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

 It is currently 15 Feb 2019, 23:27

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

February 16, 2019

February 16, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# Working simultaneously and independently at an identical

Author Message
TAGS:

### Hide Tags

Manager
Joined: 28 Aug 2010
Posts: 172
Working simultaneously and independently at an identical  [#permalink]

### Show Tags

10 Dec 2010, 05:21
1
38
00:00

Difficulty:

25% (medium)

Question Stats:

79% (01:58) correct 21% (02:27) wrong based on 902 sessions

### HideShow timer Statistics

Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?

A. 24
B. 18
C. 16
D. 12
E. 8
Math Expert
Joined: 02 Sep 2009
Posts: 52905

### Show Tags

10 Dec 2010, 05:37
6
7
ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?
A. 24
B. 18
C. 16
D. 12
E. 8

The rate of 4 machines is rate=job/time=x/6 units per day --> the rate of 1 machine 1/6*(x/6)=x/24 units per day;

Now, again as {time}*{combined rate}={job done} then 4*(m*x/24)=3x --> m=18.

Or as 3 times more job should be done in 1.5 times less days than 3*1.5=4.5 times more machines will be needed 4*4.5=18.

_________________
Manager
Status: swimming against the current
Joined: 24 Jul 2009
Posts: 185
Location: Chennai, India

### Show Tags

10 Dec 2010, 05:33
9
4
ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a
certain type can produce a total of x units of product P in 6 days. How many of these
machines, working simultaneously and independently at this constant rate, can produce a
total of 3x units of product P in 4 days?
A. 24
B. 18
C. 16
D. 12
E. 8

4 machines and 6 days so the total work done is 24

4x6=24
now 3 times the work is 72

So in 4 days if the work is to be completed its 72/4 = 18
_________________

Gonna make it this time

##### General Discussion
Manager
Joined: 25 Jun 2012
Posts: 62
Location: India
WE: General Management (Energy and Utilities)

### Show Tags

21 Sep 2012, 10:16
1
1
Rate*Time = Work
(4R)*(6)=x ( Total 4 machines)
therefore R=x/24

now again (n)*(x/24)*(4) = 3x

solving for n, we get n=18 nos.
Director
Joined: 22 Mar 2011
Posts: 599
WE: Science (Education)

### Show Tags

21 Sep 2012, 11:42
6
1
ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a
certain type can produce a total of x units of product P in 6 days. How many of these
machines, working simultaneously and independently at this constant rate, can produce a
total of 3x units of product P in 4 days?
A. 24
B. 18
C. 16
D. 12
E. 8

4 machines----------x units-----------6days
4 machines---------3x units-----------3*6 = 18 days
M machines---------3x unites----------4 days
The number of days and the number of machines which produce a certain number of units (in this case 3x) are inversely proportional.
This is because all the machines have the same constant rate.
Necessarily 4*18=M*4, therefore M = 18.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

SVP
Joined: 14 Apr 2009
Posts: 2279
Location: New York, NY

### Show Tags

21 Sep 2012, 14:19
3
1
This is a variation of the Distance = Rate * Time

Except we modify and say Output = # Machines * (Rate * Time)

X = # * r*t

X = 4 * r * 6
x = 24r
r = x/24

Solve for r because we want to find out the rate...then apply that rate to the new situation, which is output of 3x in 4 days

3x = N * r * 4

3x = N * (x/24) * 4
3x = N * (x/6)

18x = N *x
18 = N
Senior Manager
Joined: 13 Aug 2012
Posts: 420
Concentration: Marketing, Finance
GPA: 3.23
Re: Working simultaneously and independently at an identical  [#permalink]

### Show Tags

14 Nov 2012, 05:50
$$\frac{4}{m}=\frac{x}{6}==>m=\frac{24}{x}$$

Calculate number of machines to produce 3x in 4 days:

$$N(\frac{x}{24})(4)=3x==> N=18$$
_________________

Impossible is nothing to God.

