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

 It is currently 21 Oct 2019, 01:39 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.  Six machines, each working at the same constant rate

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Manager  Joined: 27 Feb 2010
Posts: 79
Location: Denver
Six machines, each working at the same constant rate  [#permalink]

Show Tags

2
63 00:00

Difficulty:   15% (low)

Question Stats: 80% (01:23) correct 20% (01:37) wrong based on 869 sessions

HideShow timer Statistics

Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?

A. 2
B. 3
C. 4
D. 6
E. 8
Math Expert V
Joined: 02 Sep 2009
Posts: 58409
Re: Help! GMATPrep question  [#permalink]

Show Tags

31
67
Welcome to GMAT Club. Below is a solution for the question. Hope it helps

Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?
A. 2
B. 3
C. 4
D. 6
E. 8

Let $$x$$ be the time needed for 1 machine to complete the job, so rate of one machine is $$\frac{1}{x}$$ (rate is the reciprocal of time) --> rate of 6 machines would be $$\frac{6}{x}$$.

As $$job=time*rate$$ --> $$1=12*\frac{6}{x}$$ --> $$x=72$$ days needed for 1 machine to complete the job.

To complete the job in 8 days $$\frac{72}{8}=9$$ machines are needed.

Difference: 9-6=3.

_________________
Senior Manager  Joined: 23 Oct 2010
Posts: 323
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38 Re: Help! GMATPrep question  [#permalink]

Show Tags

46
10
6 machines in 12 hours can make 6*12=72 units.
x machines in 8 hours can make x*8=72 units x=9

12-9=3 more machines are needed
hope it helps
_________________
Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth
General Discussion
Manager  Joined: 01 Feb 2010
Posts: 178
Re: Six machines, each working at the same constant rate  [#permalink]

Show Tags

6
zz0vlb wrote:
Six machines, each working at the same constant rate, together can complete a certain job in 12 days.
How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?
a.2
b.3
c.4
d.6
e.8

Source: GMAT Prep

let each machine work at rate of x days
1/x+1/x+1/x+1/x+1/x+1/x = 1/12
6/x = 1/12
x = 72
now y is number of machines needed to complete job in 8 days so,
y/72 = 1/8
y = 9
required = y-x = 3 hence b.
Manager  Joined: 12 Jan 2010
Posts: 223
Schools: DukeTuck,Kelogg,Darden
Re: Six machines, each working at the same constant rate  [#permalink]

Show Tags

10
zz0vlb wrote:
Six machines, each working at the same constant rate, together can complete a certain job in 12 days.
How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?

a.2
b.3
c.4
d.6
e.8

Source: GMAT Prep

Another solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 12 to 8. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original.

So 3/2* 6 = 9

So we need 9-6 = 3 more machines.
_________________
Run towards the things that make you uncomfortable daily. The greatest risk is not taking risks
http://gmatclub.com/forum/from-690-to-730-q50-v38-97356.html
Math Expert V
Joined: 02 Sep 2009
Posts: 58409
Six machines, each working at the same constant rate  [#permalink]

Show Tags

7
17
Intern  Joined: 28 Mar 2010
Posts: 26
Re: Six machines, each working at the same constant rate  [#permalink]

Show Tags

10
2
Actually, this was more simple than I thought. When I first saw this, I started to panic thinking it's a rate question. But then I took a step back, and it was the simplest of calculations.

So here's the deal:

12 days -> 6 machines: 8 days -> ?

8 days means you definitely need more machines than the 6 and in such case the equation looks like-

12 * 6 = 8 * x

Therefore, x = 72 / 8 = 9

So 9-6=3 more machines
Senior Manager  B
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 273
Re: GMAT PREP (PS)  [#permalink]

Show Tags

2
1

6 machines require 12 days = 72 machine days
how many machines to do the job in 8 days = $$\frac{72 machine-days}{8 days} = 9 machines$$

so, 3 more machines.
Manager  Joined: 10 Jan 2010
Posts: 139
Location: Germany
Concentration: Strategy, General Management
Schools: IE '15 (M)
GPA: 3
WE: Consulting (Telecommunications)
Re: Six machines, each working at the same constant rate  [#permalink]

Show Tags

1
6*12 = 72 units --> 72Units / 8hours = X --> X = 9

Manager  Status: Bunuel's fan!
Joined: 08 Jul 2011
Posts: 128
Re: Six machines, each working at the same constant rate  [#permalink]

Show Tags

3
This is how I did it

6 machines in 1hr do 1/12 job
in 1 hr, 1 machine do 1/(12*6) job
In 8 days 1 machine do 8/(12*6)=1/9

Thus there is a need of 9 machine.

But I forgot to minus and get the difference so still get this question wrong.
Senior Manager  Joined: 13 Aug 2012
Posts: 401
Concentration: Marketing, Finance
GPA: 3.23
Re: Six machines, each working at the same constant rate  [#permalink]

Show Tags

4
3
$$Rate of machine = \frac{1}{m}$$

Draw the equation for 6 machines take 12 days:
$$\frac{6}{m}=\frac{1}{12}$$
$$m=72 days$$

Let's look for the number of machines to work for 8 days:
$$\frac{N}{72}=\frac{1}{8}$$
$$N=\frac{72}{8}=9 machines$$

Answer: 9 - 6 machines = 3 machines more

B
_________________
Impossible is nothing to God.
Intern  Status: Tougher times ...
Joined: 04 Nov 2012
Posts: 35
Location: India
GMAT 1: 480 Q32 V25 WE: General Management (Manufacturing)
Six machines, each working at the same constant rate, together c  [#permalink]

Show Tags

9
3
njss750 wrote:
6 machines each working @ the same constant rate together can complete a certain job in 12 days. How many additional machines are reqd (each working at same constant rate) to finish the job in 8 days?
2
3
4
6
8

Pl xplain with wkgs

6 x 12 = (6+x) x 8

9 = 6+x

x=3
_________________
Kabilan.K
Kudos is a boost to participate actively and contribute more to the forum Tutor Joined: 20 Apr 2012
Posts: 97
Location: Ukraine
GMAT 1: 690 Q51 V31 GMAT 2: 730 Q51 V38 WE: Education (Education)
Re: 6 machines each working @ the same constant rate together  [#permalink]

Show Tags

11
You can solve this problem without any equations. Just to calculate the rate of 1 machine.

The rate of 1 machine is $$\frac{1}{6*12}=\frac{1}{72}$$ part per day.

