 255/512
[Reveal] Spoiler: OA

_________________
Senior Manager
Joined: 24 Apr 2016
Posts: 333
Re: Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]

### Show Tags

21 Mar 2017, 11:52
2
KUDOS
1
This post was
BOOKMARKED
Dwight = First Shift

Remaining Work = Total Work (Let us represent the total work as 1) = 1

Diwght completes 1/4th of the remaining work

Remaining Work = 1 - 1/4 = 3/4

Mose = First Shift

Remaining Work = 3/4

Mose completes 1/6th of the remaining work = 3/4 * 1/6 = 1/8

Remaining work = 3/4 - 1/8 = 5/8

Dwight = Second Shift

Remaining Work = 5/8

Diwght completes 1/4th of the remaining work = 5/8 * 1/4 = 5/32

Remaining work = 5/8 - 5/32 = 15/32

Mose = Second Shift

Remaining Work = 15/32

Mose completes 1/6th of the remaining work = 15/32 * 1/6 = 5/64

Remaining work = 15/32 - 5/64 = 25/64

Dwight = Third Shift

Remaining Work = 25/64

Diwght completes 1/4th of the remaining work = 25/64 * 1/4 = 25/256

Remaining work = 25/64 - 25/256 = 75/256

Work on the barn that is left to finish when Mose begins his third shift = 75/256

Answer is D. 75/256
Intern
Joined: 04 Oct 2015
Posts: 6
Location: France
Re: Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]

### Show Tags

12 Apr 2017, 13:57
6
KUDOS
quantumliner wrote:
Dwight = First Shift

Remaining Work = Total Work (Let us represent the total work as 1) = 1

Diwght completes 1/4th of the remaining work

Remaining Work = 1 - 1/4 = 3/4

Mose = First Shift

Remaining Work = 3/4

Mose completes 1/6th of the remaining work = 3/4 * 1/6 = 1/8

Remaining work = 3/4 - 1/8 = 5/8

Dwight = Second Shift

Remaining Work = 5/8

Diwght completes 1/4th of the remaining work = 5/8 * 1/4 = 5/32

Remaining work = 5/8 - 5/32 = 15/32

Mose = Second Shift

Remaining Work = 15/32

Mose completes 1/6th of the remaining work = 15/32 * 1/6 = 5/64

Remaining work = 15/32 - 5/64 = 25/64

Dwight = Third Shift

Remaining Work = 25/64

Diwght completes 1/4th of the remaining work = 25/64 * 1/4 = 25/256

Remaining work = 25/64 - 25/256 = 75/256

Work on the barn that is left to finish when Mose begins his third shift = 75/256

Answer is D. 75/256

I'm not sure if I could do this in, lets say, 90 seconds...
Instead, I identified the path:

Work remained
D1 (1-1/4)
M1 (1-1/4) - (1-1/4)x1/6 = (1-1/4)(1-1/6) = (3/4)(5/6) then:
D2 (3/4)(5/6)(3/4)
M2 (3/4)(5/6)(3/4)(5/6)
D3 (3/4)(5/6)(3/4)(5/6)(3/4) = 75/256

Manager
Joined: 20 Dec 2013
Posts: 124
Re: Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]

### Show Tags

12 Apr 2017, 14:25
2
KUDOS
1
This post was
BOOKMARKED
Bunuel wrote:
Dwight and Mose decide to build a new barn on their farm, and they begin to work in alternating shifts, with Dwight taking the first shift. During each of his shifts, Dwight does 1/4 of the remaining work. During each of his shifts, Mose does 1/6 of the remaining work. How much of the barn is left to finish when Mose begins his third shift?