Intern
Joined: 31 Aug 2014
Posts: 22
Re: Working simultaneously and independently at an identical  [#permalink]

### Show Tags

14 Sep 2015, 05:54
5
ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?

A. 24
B. 18
C. 16
D. 12
E. 8

solving in shortcut

m1 d1 h1 / w1 = m2 d2 h2/w2
4x6/x = mx4/3x

solving we get m=18

press kudos if you love my shortcut
_________________

Please press+ 1kudos if you appreciate this post and for motivation !!

Intern
Joined: 09 Apr 2016
Posts: 1
Re: Working simultaneously and independently at an identical  [#permalink]

### Show Tags

09 Apr 2016, 14:05
3
4 machines can do x work in 6 days
4 machines can do x/6 work in 1 day
1 machine can do x/6*1/4 work in 1 day

so,

n machines in 4 days= 3x work
n machines in 1 day = n * (x/6*1/4)
n machines in 4 days = n * (x/6*1/4)*4

Hence, n machines can do n*(x/6*1/4)*4 work in 4 days i.e. n*(x/6*1/4)*4 =3x ====>>>> n=18
Manager
Joined: 25 Jun 2016
Posts: 60
GMAT 1: 780 Q51 V46
Re: Working simultaneously and independently at an identical  [#permalink]

### Show Tags

08 Jan 2017, 16:41
1
3
Here's a way to solve this question quickly:

Here's a more in-depth look at a reliable approach for combined work questions with multiple identical machines:

Current Student
Joined: 20 Jan 2017
Posts: 58
Location: United States (NY)
Schools: CBS '20 (A)
GMAT 1: 750 Q48 V44
GMAT 2: 610 Q34 V41
GPA: 3.92
Re: Working simultaneously and independently at an identical  [#permalink]

### Show Tags

30 Jan 2017, 03:45
3
1) First let's set up an equation for the 4 machines and find a rate of each machine: $$4r*6=x; 4r=\frac{x}{6}, r=\frac{x}{6}*\frac{1}{4}, r=\frac{x}{24}$$
2) Now let's set up an equation for 3x units: let N be the number of machines, then $$N*\frac{x}{24}*4=3x; N*\frac{x}{6}=3x, N=\frac{3x}{x/6}=18$$

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2827
Re: Working simultaneously and independently at an identical  [#permalink]

### Show Tags

02 Feb 2017, 10:58
1
1
ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?

A. 24
B. 18
C. 16
D. 12
E. 8

We are given that 4 machines can complete x units in 6 days. Thus, the rate of the 4 machines is x/6.

Next we need to determine the number of machines needed to produce a rate of 3x/4. To calculate that number of machines, we can use the following proportion in which the value in each numerator is the number of machines and the value in each denominator is the corresponding rate of those machines. We can let n = the number of machines needed:

4/(x/6) = n/(3x/4)

24/x = 4n/3x

72x = 4nx

18 = n

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 273
Re: Working simultaneously and independently at an identical  [#permalink]

### Show Tags

21 Jul 2017, 04:00
mailnavin1 wrote:
ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a
certain type can produce a total of x units of product P in 6 days. How many of these
machines, working simultaneously and independently at this constant rate, can produce a
total of 3x units of product P in 4 days?
A. 24
B. 18
C. 16
D. 12
E. 8

4 machines and 6 days so the total work done is 24

4x6=24
now 3 times the work is 72

So in 4 days if the work is to be completed its 72/4 = 18

hi

you said total work done is 24 (4*6), without calculating any rate of any machine. is this because all machines have the same rates ...? please say to me ..

Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 273
Re: Working simultaneously and independently at an identical  [#permalink]

### Show Tags

21 Jul 2017, 04:25
Bunuel wrote:
ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?
A. 24
B. 18
C. 16
D. 12
E. 8

The rate of 4 machines is rate=job/time=x/6 units per day --> the rate of 1 machine 1/6*(x/6)=x/24 units per day;

Now, again as {time}*{combined rate}={job done} then 4*(m*x/24)=3x --> m=18.

