It is currently 17 Oct 2017, 23:17

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

Events & Promotions in June
Open Detailed Calendar

A and B are two laborers who have been given the task to build a house

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

Hide Tags

Expert Post
1 KUDOS received
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 746

Kudos [?]: 2072 [1], given: 123

A and B are two laborers who have been given the task to build a house [#permalink]

Show Tags

New post 28 Mar 2017, 10:49
1
This post received
KUDOS
Expert's post
22
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

34% (01:47) correct 66% (01:15) wrong based on 242 sessions

HideShow timer Statistics

A and B are two laborers who have been given the task to build a house. A can build a house in 20 days while B can build it in 30 days. But B went rogue and instead of building the house, he starts breaking it at the same rate. If A starts the work on the 1st day and they work alternately, in how many days will the house get built? (Assume once the house gets build, they will stop working)

A. \(60\) days

B. \(115\) days

C. \(120\) days

D. \(140\) days

E. \(121\frac{1}{3}\) days
[Reveal] Spoiler: OA

_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com


Last edited by EgmatQuantExpert on 31 Mar 2017, 13:01, edited 3 times in total.

Kudos [?]: 2072 [1], given: 123

Expert Post
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 746

Kudos [?]: 2072 [0], given: 123

Re: A and B are two laborers who have been given the task to build a house [#permalink]

Show Tags

New post 28 Mar 2017, 10:50
The official solution has been posted. Looking forward to a healthy discussion..:)
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com


Last edited by EgmatQuantExpert on 31 Mar 2017, 13:01, edited 1 time in total.

Kudos [?]: 2072 [0], given: 123

Intern
Intern
avatar
S
Joined: 14 May 2014
Posts: 17

Kudos [?]: 9 [0], given: 9

Re: A and B are two laborers who have been given the task to build a house [#permalink]

Show Tags

New post 28 Mar 2017, 21:35
Answer is B, right?
after 118 days, A and B build 59/60, it takes A 1/3 days to build 1/60 of the house.
Totally it takes 118+1/3 days

Kudos [?]: 9 [0], given: 9

Expert Post
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 746

Kudos [?]: 2072 [0], given: 123

Re: A and B are two laborers who have been given the task to build a house [#permalink]

Show Tags

New post 31 Mar 2017, 03:48
trangphamthuy91 wrote:
Answer is B, right?
after 118 days, A and B build 59/60, it takes A 1/3 days to build 1/60 of the house.
Totally it takes 118+1/3 days



Hey,

The answer is choice B but the options have been modified a bit. Please check. :)

Thanks,
Saquib
Quant Expert
e-GMAT

Aiming to score Q50 or higher in GMAT Quant? Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Register

Image
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com


Last edited by EgmatQuantExpert on 31 Mar 2017, 13:00, edited 1 time in total.

Kudos [?]: 2072 [0], given: 123

Expert Post
3 KUDOS received
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 746

Kudos [?]: 2072 [3], given: 123

Re: A and B are two laborers who have been given the task to build a house [#permalink]

Show Tags

New post 31 Mar 2017, 03:55
3
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED

Solution




    • Let us assume that building the house is equivalent to 60 units of works (LCM of 20 and 30 days).
      o Thus, efficiency of A = \(\frac{(Work)}{(Time)}\) \(= \frac{60}{20} = 3\) units/day.
      o And Efficiency of B \(= \frac{60}{30} = 2\) units/day.

    • As per the question:
      o A starting working on the first day and on the second day B comes and breaks the house at his own rate.

      o Thus, the pattern is like this ABABABABAB…..ABABA...

    • From the above we can infer that:

      o On day 1 A build 3 units. (As its efficiency is 3 units per day)

      o On day 2 B breaks 2 units. (As its efficiency is 2 units per day)

      o Thus, in 2 days only 1 unit of house is built.

      o But we need to build 60 units.

        AND (important!), we need to ensure that the last day A comes and build the wall.

         The reason for this is that on the last day, you cannot break the house and still make it! The house will be built on the last day when A comes to work.
      o Thus, we know that we can build 1 units in 2 days.

      o To build 57 units(the last three unit will be done by A), we will take (57*2) = 114 days.

      o On the 114th day, B had come to break it.

         Thus, the next day A will come and complete the remaining portion of 3 units in \(3\) days.

      o Hence the total time taken would be \(115\) days.

    • And the correct answer is Option B.


Thanks,
Saquib
Quant Expert
e-GMAT

Aiming to score Q50 or higher in GMAT Quant? Attend this webinar on 2ndApril to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Register

Image
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com


Last edited by EgmatQuantExpert on 31 Mar 2017, 13:02, edited 2 times in total.

