Find all School-related info fast with the new School-Specific MBA Forum

It is currently 16 Sep 2014, 19:43

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A husband and wife started painting their house, but husband

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 15

Kudos [?]: 195 [0], given: 11

GMAT ToolKit User GMAT Tests User
Re: A husband and wife started painting their house, but husband [#permalink] New post 14 Nov 2012, 06:36
Setup the Rate Equation:

\frac{1}{20}(d-10) + \frac{1}{15}(d)=1
3d-15+4d=60
d=\frac{75}{7}

Answer: C
_________________

Impossible is nothing to God.

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29655
Followers: 3492

Kudos [?]: 26236 [0], given: 2707

Re: A husband and wife started painting their house, but husband [#permalink] New post 08 Jul 2013, 00:09
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

To find DS questions by Kudos, sort by Kudos here: gmat-data-sufficiency-ds-141/
To find PS questions by Kudos, sort by Kudos here: gmat-problem-solving-ps-140/

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 19 Feb 2013
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: A husband and wife started painting their house, but husband [#permalink] New post 08 Jul 2013, 04:34
Where am i going wrong?

Combined work rate= 7/60

Time H and W should have taken= 60/7

Time H & W worked together = 60/7 - 5= 25/7

In 25/7 days they did= 25/7 * 7/60= 5/12

Work left for wife to do= 7/12

Time taken by wife to do 7/12= 7/12 * 15= 35/4

Total Time- 35/4+25/7 ?????
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29655
Followers: 3492

Kudos [?]: 26236 [0], given: 2707

Re: A husband and wife started painting their house, but husband [#permalink] New post 08 Jul 2013, 04:49
Expert's post
rahulmathur9818 wrote:
Where am i going wrong?

Combined work rate= 7/60

Time H and W should have taken= 60/7

Time H & W worked together = 60/7 - 5= 25/7

In 25/7 days they did= 25/7 * 7/60= 5/12

Work left for wife to do= 7/12

Time taken by wife to do 7/12= 7/12 * 15= 35/4

Total Time- 35/4+25/7 ?????


Actual time would be more than 60/7 days. Check here: a-husband-and-wife-started-painting-their-house-but-husband-77973.html#p1035303

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 17 Dec 2012
Posts: 395
Location: India
Followers: 13

Kudos [?]: 180 [1] , given: 10

Re: A husband and wife started painting their house, but husband [#permalink] New post 08 Jul 2013, 05:48
1
This post received
KUDOS
johnnybravo86 wrote:
A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days?

A. 40/7
B. 50/7
C. 75/7
D. 55/7


1. In a normal scenario both the husband and wife would have taken 1/ (1/15+ 1/20) days = 60/7 days to complete the task
2. what did not happen was they definitely did not work together for 5 days. So subtract 5 days work together =5*7/60 = 7/12 th of the work
3. what did happen was the wife definitely worked alone for 5 days. So add 5 days of work of the wife = 5/15 = 1/3 rd of the work= 4/12 th of the work
4. From (2) and (3) we see 7/12- 4/12 = 3/12 th or 1/4 th of the work still remains.
5. this additional 1/4 th work would have been done by both because the wife worked alone for only 5 days which we have accounted for. So time taken for this work is 1/4 * 60/7 =15/7
6. Total time taken to complete the whole work in the altered scenario is 60/7 + 15/7 = 75/7
_________________

Srinivasan Vaidyaraman
Sravna Test Prep
http://www.sravna.com/courses.php

Classroom Courses in Chennai
Online and Correspondence Courses

Intern
Intern
avatar
Joined: 03 Sep 2013
Posts: 9
Followers: 0

Kudos [?]: 1 [0], given: 2

Re: A husband and wife started painting their house, but husband [#permalink] New post 07 Nov 2013, 11:41
Husband(working alone) completes the job in 20 days, implying a per day completion of 5% of total job
Wife(working alone) completes the job in 15 days, implying a per day completion of 20/3% of total job

If we let the total no of days for work completion to be equal to 'T' days, then,