Or as 3 times more job should be done in 1.5 times less days than 3*1.5=4.5 times more machines will be needed 4*4.5=18.

hi

"3 times more job should be done in 1.5 times less days than 3*1.5=4.5 times more machines will be needed 4*4.5=18."

i must say beautiful concept. please clarify the science underlying this concept ...

if this was such that 3 times more jobs be done within the same amount of time, 3 times more machines would be needed, provided all machines have the same rates..
if this was such that 3 times more jobs be done in 1.5 times more days, 1.5 times more machines would be needed, provided all machines have the same rates...

am I right ..?

Intern
Joined: 27 Jan 2017
Posts: 1
Working simultaneously and independently at an identical  [#permalink]

### Show Tags

05 Aug 2017, 08:21
Perhaps someone can chime in on my solution -

I've just took the LCM of 4 and 6 to be 12 thus X = 12.

4 Machines create a total product P of 12 in 6 days, working at a rate of 0.5 per machine per day.

We need 3x of product so 3(12) = 36 of product within 4 days.

So how many machines will it take to create 36 units of product at a rate of 0.5 per day within 4 days?

18.

Is this a valid solution? Was easier for me to conceptualize than other more sophisticated answers.
Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 689
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Re: Working simultaneously and independently at an identical  [#permalink]

### Show Tags

05 Aug 2017, 13:34
1
ajit257 wrote:
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?

A. 24
B. 18
C. 16
D. 12
E. 8

This is a wonderful problem to make an educated guess on. Rates & work problems are great for guessing in general.

Four machines make a certain amount of stuff in 6 days. We want to make three times as much stuff. That means we need at least three times as many machines, unless we also get extra time! (We don't.) So, eliminate 8.

We also have fewer days to spend making the stuff than we did originally. So, we can't get away with just having three times as many machines. We need more than three times as many. Eliminate 12.

Do we need 24 machines, though? That's 6 times as many as we had before. If you have six times as many machines, and you're only trying to make three times as much stuff, you should need half as much time. But we needed 4 days, not 3. Eliminate 24.

Guess 16 or 18 and move on!
_________________

Chelsey Cooley | Manhattan Prep | Seattle and Online

My latest GMAT blog posts | Suggestions for blog articles are always welcome!

Status: It's now or never
Joined: 10 Feb 2017
Posts: 185
Location: India
GMAT 1: 650 Q40 V39
GPA: 3
WE: Consulting (Consulting)
Working simultaneously and independently at an identical  [#permalink]

### Show Tags

18 Sep 2017, 03:11
Please correct me if I am wrong: I tried to make it simpler by step-by-step approach:
- 4M produces x units in 6 days
- 4M produces 3x units in (3) (6) = 18 days
- 4M produces 3x units in 18 days, so double the machines and half the number of days to 4 until you arrive at the number you want

We have about 16 machines producing 3x units in 4.5 days, clearly. Therefore, eliminate other options, and pick up something more than 16 days, i.e. 18 (answer choice 'B')
_________________

Class of 2019: Mannheim Business School
Class 0f 2020: HHL Leipzig

Intern
Joined: 18 Jul 2018
Posts: 15
Re: Working simultaneously and independently at an identical  [#permalink]

### Show Tags

04 Sep 2018, 07:03
Hi math expert Bunuel,
Can you please let me know about any practice problems similar to this?
Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 52905
Re: Working simultaneously and independently at an identical  [#permalink]

### Show Tags

04 Sep 2018, 07:12
VQ wrote:
Hi math expert Bunuel,
Can you please let me know about any practice problems similar to this?
Thanks

17. Work/Rate Problems

On other subjects:
ALL YOU NEED FOR QUANT ! ! !
_________________
Director
Joined: 11 Feb 2015
Posts: 711
Re: Working simultaneously and independently at an identical  [#permalink]

### Show Tags

15 Oct 2018, 06:12
Rate = work/time

Therefore rate of one machine is x/24

Number of machines * $$\frac{x}{24}$$ *4 = 3x

or Number of Machines = 18
_________________

"Please hit +1 Kudos if you like this post"

_________________
Manish

"Only I can change my life. No one can do it for me"

Re: Working simultaneously and independently at an identical   [#permalink] 15 Oct 2018, 06:12
Display posts from previous: Sort by