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

It is currently 16 Nov 2018, 16:33

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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     November 17, 2018

     November 17, 2018

     07:00 AM PST

     09:00 AM PST

    Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • GMATbuster's Weekly GMAT Quant Quiz # 9

     November 17, 2018

     November 17, 2018

     09:00 AM PST

     11:00 AM PST

    Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

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
User avatar
V
Joined: 02 Sep 2009
Posts: 50619
Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

Show Tags

New post 21 Mar 2017, 03:59
1
11
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

70% (03:15) correct 30% (03:14) wrong based on 189 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

_________________

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

Most Helpful Community Reply
Intern
Intern
avatar
B
Joined: 04 Oct 2015
Posts: 5
Location: France
Premium Member
Re: Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

Show Tags

New post 12 Apr 2017, 12:57
6
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

8-)
General Discussion
Senior Manager
Senior Manager
avatar
G
Joined: 24 Apr 2016
Posts: 332
Re: Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

Show Tags

New post 21 Mar 2017, 10:52
2
1
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
Manager
Manager
User avatar
Joined: 20 Dec 2013
Posts: 123
Re: Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

Show Tags

New post 12 Apr 2017, 13:25
2
1
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
http://www.youtube.com/perfectscores

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

Show Tags

New post 12 Apr 2017, 13:30
This seems like it would take too long

Posted from my mobile device
Manager
Manager
User avatar
Joined: 20 Dec 2013
Posts: 123
Re: Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

Show Tags

New post 12 Apr 2017, 13:31
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
http://www.youtube.com/perfectscores

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

Show Tags

New post 16 Jun 2017, 17:46
Why do you have to multiply the remaining amount of work by the amount being completed (as opposed to subtract)?
DS Forum Moderator
avatar
P
Joined: 21 Aug 2013
Posts: 1365
Location: India
Premium Member
Re: Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

Show Tags

New post 16 Jun 2017, 20:53
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
Intern
User avatar
B
Joined: 23 Jun 2013
Posts: 9
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

New post 12 Dec 2017, 22:35
1
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
Intern
avatar
B
Joined: 18 Nov 2016
Posts: 7
GMAT ToolKit User
Re: Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

Show Tags

New post 17 Dec 2017, 02:39
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
Senior Manager
User avatar
G
Status: Active
Affiliations: NA
Joined: 23 Oct 2012
Posts: 274
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

New post 17 Dec 2017, 05:08
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 :)

GMAT Club Bot
Re: Dwight and Mose decide to build a new barn on their farm, and they beg &nbs [#permalink] 17 Dec 2017, 05:08
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  


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®.