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

 It is currently 12 Dec 2018, 21:22

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### The winning strategy for 700+ on the GMAT

December 13, 2018

December 13, 2018

08:00 AM PST

09:00 AM PST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
• ### GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

December 14, 2018

December 14, 2018

09:00 AM PST

10:00 AM PST

10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

# D01-30

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51122

### Show Tags

15 Sep 2014, 23:12
00:00

Difficulty:

35% (medium)

Question Stats:

76% (01:39) correct 24% (01:54) wrong based on 87 sessions

### HideShow timer Statistics

Painters A and B can paint a house working alone in 20 and 30 days respectively. They started painting a house together but then A left after a number of days but then rejoined B before the job was completed. If B worked alone for 5 days and then A and B together completed the work in 4 days, after how many days of working together, did A leave B?

A. 4
B. 5
C. 6
D. 7
E. 8

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 51122

### Show Tags

15 Sep 2014, 23:13
Official Solution:

Painters A and B can paint a house working alone in 20 and 30 days respectively. They started painting a house together but then A left after a number of days but then rejoined B before the job was completed. If B worked alone for 5 days and then A and B together completed the work in 4 days, after how many days of working together, did A leave B?

A. 4
B. 5
C. 6
D. 7
E. 8

The rate of A is $$\frac{1}{20}$$ job/day;

The rate of B is $$\frac{1}{30}$$ job/day;

The combined rate of A and B is $$\frac{1}{20}+\frac{1}{30}=\frac{1}{12}$$ job/day.

In 5 days that B worked alone (2nd stage) $$5*\frac{1}{30}=\frac{2}{12}$$ of the job was done;

In 4 day that A and B worked together (3rd stage) $$4*\frac{1}{12}=\frac{4}{12}$$ of the job was done;

So, in the 1st stage of the work $$1-\frac{2}{12}-\frac{4}{12}=\frac{6}{12}$$ part of the job was done by A and B together, which at the rate of $$\frac{1}{12}$$ job/day took them 6 days.

_________________
Manager
Joined: 11 Oct 2013
Posts: 106
Concentration: Marketing, General Management
GMAT 1: 600 Q41 V31

### Show Tags

08 Dec 2015, 05:01
2
1
I prefer assuming total work before solving such questions. Helps me to avoid fractions.

ALONE
A finishes work in 20 days
B finishes work in 30 days

Taking LCM of 20 and 30 (Or any convenient common mulitple) --> 120
So if total work is 120, then to finish 120 units of work as per their current rate
A finishes work 120/20 = 6 units per day
B finishes work 120/30 = 4 units per day
Both together finish 6 + 4 = 10 units per day.

Coming back to what's asked -
B alone worked for 5 days, so 4*5 = 20 units of total 120 units is done
Together they worked for 4 hours before finishing the work = 10*4 = 40 units.
We've got 40 + 20 = 60 units done.
120-60 = 60 units pending.
This work is nothing but the work that A & B did together before A left B alone to suffer.
Hence 60/10 = 6 days!

+Kudos, if this helped!
_________________

Its not over..

Intern
Joined: 23 Sep 2015
Posts: 39

### Show Tags

15 Feb 2016, 04:56
I think this the explanation isn't clear enough, please elaborate.
Math Expert
Joined: 02 Aug 2009
Posts: 7106

### Show Tags

15 Feb 2016, 05:24
1
nishantdoshi wrote:
I think this the explanation isn't clear enough, please elaborate.

Hi,
Lets divide the work in two parts, one when B worked alone and second when both worked together..
Since B can finish work in 30 days, His 1 day work = 1/30 of total..
so in 5 days, he will finish= 5/30= 1/6 of work..

now second part, when both work together..
we should not confuse in two different time frames, that is one at the start and other in the end.. we just require how many days both worked together..
one day work of both= 1/20 + 1/30 = 5/60= 1/12..
so they have to finish 1-1/6 work= 5/6..
it will be done in (5/6)/(1/12)= 5*12/6= 10..
so both work for 10 days together..
In the second part they worked for 4 days to finish the work..
so they worked for 10-4=6 days initially..
ans 6