A. 1/24
B. 5/36
C. 25/72
D. 75/256
E. 255/512

Let total work be 256 units
Work remaining at the 5th shift (because Mose's third shift will be the sixth shift) = (256) *(3/4)*(5/6)*(3/4)*(5/6)*(3/4) = 75

Hence the answer is D
_________________

76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org

Manager
Joined: 09 Oct 2016
Posts: 89
Location: United States
GMAT 1: 740 Q49 V42
GPA: 3.49
Re: Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]

### Show Tags

12 Apr 2017, 14:30
This seems like it would take too long

Posted from my mobile device
Manager
Joined: 20 Dec 2013
Posts: 124
Re: Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]

### Show Tags

12 Apr 2017, 14:31
gmathopeful19 wrote:
This seems like it would take too long

Posted from my mobile device

It wouldn't if you assume the work to be of 256 units.
_________________

76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org

Intern
Joined: 29 Jan 2017
Posts: 47
Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]

### Show Tags

16 Jun 2017, 18:46
Why do you have to multiply the remaining amount of work by the amount being completed (as opposed to subtract)?
DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1015
Location: India
Re: Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]

### Show Tags

16 Jun 2017, 21:53
This is something that we have to keep dividing by 4 and 6 (since 3/4 work is left, and 5/6 work is left), so better take a number which has atleast three 4's and three 6's. So lets take the initial barn work to be 4^3 * 6^3.

First shift:
Dwight does = 1/4 and work remaining = 3/4 * 4^3 * 6^3 = 3 * 4^2 * 6^3
Then Mose does = 1/6 and work remaining = 5/6 * 3 * 4^2 * 6^3 = 3 * 5 * 4^2 * 6^2

Second shift
Dwight does= 1/4 and remaining = 3/4 * 3 * 5 * 4^2 * 6^2 = 3^2 * 4 * 5 * 6^2
Mose does = 1/6 and work remaining = 5/6 * 3^2 * 4 * 5 * 6^2 = 3^2 * 5^2 * 4 * 6

Third Shift
Dwight does = 1/4 and work remaining for Mose = 3/4 * 3^2 * 5^2 * 4 * 6 = 3^3 * 5^2 * 6

So the fraction of work left = (3^3 * 5^2 * 6)/(4^3 * 6^3) = (27*25)/(64*36) = 75/256

Thus D is answer
Intern
Joined: 24 Jun 2013
Posts: 11
Location: India
Concentration: General Management, Economics
Schools: Tuck '19
GPA: 3.2
WE: Information Technology (Consulting)
Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]

### Show Tags

12 Dec 2017, 23:35
1
KUDOS
Let the work to be completed be 1.
D completes 1/4 of the remaining work. Therefore work remaining is $$(1-1/4)$$.
M completes 1/6 of the remaining work. Hence $$[(1-1/4)-(1-1/4)(1/6)]$$. Therefore work remaining is $$(1-1/4)(1-1/6)$$.

Hence work remaining when M starts work 3rd time is $$(1-1/4)^3*(1-1/6)^2 = 75/256$$
Intern
Joined: 19 Nov 2016
Posts: 7
Re: Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]

### Show Tags

17 Dec 2017, 03:39
PerfectScores wrote:
gmathopeful19 wrote:
This seems like it would take too long

Posted from my mobile device

It wouldn't if you assume the work to be of 256 units.

Can you explain why we assume the work to be of 256 units please?
Thank a lot.
Senior Manager
Status: Active
Affiliations: NA
Joined: 24 Oct 2012
Posts: 309
GMAT 1: 590 Q50 V21
GMAT 2: 600 Q48 V25
GMAT 3: 730 Q51 V37
GPA: 3.5
Re: Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]

### Show Tags

17 Dec 2017, 06:08
khiemchii wrote:
PerfectScores wrote:
gmathopeful19 wrote:
This seems like it would take too long

Posted from my mobile device

It wouldn't if you assume the work to be of 256 units.

Can you explain why we assume the work to be of 256 units please?
Thank a lot.

Hi,
Lets say total work is 256 .

D does 1/4 and M does 1/ of the remaining Unit .

Ist Attempt:

D = 1/4*256 = 64 , M = (256-64)*1/6 = 32

2nd Attempt:

D = (256 - 96)*1/4 = 40 , M = (256 - 136) *1/6= 20

3rd Attempt:

D = (256-156)*1/4= 25

At this point work remaining for M is 75 out of 256 . Hence 75/256 is answer
_________________

#If you like my post , please encourage me by giving Kudos

Re: Dwight and Mose decide to build a new barn on their farm, and they beg   [#permalink] 17 Dec 2017, 06:08
Display posts from previous: Sort by

# Dwight and Mose decide to build a new barn on their farm, and they beg

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

 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®.