Kudos [?]: 2072 [3], given: 123

2 KUDOS received
Manager
Manager
avatar
S
Joined: 25 Apr 2016
Posts: 53

Kudos [?]: 16 [2], given: 282

Re: A and B are two laborers who have been given the task to build a house [#permalink]

Show Tags

New post 31 Mar 2017, 04:16
2
This post received
KUDOS
But the premise says that once the work gets completed they no longer work and after accomplishing 57 units of work in 114 days,'A' will come and complete those remaining 3 units in a day's time.Thus, altogether they would take 115 days instead

Kudos [?]: 16 [2], given: 282

Expert Post
1 KUDOS received
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 746

Kudos [?]: 2072 [1], given: 123

Re: A and B are two laborers who have been given the task to build a house [#permalink]

Show Tags

New post 31 Mar 2017, 13:04
1
This post received
KUDOS
Expert's post
attari92 wrote:
But the premise says that once the work gets completed they no longer work and after accomplishing 57 units of work in 114 days,'A' will come and complete those remaining 3 units in a day's time.Thus, altogether they would take 115 days instead


Hey Attari92,


That is an excellent point that you have put forward! And you are correct. I somehow missed that while making the question and posting the solution.
My bad! I have modified the solution and the options.

Once again, awesome observation! :)


Thanks,
Saquib
Quant Expert
e-GMAT

Aiming to score Q50 or higher in GMAT Quant? Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Register

Image
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Kudos [?]: 2072 [1], given: 123

1 KUDOS received
Manager
Manager
avatar
S
Joined: 21 Apr 2016
Posts: 198

Kudos [?]: 17 [1], given: 79

GMAT ToolKit User Reviews Badge
Re: A and B are two laborers who have been given the task to build a house [#permalink]

Show Tags

New post 15 May 2017, 19:20
1
This post received
KUDOS
EgmatQuantExpert wrote:
Q.
A and B are two laborers who have been given the task to build a house. A can build a house in 20 days while B can build it in 30 days. But B went rogue and instead of building the house, he starts breaking it at the same rate. If A starts the work on the 1st day and they work alternately, in how many days will the house get built? (Assume once the house gets build, they will stop working)



A. \(60\) days
B. \(115\) days
C. \(120\) days
D. \(140\) days
E. \(121\frac{1}{3}\) days


Options are quite straightforward. I was looking for an odd number of days, as it is given that they will stop as soon as the house is built. Only option (B) fits this criterion.

In all other options there is some destruction from laborer B

Kudos [?]: 17 [1], given: 79

1 KUDOS received
Intern
Intern
User avatar
B
Joined: 12 Nov 2016
Posts: 29

Kudos [?]: 15 [1], given: 27

Location: Nepal
Concentration: Accounting, Economics
GPA: 3.63
WE: Account Management (Accounting)
Re: A and B are two laborers who have been given the task to build a house [#permalink]

Show Tags

New post 03 Jun 2017, 00:32
1
This post received
KUDOS
B cannot work in the last day because he is a demolisher and the house won't be fully built. Hence A must work in the last day to sort the wreckages out by B in the previous day and finish building the house. As A is starting the work and he is finishing it, the number of days must be odd. Only option B fits.

Posted from my mobile device

Kudos [?]: 15 [1], given: 27

Intern
Intern
avatar
B
Joined: 08 Dec 2016
Posts: 32

Kudos [?]: 2 [0], given: 486

CAT Tests
Re: A and B are two laborers who have been given the task to build a house [#permalink]

Show Tags

New post 11 Jun 2017, 13:06
Probably I don't understand the question, as it is stated my solution is:
(1/20-1/30)= 1/60 in 2 days --> in order to build 59/60 it takes 118 days, than A comes and finish the work in 1/3 days.
Therefore the solution should be 118(1/3).

Expert comment really appreciated.

Thanks,
Matt

Kudos [?]: 2 [0], given: 486

1 KUDOS received
BSchool Forum Moderator
User avatar
P
Joined: 26 Feb 2016
Posts: 1449

Kudos [?]: 593 [1], given: 16

Location: India
Concentration: General Management, Leadership
WE: Sales (Retail)
Premium Member CAT Tests
Re: A and B are two laborers who have been given the task to build a house [#permalink]

Show Tags

New post 11 Jun 2017, 13:27
1
This post received
KUDOS
We will not need to do the same for 118 days.

