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

 It is currently 09 Dec 2019, 13:55

### 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

# Angela, Bernie, and Colleen can complete a job, all working together,

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59622
Angela, Bernie, and Colleen can complete a job, all working together,  [#permalink]

### Show Tags

14 Jul 2015, 00:56
1
00:00

Difficulty:

5% (low)

Question Stats:

94% (00:57) correct 6% (02:08) wrong based on 98 sessions

### HideShow timer Statistics

Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?

A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours

Kudos for a correct solution.

_________________
Manager
Joined: 26 Dec 2011
Posts: 115
Schools: HBS '18, IIMA
Re: Angela, Bernie, and Colleen can complete a job, all working together,  [#permalink]

### Show Tags

14 Jul 2015, 01:57
Bunuel wrote:
Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?

A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours

Kudos for a correct solution.

Solution -
A+B+C complete the job in 4 hours.
A+B complete the job in 5 hours.

A+B and C complete the job in 4 hours --> 1/(A+B) + 1/C = 1/4 -->1/5+1/C=1/4 ----> C=20 hours. ANS E
CEO
Joined: 20 Mar 2014
Posts: 2560
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Angela, Bernie, and Colleen can complete a job, all working together,  [#permalink]

### Show Tags

14 Jul 2015, 04:16
Bunuel wrote:
Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?

A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours

Kudos for a correct solution.

Let A,B,C denote the hours in which Anglea, Bernie and Colleen can finish the jobs individually.

Thus (1/A)+ (1/B)+(1/C) = 1/4 and (1/A)+(1/B) = 1/5 ----> 1/C = 1/20 ---> C = 20 Hours. Thus E is the correct answer.
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: Angela, Bernie, and Colleen can complete a job, all working together,  [#permalink]

### Show Tags

14 Jul 2015, 05:33
Bunuel wrote:
Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?

A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours

Kudos for a correct solution.

Let, Total work = 20 Units

All working together, in 4 hours finish work = 20 Units
i.e. All working together, in 1 hour finish work = 20/4 = 5 Units

Angela and Bernie, working together at their respective rates, can complete in 5 hours = 20 Units
i.e. Angela and Bernie, working together at their respective rates, can complete in 1 hours = 20/5 = 4 Units

i.e. 1 hour work of Colleen = 5 - 4 = 1 Unit
i.e. Time taken by Colleen to finish 20 unit work = 20*1 = 20 days

_________________
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
Senior Manager
Joined: 28 Jun 2015
Posts: 279
Concentration: Finance
GPA: 3.5
Re: Angela, Bernie, and Colleen can complete a job, all working together,  [#permalink]

### Show Tags

14 Jul 2015, 06:53
Let the work done by Angela (A), Bernie (B), and Colleen (C) per hour => 1/A + 1/B + 1/C = 1/4

1/A + 1/B = 1/5

So, 1/C = 1/4 - 1/5 = 5-4/20 = 1/20 = 20 hours. Ans (E).
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
Manager
Joined: 20 Jul 2011
Posts: 78
GMAT 1: 660 Q49 V31
Re: Angela, Bernie, and Colleen can complete a job, all working together,  [#permalink]

### Show Tags

18 Jul 2015, 06:39
Bunuel wrote:
Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?

A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours

Kudos for a correct solution.

Work done in one hour => 1/A + 1/B + 1/C = 1/4 and 1/A + 1/B = 1/5

Hence 1/C = 1/4 - 1/5 = 1/20 => C = 20 hours to complete the job alone

Option E
Math Expert
Joined: 02 Aug 2009
Posts: 8289
Re: Angela, Bernie, and Colleen can complete a job, all working together,  [#permalink]

### Show Tags

18 Jul 2015, 06:43
1
Bunuel wrote:
Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?

A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours

Kudos for a correct solution.

one hour work of all three - one hour work of two other than C=one hour work of C..
$$\frac{1}{4}-\frac{1}{5}=\frac{1}{20}$$..
ans 20 E
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 59622
Re: Angela, Bernie, and Colleen can complete a job, all working together,  [#permalink]

### Show Tags

19 Jul 2015, 13:26
Bunuel wrote:
Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 5 hours. How long would it take Colleen, working alone, to complete the entire job?

A. 8 hours
B. 10 hours
C. 12 hours
D. 16 hours
E. 20 hours

Kudos for a correct solution.

800score Official Solution:

If Angela, Bernie, and Colleen can complete a job in 4 hours, they can complete 1/4 of the job in an hour. Furthermore, if Angela and Bernie can complete the same job in 5 hours, they can do 1/5 of the entire job in an hour.

If the three of them can do 1/4 of a job in an hour, and without Colleen the other two can do 1/5 of a job in an hour, then the amount of the job Colleen can do in an hour is the difference of these results:
1/4 – 1/5 = 5/20 – 4/20 = 1/20.

Since Colleen can do 1/20 of the job in an hour, it will take her 20 hours to do the entire job by herself.

The correct answer is choice (E).
_________________
Re: Angela, Bernie, and Colleen can complete a job, all working together,   [#permalink] 19 Jul 2015, 13:26
Display posts from previous: Sort by