Wife works for all T days; husband works for T-5 days (leaves work 5 days before completion of work)

Setting up an equation for 100% completion of work -

(T-5)*5% + T*20/3% = 100%

Solving for T, T = 75/7 days
Intern
Intern
User avatar
Joined: 03 Apr 2013
Posts: 12
Followers: 0

Kudos [?]: 2 [0], given: 11

GMAT ToolKit User
Re: A husband and wife started painting their house, but husband [#permalink] New post 16 Nov 2013, 12:41
Hey johnnybravo86, whenever you come across such problems where you people work for different number of days or some days more or less, the best approach is to add up their individual work and not as a whole,
In this problem, lets consider the work to be done as a single unit i.e. 1.
now going according to the words of the question, let the wife work for x days. Thus, the husband works for x-5 days.
Now their respective efficiencies(fraction of work done per day) are given as,
H W
1/20 1/15
now simply multiply and add
The final equation is

x/15 + (x-5)/20 = 1
solve for x, it comes out to be 75/7, which is the OA.
Kudos me! :)
Manager
Manager
User avatar
Joined: 10 Mar 2013
Posts: 200
Followers: 0

Kudos [?]: 8 [0], given: 1737

CAT Tests
Re: A husband and wife started painting their house, but husband [#permalink] New post 17 Nov 2013, 05:16
t/15 + (1/20)(t-5) = 1
4t/60 + 3(t-5)/60 = 1
7t -15 = 60
7t = 75
t = 75/7
Manager
Manager
avatar
Joined: 26 Sep 2013
Posts: 232
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Followers: 2

Kudos [?]: 37 [0], given: 40

Re: Work & Rate problem [#permalink] New post 21 Nov 2013, 09:32
Bunuel wrote:
A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days?
A. 40/7
B. 50/7
C. 75/7
D. 55/7

As pointed out above there are several ways to solve this problem. Below are probably two shortest approaches:

Approach #1:
Rate of husband \frac{1}{20} job/day;
Rate of wife \frac{1}{15} job/day;
Combined rate: \frac{1}{20}+\frac{1}{15}=\frac{7}{60} job/day;

During the last 5 days, when the wife worked alone, she completed \frac{5}{15}=\frac{1}{3}rd of the job;
Hence, remaining \frac{2}{3}rd of the job was done by them working together in time=\frac{job'}{rate}=\frac{(\frac{2}{3})}{(\frac{7}{60})}=\frac{40}{7} days;

Total time needed to complete the whole job: 5+\frac{40}{7}=\frac{75}{7} days.

Answer: C.

Approach #2:
It's based on observing the answer choices. On the PS section always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question.

Combined rate of the husband and wife is \frac{7}{60} job/day, which means that working together they'll complete the job in \frac{60}{7} days (time is reciprocal of rate). As they worked together only some part of the total time, then actual time would be more than \frac{60}{7} days. Only \frac{75}{7} is more than this value (answer choice C), so it must be correct.

Answer: C.

Hope it helps.



Could you possibly help me figure out why my method didn't work for solving:

I combined their two rates, and came up with \frac{7}{60} per day, so the whole job, combined, would have taken them \frac{60}{7}, or 8 4/7 days to complete. The husband left 5 days before this, so they worked together for 3 4/7 days, or \frac{25}{7}. The amount of work they completed was \frac{7}{60}* \frac{25}{7}=25/60 of the job. This leaves \frac{35}{60}of the job for the wife to complete alone. She can work at a rate of 4/60 per day. So that means she completed the remaining 35/60 in 8 3/4 days, not 5. This combined with the 3 4/7 that they worked on it together gives you a number of about 12.32, which is obviously not correct. Where did I go wrong? I'm having trouble reconciling how the wife only needed 5 days working at the rate given, when we can see how much work they did combined, and it leaves more than 5 days worth of work for her.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29655
Followers: 3492