So, 1 machine in 8 days can do $$\frac{8}{72}=\frac{1}{9}$$.

So, to finish the job in 8 days we need 9 machines. Therefore 3 additional machines are required.

The answer is B.
_________________
I'm happy, if I make math for you slightly clearer
And yes, I like kudos:)
Intern  Joined: 24 Mar 2011
Posts: 40
Location: India
Concentration: Marketing, Operations
Schools: Schulich '16 (A)
GMAT 1: 690 Q48 V36 WE: Operations (Telecommunications)
Re: Six machines, each working at the same constant rate  [#permalink]

Show Tags

1
srkaleem wrote:
Six machines, each working at the same constant rate, together can complete a job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

A. 2
B. 3
C. 4
D. 6
E. 8

Somehow, I found below method to be working for me -
6 Machines in 12 Days do 1 Work i.e. in notation form
6M * 12D = 1W,
so 1M * 1D = [1/(6*12)] W
How many Machines in 8 Days will complete 1 Work? i.e.
xM * 8D = [(x*8)/(6*12)] W = 1W

Solving for x in [(x*8)/(6*12)] = 1, we get x = 9 i.e. 9 Machines in 8 Days will do 1 Work. So 9-6=3 Machines more are required.

Ans - B
Senior Manager  Joined: 10 Jul 2013
Posts: 289
Re: Six machines, each working at the same constant rate  [#permalink]

Show Tags

2
1
srkaleem wrote:
Six machines, each working at the same constant rate, together can complete a job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

A. 2
B. 3
C. 4
D. 6
E. 8

Here, 6 × 1/X = 1/12 or, X=72 . 2nd case, n × 1/72 = 1/8 or, n = 9 . additional = 9-6 = 3
_________________
Asif vai.....
Intern  Joined: 27 Mar 2014
Posts: 5
Concentration: Accounting
GMAT Date: 09-04-2014
GPA: 4
Re: Six machines, each working at the same constant rate  [#permalink]

Show Tags

1
since machine and work in inversely related. thus it is inverse proportion

6 x 12 = 8 x N (let n be the number of person required.)

N=9

thus the number of additional person is 9-6 = 3
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1747
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Six machines, each working at the same constant rate  [#permalink]

Show Tags

2
6 Machines do $$\frac{1}{12}$$ work in 1 day

We require $$\frac{1}{8}$$ work to be done in 1 day

Multiplication factor$$= \frac{\frac{1}{8}}{\frac{1}{12}} = \frac{1}{8} * 12 = \frac{3}{2}$$

Additional machines required $$= 6 * \frac{3}{2} - 6 = 9 - 6 = 3$$

_________________
Kindly press "+1 Kudos" to appreciate Intern  Joined: 10 Dec 2014
Posts: 20
GMAT Date: 12-30-2014
Re: Six machines, each working at the same constant rate  [#permalink]

Show Tags

1
Six Machines:combined rate=6x
Time=12
Let Job be J

6x*12=J

Let M be the number of machines required to complete job in 8 days
Then
Mx*8=J

6x*12=Mx*8

M=9

Is this approach correct??
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15294
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Six machines, each working at the same constant rate  [#permalink]

Show Tags

3
Hi All,

We're told that 6 machines, working at the same constant rate, can finish a job in 12 days. We're asked for the number of EXTRA machines will you need to finish the job in 8 days?

This type of question is easiest to solve if you convert the info into "work units" Here, we start with 6 machines working for 12 days. This equals (6)(12) = 72 machine-days of work to finish the job.

If we wanted to finish the job in 8 days, it would still take 72 machine-days of work, so we'd need 72/8 = 9 machines.

We already have 6 machines, so we need 3 MORE machines to get the job done in 8 days.

GMAT assassins aren't born, they're made,
Rich
_________________
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8117
Location: United States (CA)
Re: Six machines, each working at the same constant rate  [#permalink]

Show Tags

2
srkaleem wrote:
Six machines, each working at the same constant rate, together can complete a job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

A. 2
B. 3
C. 4
D. 6
E. 8

We are given that six machines, each working at the same constant rate, together can complete a certain job in 12 days. Since rate = work/time and if we consider work as 1, the rate of the six machines is 1/12.

We need to determine how many additional machines, each working at the same constant rate, will be needed to complete the same job in 8 days. In other words we need to determine how many additional machines are needed to work at a rate of 1/8. Since each machine works at the same constant rate, we can use a proportion to first determine the number of machines needed to work at the rate of 1/8.

Our proportion is as follows: 6 machines is to a rate of 1/12 as x machines is to a rate of 1/8.

6/(1/12) = x/(1/8)

72 = 8x

x = 9

So we need 9 – 6 = 3 more machines.

_________________

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: Six machines, each working at the same constant rate   [#permalink] 25 Jun 2018, 12:12

Go to page    1   2    Next  [ 25 posts ]

Display posts from previous: Sort by

Six machines, each working at the same constant rate

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  