Doing this for 114 days will complete 57/60 of the work as per your login and on the 115th day when A does 1/20th of the work

57/60 + 1/20 = 60/60(Work finished)

Hope it helps!!

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
_________________

Stay hungry, Stay foolish

2017-2018 MBA Deadlines

Class of 2020: Rotman Thread | Schulich Thread
Class of 2019: Sauder Thread

Kudos [?]: 593 [1], given: 16

Intern
Intern
avatar
B
Joined: 08 Dec 2016
Posts: 32

Kudos [?]: 2 [0], given: 486

CAT Tests
Re: A and B are two laborers who have been given the task to build a house [#permalink]

Show Tags

New post 11 Jun 2017, 13:46
pushpitkc wrote:
We will not need to do the same for 118 days.

Doing this for 114 days will complete 57/60 of the work as per your login and on the 115th day when A does 1/20th of the work

57/60 + 1/20 = 60/60(Work finished)

Hope it helps!!

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app


Thansks Pushpitkc. You are right. Now I get IT.

+ 1 kudos for you.

Matt

Posted from my mobile device

Kudos [?]: 2 [0], given: 486

Intern
Intern
avatar
B
Joined: 28 Jun 2017
Posts: 6

Kudos [?]: 0 [0], given: 33

Re: A and B are two laborers who have been given the task to build a house [#permalink]

Show Tags

New post 12 Aug 2017, 05:20
Let A be the work done per day by A ( 1/20) and B be the work done by B per day (1/30)
As work done must be equal to 1, we will start the work with A and end the work with A, as once the house is constructed work will stop:

A-B+A-B+......A-B+A =1

=> 1/20-1/30+1/20-1/30...+1/20-1/30=1

Had the work been done for 3 days .. the condition would have been - A-B+A => 2A-B
Had the work been done for 5 days .. the condition would have been A-B+A-B+A=> 3A-2B
Had the work been done for 7 days .. the condition would have been A-B+A-B+A-B+A=> 4A-3B

this means - (n+1)A-nB=1
(n+1)/20 - n/30=1
=> n = 57 ( no of days B will work)A
now, A works one day more than B( from above)=> n+1=58

Total no of days - 58+57=115 days.

Kudos [?]: 0 [0], given: 33

1 KUDOS received
Intern
Intern
avatar
B
Joined: 15 Oct 2016
Posts: 1

Kudos [?]: 1 [1], given: 12

GMAT 1: 600 Q44 V28
GMAT 2: 640 Q47 V32
Re: A and B are two laborers who have been given the task to build a house [#permalink]

Show Tags

New post 02 Oct 2017, 10:35
1
This post received
KUDOS
"Assume once the house gets build, they will stop working"
A will keep building the house while B breaks it the next day. Therefore, when A finally completes the house, "they will stop working". Thus, B will be working one day less than A eventually as shown below:

Make,Break,Make,Break...Make,Break,MAKE

Equation:

Work of A - Work of B = 1
[1/20 x T] - [1/30 x (t-1)] = 1

Solve for T (A's days) -> 58
Calculate T-1 (B's days) -> 57
Total days for house to be built = 58 + 57 = 115

Kudos [?]: 1 [1], given: 12

Intern
Intern
avatar
B
Status: Target 760
Joined: 20 Aug 2014
Posts: 10

Kudos [?]: 5 [0], given: 2

Location: India
Concentration: Strategy, Economics
GPA: 3.25
WE: Corporate Finance (Investment Banking)
A and B are two laborers who have been given the task to build a house [#permalink]

Show Tags

New post 16 Oct 2017, 11:05
EgmatQuantExpert wrote:
A and B are two laborers who have been given the task to build a house. A can build a house in 20 days while B can build it in 30 days. But B went rogue and instead of building the house, he starts breaking it at the same rate. If A starts the work on the 1st day and they work alternately, in how many days will the house get built? (Assume once the house gets build, they will stop working)

A. \(60\) days

B. \(115\) days

C. \(120\) days

D. \(140\) days

E. \(121\frac{1}{3}\) days

This is a beautiful question. A builds the house at a rate of \(\frac{1}{10}\) and b breaks the house at a rate of \(\frac{1}{30}\). So, in 2 days, the work completed will be \(\frac{1}{20}\)-\(\frac{1}{30}\)=\(\frac{1}{60}\). But remember, A started first, so the house will be completed a figure that is less than 120. So, B

Kudos [?]: 5 [0], given: 2

A and B are two laborers who have been given the task to build a house   [#permalink] 16 Oct 2017, 11:05
Display posts from previous: Sort by

A and B are two laborers who have been given the task to build a house

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.