Kudos [?]: 26236 [1] , given: 2707

Re: Work & Rate problem [#permalink] New post 22 Nov 2013, 00:50
1
This post received
KUDOS
Expert's post
AccipiterQ wrote:
Bunuel wrote:
A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days?
A. 40/7
B. 50/7
C. 75/7
D. 55/7

As pointed out above there are several ways to solve this problem. Below are probably two shortest approaches:

Approach #1:
Rate of husband \frac{1}{20} job/day;
Rate of wife \frac{1}{15} job/day;
Combined rate: \frac{1}{20}+\frac{1}{15}=\frac{7}{60} job/day;

During the last 5 days, when the wife worked alone, she completed \frac{5}{15}=\frac{1}{3}rd of the job;
Hence, remaining \frac{2}{3}rd of the job was done by them working together in time=\frac{job'}{rate}=\frac{(\frac{2}{3})}{(\frac{7}{60})}=\frac{40}{7} days;

Total time needed to complete the whole job: 5+\frac{40}{7}=\frac{75}{7} days.

Answer: C.

Approach #2:
It's based on observing the answer choices. On the PS section always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question.

Combined rate of the husband and wife is \frac{7}{60} job/day, which means that working together they'll complete the job in \frac{60}{7} days (time is reciprocal of rate). As they worked together only some part of the total time, then actual time would be more than \frac{60}{7} days. Only \frac{75}{7} is more than this value (answer choice C), so it must be correct.

Answer: C.

Hope it helps.



Could you possibly help me figure out why my method didn't work for solving:

I combined their two rates, and came up with \frac{7}{60} per day, so the whole job, combined, would have taken them \frac{60}{7}, or 8 4/7 days to complete. The husband left 5 days before this, so they worked together for 3 4/7 days, or \frac{25}{7}. The amount of work they completed was \frac{7}{60}* \frac{25}{7}=25/60 of the job. This leaves \frac{35}{60}of the job for the wife to complete alone. She can work at a rate of 4/60 per day. So that means she completed the remaining 35/60 in 8 3/4 days, not 5. This combined with the 3 4/7 that they worked on it together gives you a number of about 12.32, which is obviously not correct. Where did I go wrong? I'm having trouble reconciling how the wife only needed 5 days working at the rate given, when we can see how much work they did combined, and it leaves more than 5 days worth of work for her.


If they work together they can complete the job in 60/7 days. But if one of them does not work for all that period then the time to complete would increase. Thus you cannot say that when husband left 5 days before, then they worked together for 60/7-5 days.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 26 Sep 2013
Posts: 232
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Followers: 2

Kudos [?]: 37 [0], given: 40

Re: Work & Rate problem [#permalink] New post 22 Nov 2013, 16:30
Bunuel wrote:
AccipiterQ wrote:
Bunuel wrote:
A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days?
A. 40/7
B. 50/7
C. 75/7
D. 55/7

As pointed out above there are several ways to solve this problem. Below are probably two shortest approaches:

Approach #1:
Rate of husband \frac{1}{20} job/day;
Rate of wife \frac{1}{15} job/day;
Combined rate: \frac{1}{20}+\frac{1}{15}=\frac{7}{60} job/day;

During the last 5 days, when the wife worked alone, she completed \frac{5}{15}=\frac{1}{3}rd of the job;
Hence, remaining \frac{2}{3}rd of the job was done by them working together in time=\frac{job'}{rate}=\frac{(\frac{2}{3})}{(\frac{7}{60})}=\frac{40}{7} days;

Total time needed to complete the whole job: 5+\frac{40}{7}=\frac{75}{7} days.

Answer: C.

Approach #2:
It's based on observing the answer choices. On the PS section always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question.

Combined rate of the husband and wife is \frac{7}{60} job/day, which means that working together they'll complete the job in \frac{60}{7} days (time is reciprocal of rate). As they worked together only some part of the total time, then actual time would be more than \frac{60}{7} days. Only \frac{75}{7} is more than this value (answer choice C), so it must be correct.

Answer: C.

Hope it helps.



