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

 It is currently 07 Dec 2019, 12:39 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Three copying machines A, B, and C, working together at their

Author Message
TAGS:

### Hide Tags

e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
Three copying machines A, B, and C, working together at their  [#permalink]

### Show Tags 00:00

Difficulty:   5% (low)

Question Stats: 81% (01:15) correct 19% (01:19) wrong based on 199 sessions

### HideShow timer Statistics

Solve Time and Work Problems Efficiently using Efficiency Method! - Exercise Question #1

Three copying machines A, B, and C, working together at their respective constant rates, can do a copying work in 2 hours. B and C, working together at their respective constant rates, can do the same copying job in 4 hours. How many hours would it take A, working alone at its constant rate, to do the same job?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours

To solve question 2: Question 2

To read the article: Solve Time and Work Problems Efficiently using Efficiency Method!

_________________

Originally posted by EgmatQuantExpert on 23 May 2018, 04:12.
Last edited by EgmatQuantExpert on 13 Aug 2018, 05:56, edited 1 time in total.
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4834
Location: India
GPA: 3.5
Re: Three copying machines A, B, and C, working together at their  [#permalink]

### Show Tags

EgmatQuantExpert wrote:
Three copying machines A, B, and C, working together at their respective constant rates, can do a copying work in 2 hours. B and C, working together at their respective constant rates, can do the same copying job in 4 hours. How many hours would it take A, working alone at its constant rate, to do the same job?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours

Let the total work be 4 units...

So, Efficiency of A + B + C = 2 unit/hr.

Further Efficiency of B + C = 1 unit/hr

So, Efficiency of A = 1 unit/Hr

So, the time required by A to complete the work will be 4 Hours, answer must be (C)
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
Re: Three copying machines A, B, and C, working together at their  [#permalink]

### Show Tags

2

Solution

Given:
In this question it is mentioned that
• Three printing presses A, B, and C, working together at their respective constant rates, take 2 hours to do a certain printing job.
• However, if only B and C are working, they can complete the same printing job in 4 hours.

To find:
• The number of days A alone will take to complete the job

Approach and Working:
As the job remains same, we can assume the total job to be the 12 units (multiple of the LCM of 2 and 4)
• A, B, and C together take 2 hours to complete 12 units of work
• Therefore, in 1 hour all of them will do $$\frac{12}{2}$$ = 6 units of work
• B and C together take 4 hours to complete 12 units of work
• Therefore, in 1 hour they will do $$\frac{12}{4}$$ = 3 units of work
Now, in 1-hour time, A, B, and C together do 6 units, out of which B and C do 3 units work
• Therefore, in 1 hour, A will do (6 – 3) = 3 units of work
So, working alone at this constant rate, A will take $$\frac{12}{3}$$ days = 4 hours to complete the same job.

Hence, the correct answer is option C.

Important Observation

• As mentioned in the article, when we assume the total job to be the LCM of the given number of hours, the calculation becomes much easy as we can avoid fractional calculations. However, in this case we have assumed the total job to be a multiple of the LCM, which shows not only the LCM but any multiple of LCM value can give you the same answer.

_________________

Originally posted by EgmatQuantExpert on 26 May 2018, 11:35.
Last edited by EgmatQuantExpert on 26 May 2018, 13:11, edited 2 times in total.
Director  V
Joined: 12 Feb 2015
Posts: 959
Re: Three copying machines A, B, and C, working together at their  [#permalink]

### Show Tags

2
The rate at which A,B & C work together is $$\frac{1}{2}$$ [i.e. half of one work is done in one hour by A, B & C working together]
The rate at which B & C work together is $$\frac{1}{4}$$ [i.e. one-fourth of one work is done in one hour by B & C working together]
The rate at which A works is $$\frac{1}{2}-\frac{1}{4} = \frac{1}{4}$$ [i.e. one-fourth of one work is done in one hour by Machine A alone]
Therefore the time taken by A alone is 4 hours.
_________________
________________
Manish "Only I can change my life. No one can do it for me"
Director  V
Joined: 12 Feb 2015
Posts: 959
Re: Three copying machines A, B, and C, working together at their  [#permalink]

### Show Tags

LCM Method:-

A, B & C working together take 2 hours
B & C working together take 4 hours
A alone ?

LCM of 2 & 4 is 4 therefore:-
A, B & C working together make 4/2, i.e. 2 units per hour
B & C working together make 4/4, i.e. 1 units per hour
There A alone will make 1 units per hour. To make 4 units, Machine A will take 4 hours at the rate of 1 units per hour
_________________
________________
Manish "Only I can change my life. No one can do it for me"
Intern  B
Joined: 16 May 2017
Posts: 48
GPA: 3.8
WE: Medicine and Health (Health Care)
Re: Three copying machines A, B, and C, working together at their  [#permalink]

### Show Tags

Rate of work of A,B & C together=1/2 (work/hr)
Rate of work of B & C together=1/4 (work/hr)
Rate of work of A=1/2-1/4= 1/4 (work/hr)
So, time taken by A to finish job alone= 4 hrs

Ans-(C)
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8622
Location: United States (CA)
Re: Three copying machines A, B, and C, working together at their  [#permalink]

### Show Tags

EgmatQuantExpert wrote:
Solve Time and Work Problems Efficiently using Efficiency Method! - Exercise Question #1

Three copying machines A, B, and C, working together at their respective constant rates, can do a copying work in 2 hours. B and C, working together at their respective constant rates, can do the same copying job in 4 hours. How many hours would it take A, working alone at its constant rate, to do the same job?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours

Let a, b, and c be the number of hours A, B, and C take to finish the job alone, respectively. Their respective rates are 1/a, 1/b, and 1/c. We have:

1/a + 1/b + 1/c = 1/2

and

1/b + 1/c = 1/4

Subtracting the second equation from the first, we have:

1/a = 1/4

a = 4

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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. Re: Three copying machines A, B, and C, working together at their   [#permalink] 13 Apr 2019, 19:15
Display posts from previous: Sort by

# Three copying machines A, B, and C, working together at their  