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

 It is currently 18 Oct 2019, 14:37

### 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

# Working alone, Manuel finishes cleaning half the house in a third of

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58453
Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

### Show Tags

12 Oct 2015, 22:20
2
10
00:00

Difficulty:

35% (medium)

Question Stats:

76% (02:03) correct 24% (02:14) wrong based on 337 sessions

### HideShow timer Statistics

Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together?

A. 1.5
B. 2
C. 2.4
D. 3
E. 3.6

Kudos for a correct solution.

_________________
Intern
Joined: 15 Aug 2014
Posts: 18
GMAT 1: 670 Q49 V33
Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

### Show Tags

12 Oct 2015, 22:40
3
1
Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone.

Manuel alone cleans the entire house in 6 hours.=>Manuel alone cleans the HALF OF entire house in 3 hours,WHICH IS
in a third of the time it takes Nick to clean the entire house alone.

SO,3 = 1/3 *time it takes Nick to clean the entire house alone
So,Nick takes 9 hours.
So,together,they in 1 hour they will do 1/9 + 1/6. Ans-3.6 hrs
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

### Show Tags

12 Oct 2015, 23:11
1
1
Bunuel wrote:
Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together?

A. 1.5
B. 2
C. 2.4
D. 3
E. 3.6

Kudos for a correct solution.

Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone

i.e. Manuel finishes cleaning FULL house in TWO third of the time it takes Nick to clean the entire house alone

i.e. M = (3/2)N where M and N are efficiencies of Manuel and Nick

Time taken by M to clean House = 6 hours
i.e. Time taken by N to clean House = (3/2)*6 = 9 hours

1 Hour work of both M and N working together = (1/6)+(1/9) = (3+2)/18 = 5/18

5/18 House is cleaned by them together in 1 hours
Full House will be cleaned by them together in 1/(5/18) = 18/5 = 3.6 hours

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Manager
Joined: 02 Jul 2015
Posts: 101
Schools: ISB '18
GMAT 1: 680 Q49 V33
Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

### Show Tags

13 Oct 2015, 05:36
1

Manuel does the complete house in 6 hours while Nick does it in 9 hours. 1/ (1/6+1/9)= 3.6
Senior Manager
Joined: 10 Mar 2013
Posts: 465
Location: Germany
Concentration: Finance, Entrepreneurship
Schools: WHU MBA"20 (A)
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

### Show Tags

13 Oct 2015, 06:10
Bunuel wrote:
Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together?

A. 1.5
B. 2
C. 2.4
D. 3
E. 3.6

Kudos for a correct solution.

Manuel needs 6 Hours to complete the job
Nich needs 9 Hours to complete the job
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660
Intern
Joined: 21 Nov 2014
Posts: 1
Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

### Show Tags

15 Oct 2015, 01:31

1) Nike's time to clean the house is t, Manuel's time to clean 1/2 of the house is 1/3*t.

2) Manuel cleans 1/2 of the house is 3 hours (1/2*6 hours)

3) Nike's time t=1/3*3 = 9 hours

4) Manuel's rate (r1) - 1/6 house/hour; Nike's rate (r2) - 1/9 house/hour. r1+r2 = 1/6 + 1/9 = 5/18.

5) Time to clean the entire house for Nick and Manuel is 18/5 hours = 3.6 hours.
Senior Manager
Joined: 24 Nov 2015
Posts: 490
Location: United States (LA)
Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

### Show Tags

06 May 2016, 13:48
If Manuel cleans the entire house alone in 6 hrs, then he cleans half the house in 3 hrs
But we know that this is 1/3rd the time required by Nick to clean the entire house alone
so Nick requires 9 hrs to clean the the entire house alone
combined rate when both Manuel and Nick work together is
$$\frac{1}{6}$$+ $$\frac{1}{9}$$ = $$\frac{5}{18}$$

Time required = $$\frac{18}{5}$$ = 3.6 hrs

Manager
Joined: 27 Apr 2016
Posts: 93
Location: Brazil
GMAT 1: 610 Q37 V36
GPA: 2.7
WE: Information Technology (Education)
Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

### Show Tags

06 May 2016, 14:26
1
This question is easier than most because if Manuel and and Nick both cleaned the house at the same rate (6 hours / house) they would clean one house together in 3 hours, but since Nick is slower than Manuel, you know very quickly that the answer is > 3, and the only option greater than 3 is 3.6 (E).
_________________
The errant cosmos works against me!
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4009
Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

### Show Tags

15 May 2018, 05:44
Top Contributor
Bunuel wrote:
Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together?

A. 1.5
B. 2
C. 2.4
D. 3
E. 3.6

Kudos for a correct solution.

Another option for many work questions is to assign a nice value to the given job.
Here, a nice value will be one that works well with the given numbers (6 hours, 1/2 the time, 1/3 of the time)
Let's say the entire job of cleaning the house consists of cleaning 36 rooms.

Manuel alone cleans the ENTIRE house in 6 hours.
So, Manuel can clean 36 rooms in 6 hours
So, Manuel's RATE = 6 rooms per HOUR

Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone.
Half the house = 18 rooms
Since Manuel's RATE is 6 rooms per hour, Manuel can clean 18 rooms in 3 hours
We're told that this cleaning time is 1/3 of the time it takes Nick to clean the ENTIRE house alone
So, it must take Nick 9 hours to clean the ENTIRE house alone
The ENTIRE house consists of cleaning 36 rooms.
Rate = output/time
So, Nick's rate = 36/9 = 4 rooms per hour

How many hours will it take Nick and Manuel to clean the entire house if they work TOGETHER?
Manuel's RATE = 6 rooms per hour
Nick's rate = 4 rooms per hour
So, their COMBINED rate = 6 + 4 = 10 rooms per hour

time = output/rate
So, time = 36/10 = 3.6 hours

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

### Show Tags

16 May 2018, 10:42
Bunuel wrote:
Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together?

A. 1.5
B. 2
C. 2.4
D. 3
E. 3.6

We see that Manuel’s rate is 1/6, so it takes him 3 hours to clean half the house. This means it will take Nick 9 hours to clean the entire house. Thus, Nick’s rate is 1/9.

Working together, their combined rate is 1/6 + 1/9 = 3/18 + 2/18 = 5/18, so the time it takes them to clean the entire house is 1/(5/18) = 18/5 = 3.6 hours.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Joined: 01 Apr 2012
Posts: 16
Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

### Show Tags

19 May 2018, 06:15
Bunuel wrote:
Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together?

A. 1.5
B. 2
C. 2.4
D. 3
E. 3.6

Kudos for a correct solution.

Manuel can finish half the house in 1/3 of the time Nick takes
Implies Manuel can complete full house i.e 1/2 x 2 in 1/3 x 2 = 2/3 of the time taken by nick

Nick hourly rate is 1/6
Manuel rate = 2/3 of 1/6 = 1/9
Together 1/6 + 1/9 = 15/54

Or time taken 54/15 = 3.6 hours
Intern
Joined: 17 Apr 2013
Posts: 34
Re: Working alone, Manuel finishes cleaning half the house in a third of  [#permalink]

### Show Tags

08 Oct 2018, 15:36
I can rewrite as the following:

1/3:1/2=6:x since Manuel alone cleans the entire house in 6 hours"
So, x=9.
When they work together, it can be expressed as the following rates:
1/6+1/3=1/h
or (9+6)/54=15/54=1/h
h=54/15=3.6
Re: Working alone, Manuel finishes cleaning half the house in a third of   [#permalink] 08 Oct 2018, 15:36
Display posts from previous: Sort by