Could you possibly help me figure out why my method didn't work for solving:

I combined their two rates, and came up with \frac{7}{60} per day, so the whole job, combined, would have taken them \frac{60}{7}, or 8 4/7 days to complete. The husband left 5 days before this, so they worked together for 3 4/7 days, or \frac{25}{7}. The amount of work they completed was \frac{7}{60}* \frac{25}{7}=25/60 of the job. This leaves \frac{35}{60}of the job for the wife to complete alone. She can work at a rate of 4/60 per day. So that means she completed the remaining 35/60 in 8 3/4 days, not 5. This combined with the 3 4/7 that they worked on it together gives you a number of about 12.32, which is obviously not correct. Where did I go wrong? I'm having trouble reconciling how the wife only needed 5 days working at the rate given, when we can see how much work they did combined, and it leaves more than 5 days worth of work for her.


If they work together they can complete the job in 60/7 days. But if one of them does not work for all that period then the time to complete would increase. Thus you cannot say that when husband left 5 days before, then they worked together for 60/7-5 days.

Hope it's clear.



absolutely, thank you!
Intern
Intern
avatar
Joined: 21 May 2013
Posts: 8
Followers: 0

Kudos [?]: 1 [0], given: 7

Re: A husband and wife started painting their house, but husband [#permalink] New post 27 Apr 2014, 09:46
johnnybravo86 wrote:
A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days?

A. 40/7
B. 50/7
C. 75/7
D. 55/7


Here's my simple solution.

Let total time taken for the job together = T
Husband worked for days = T-5
Wife worked for days = T

Then, according to individual rates,

(T-5)/20 + T/15 = 1
=> 35T = 375
or, T = 75/7

Ans. C. 75/7
Senior Manager
Senior Manager
avatar
Joined: 28 Apr 2014
Posts: 290
Followers: 0

Kudos [?]: 23 [0], given: 46

GMAT ToolKit User
Re: Work & Rate problem [#permalink] New post 28 Apr 2014, 02:39
Bunuel wrote:
A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days?
A. 40/7
B. 50/7
C. 75/7
D. 55/7

As pointed out above there are several ways to solve this problem. Below are probably two shortest approaches:

Approach #1:
Rate of husband \frac{1}{20} job/day;
Rate of wife \frac{1}{15} job/day;
Combined rate: \frac{1}{20}+\frac{1}{15}=\frac{7}{60} job/day;

During the last 5 days, when the wife worked alone, she completed \frac{5}{15}=\frac{1}{3}rd of the job;
Hence, remaining \frac{2}{3}rd of the job was done by them working together in time=\frac{job'}{rate}=\frac{(\frac{2}{3})}{(\frac{7}{60})}=\frac{40}{7} days;

Total time needed to complete the whole job: 5+\frac{40}{7}=\frac{75}{7} days.

Answer: C.

Approach #2:
It's based on observing the answer choices. On the PS section always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question.

Combined rate of the husband and wife is \frac{7}{60} job/day, which means that working together they'll complete the job in \frac{60}{7} days (time is reciprocal of rate). As they worked together only some part of the total time, then actual time would be more than \frac{60}{7} days. Only \frac{75}{7} is more than this value (answer choice C), so it must be correct.

Answer: C.

Hope it helps.



Approach # 2 definitely the smart way to think and work over here !!
Re: Work & Rate problem   [#permalink] 28 Apr 2014, 02:39
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic In England before 1660, a husband controlled his wife's rs2010 12 03 Apr 2009, 13:49
Clark and Florence Wallace, a husband-and-wife medical team, binho12 1 09 Oct 2006, 05:08
Clark and Florence Wallace, a husband-and-wife medical team, rkatl 11 28 Jul 2006, 06:36
Clark and Florence Wallace, a husband-and-wife medical team, gmacvik 5 16 Jan 2006, 23:09
Clark and Florence Wallace, a husband-and-wife medical team, nakib77 6 26 Oct 2005, 12:06
Display posts from previous: Sort by

A husband and wife started painting their house, but husband

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page   Previous    1   2   [ 33 posts ] 



GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.