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 29 Nov 2015
Posts: 6

### Show Tags

19 Apr 2016, 22:32
I think this is a high-quality question and I agree with explanation.
Manager
Joined: 23 Apr 2014
Posts: 63
Location: United States
GMAT 1: 680 Q50 V31
GPA: 2.75

### Show Tags

16 Jul 2016, 09:56
I think this is a high-quality question and I agree with explanation.
Manager
Joined: 03 Dec 2013
Posts: 70
Location: United States (HI)
GMAT 1: 660 Q49 V30
GPA: 3.56

### Show Tags

22 Aug 2016, 11:00
I think this is a high-quality question and I agree with explanation. Great question. I freaked out when I first faced it but was able to solve it within 2 mins! Thanks
Intern
Status: Preparation
Joined: 29 Mar 2016
Posts: 12
Location: India
Concentration: General Management, Technology
GPA: 4

### Show Tags

30 Nov 2016, 18:55
I will go with this approach,

rate of A= 1/20 job per day
rate of B = 1/30 job per day

when they work together the no of days required to complete the task = 1/20 + 1/30 = 3+2/60 = 5/60 = 1/12

when A and B were working together let us assume that after X days A left the working while ,
so the work completed in X days by both of them = x * 1/12= x/12

so the work remaining = 1-x/12 = 12-x/12

Now B worked for 5 days , so total work done by B in 5 days = 5*1/30 = 1/6

now the total work remaining = total work remaining after x days - work done alone by B in 5 days
= 12-x/12 - 1/6
= 10-x/12

now A rejoined the work and they both completed the remaining work in 4 days
remaining work = 4 days of work for A and B
10-x/12 = 4/12
10-x = 4
x= 6

so the no of days after which A left working together is 6
Intern
Joined: 02 Jan 2017
Posts: 1

### Show Tags

29 Jan 2017, 06:35
I think this is a poor-quality question and I don't agree with the explanation. 1/20 + 1/30 is not 1/12
Intern
Joined: 13 Mar 2016
Posts: 18
Location: India
Concentration: General Management, Entrepreneurship
WE: General Management (Energy and Utilities)

### Show Tags

29 Jan 2017, 09:18
1
let for x days A worked with B before he left
Now
A worked for X+ 4 days
B worked for X+4+5 ie. X+9 days.

(X+4)/20 + (x+9)/30 =1
solve this you will get X=6
Math Expert
Joined: 02 Sep 2009
Posts: 51122

### Show Tags

29 Jan 2017, 09:20
Abosse0 wrote:
I think this is a poor-quality question and I don't agree with the explanation. 1/20 + 1/30 is not 1/12

Actually it is exactly 1/12.

1/20 + 1/30 = 3/60 + 2/60 = 5/60 = 1/12.
_________________
SVP
Joined: 26 Mar 2013
Posts: 1910

### Show Tags

30 Jan 2017, 08:15
1
Bunuel wrote:
Painters A and B can paint a house working alone in 20 and 30 days respectively. They started painting a house together but then A left after a number of days but then rejoined B before the job was completed. If B worked alone for 5 days and then A and B together completed the work in 4 days, after how many days of working together, did A leave B?

A. 4
B. 5
C. 6
D. 7
E. 8

Given from the prompt:

A & B worked together + B worked alone + A& B joined again to complete work

Combined rate = 1/20+ 1/30 = (3+2)/60=5/60= 1/12 job/day

Let T= time for both A & B together before A leaving B

To solve the question:

Use the standard formula

Work = rate * time

Following the sequence stated by prompt

T *1/12 + 5 *1/30 + 4 *1/12 = 1 .............( the work here is one house)

T /12 + 1/6 + 1/3 = 1

T /12 + 3/6= 1

T /12 = 1/2 .......T=6

Intern
Joined: 20 Apr 2017
Posts: 2
GMAT 1: 680 Q46 V35
GPA: 3.37

### Show Tags

18 May 2017, 01:58
I think this is a high-quality question.
Intern
Joined: 22 May 2017
Posts: 1
Location: United States (TX)
Concentration: General Management, Strategy
GMAT 1: 680 Q50 V32
GPA: 3.24
WE: Supply Chain Management (Energy and Utilities)

### Show Tags

07 Jul 2017, 11:38
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 13 Oct 2017
Posts: 39

### Show Tags

15 Mar 2018, 10:57
swanidhi wrote:
I prefer assuming total work before solving such questions. Helps me to avoid fractions.

ALONE
A finishes work in 20 days
B finishes work in 30 days

Taking LCM of 20 and 30 (Or any convenient common mulitple) --> 120
So if total work is 120, then to finish 120 units of work as per their current rate
A finishes work 120/20 = 6 units per day
B finishes work 120/30 = 4 units per day
Both together finish 6 + 4 = 10 units per day.

Coming back to what's asked -
B alone worked for 5 days, so 4*5 = 20 units of total 120 units is done
Together they worked for 4 hours before finishing the work = 10*4 = 40 units.
We've got 40 + 20 = 60 units done.
120-60 = 60 units pending.
This work is nothing but the work that A & B did together before A left B alone to suffer.
Hence 60/10 = 6 days!

+Kudos, if this helped!

Hi Experts,

I'm familiar with the LCM method - I picked that up from Economist GMAT...however, I'm still struggling with the logic of the final stage I highlighted...What's the logic behind how we know to use the combined rate and the remaining 60 units to get 6 days?

Best wishes,

Tosin
Intern
Joined: 22 Dec 2016
Posts: 1
Location: United States (NC)
GMAT 1: 710 Q47 V40
GPA: 3.63

### Show Tags

28 May 2018, 10:49
I solved by setting up a table and following the story in the problem.

W R T
Painter A 60 60 / 20 = 3 20
Painter B 60 60 / 30 = 2 30
combined 60 3 + 2 = 5 12

Painter B worked alone for 5 days at a rate of 2 (things) per day for a total of 10 (things)
Painters A and B worked together for 4 days at a rate of 5 (things) per day for a total of 20 (things)

1 whole house = 60 (things)

60 - 10 - 20 = 30 (things) that A and B worked on together at their combined rate

30 / 5 = 6 days
Intern
Joined: 12 Sep 2016
Posts: 10
GMAT 1: 640 Q44 V34
WE: Accounting (Consulting)

### Show Tags

05 Oct 2018, 00:21
Let's pick up a Number which is the LCM of both of A and B's rates, for eg. 60.
Here, let 60 be the total units of work to be done.

So, if A takes 20 days to finish 60 units, it means he accomplishes 60/20= 3 units per day.
Similarly, if B takes 30 days to finish 60 units, he accomplishes 60/30= 2 units per day

Now, the total work done by them in 1 day= 3+2= 5 units.

For the 5 days B worked by himself, he gets 5*2 units= 10 units done.
The 4 days A and B work together in the end, they get 4* 5 units= 20 units done.
Total work done= 30 units.
Leftover work= 60-30 units= 30 units. This is the work that A and B must have done together, before A left.

So, given the combined rate, A and B together must have done 30 units in 30/5= 6 days!
Intern
Joined: 15 Jan 2018
Posts: 4

### Show Tags

07 Nov 2018, 20:49
I think this is a poor-quality question and I agree with explanation. The comment mentions that A left but B rejoined, rather than A rejoined.
Re D01-30 &nbs [#permalink] 07 Nov 2018, 20:49
Display posts from previous: Sort by

# D01-30

Moderators: chetan2u, Bunuel

 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®.