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Intern  B
Joined: 15 Oct 2017
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Working simultaneously and independently at an identical constant rate  [#permalink]

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Hi guys,

It's always tricky for me to answer this kind of question. I tried Bunuel's method, but somehow I found VeritasPrepKarishma 's method easier. I hope what I posted below is correct. Attachments Resized.jpg [ 77.49 KiB | Viewed 1242 times ]

Intern  Joined: 23 Jan 2018
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Re: Working simultaneously and independently at an identical constant rate  [#permalink]

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Hello,

I follow a very simple approach that is shown to us in the Gmat Club Math Book.

Let d = number of days; n = number of machines

So, firstly, we get this expression from what is said in the exercise:

(x/d)*4=(x/6)

But since we know 1 job done is equivalent to x, in this case, we can represent it as the following:

(1/d)*4=(1/6) which gives us d=24 days

Thus: (1/24)*n=(3/4) ,which gives us n=18
Manager  S
Joined: 23 Dec 2011
Posts: 54
Re: Working simultaneously and independently at an identical constant rate  [#permalink]

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Let us pick numbers.

Let x = 240

Rate 240/6 = 40/ day
Total unit to produce 240 * 3= 720
Machines required = 720/40 = 18.
Intern  Joined: 28 Jul 2018
Posts: 1
Re: Working simultaneously and independently at an identical constant rate  [#permalink]

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4M = x units in 6 days
?M = 3x units in 4 days

*** (R)(T)=W ***

1M = x/4 units in 6 days, so
1M = 3(x/4 units) in 18 days, so
M = 3x units in 72 days, so
72/4 = 36/2 = 18
GMAT Club Legend  V
Joined: 12 Sep 2015
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Re: Working simultaneously and independently at an identical constant rate  [#permalink]

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Top Contributor
Bunuel 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

Kudos for a correct solution.

Let's assign a nice value to x (a value that will work well with all of the numbers 3, 4 and 6.

Let's say x = 24

GIVEN: 4 machines make x units in 6 days
This means 4 machines make 24 units in 6 days
So, 4 machines make 4 units in 1 day [if you divide the work time by 6, the output is also divided by 6]
So, 1 machine makes 1 unit in 1 day [if you divide the number of machines by 4, the output is also divided by 4]

From here, we can answer the question 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?
If x = 24, 3x = 72
Our goal is to make 72 units in 4 days.

So, 1 machine makes 4 units in 4 days [if you multiply the work time by 4, the output is also multiplied by 4]
So, 18 machines make 72 units in 4 days [if you multiply the number of machines by 18, the output is also multiplied by 18]

Cheers,
Brent
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Working simultaneously and independently at an identical constant rate  [#permalink]

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Bunuel 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

Kudos for a correct solution.

Using the method discussed in this post: http://www.veritasprep.com/blog/2013/02 ... variation/

4 machines --- x units --- 6 days
? machines --- 3x units -- 4 days

Machines required = 4 * (3x/x) * (6/4) = 18

Wonderful article http://www.veritasprep.com/blog/2013/02 ... variation/
you just have to transform your mind to adopt this method as it is fast. The problem with such type of questions is that people tend to enjoy every minute details of the problem. The problem on GMAT is that you don't have time to enjoy all those pleasures of solving a problem. set a pattern and do away with it this is not a test to calibrate a humans ability nor it is there to enjoy problem in Mathematics . you are not a scientist who has to go deep into problen to enjoy and understand it, if you are one then i feel sorry to inform you that you have to dispose of your inquisitive inclination to enjoy math in detail. Beat the GMAT hard and do away with this test forever to enjoy nature and science in excruciating details.

Nice job Karishma.
Qute of the Day.
You are pretty but I am prettier. Have a nice day.
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If you like this post, be kind and help me with Kudos!

Cheers!

Originally posted by alitariquet on 08 Sep 2018, 23:43.
Last edited by alitariquet on 12 Sep 2018, 05:38, edited 1 time in total.
Manager  S
Joined: 11 Aug 2018
Posts: 110
Working simultaneously and independently at an identical constant rate  [#permalink]

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VeritasPrepKarishma wrote:
Bunuel 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

Kudos for a correct solution.

Using the method discussed in this post: http://www.veritasprep.com/blog/2013/02 ... variation/

4 machines --- x units --- 6 days
? machines --- 3x units -- 4 days

Machines required = 4 * (3x/x) * (6/4) = 18

Quote:
In the end, you took 6/4 because the machines have fewer days to do more (3x) work, so more machines will be needed and therefore one has to multiply with the value greater than 1, i.e. 6/4 and not 4/6. Is that a correct reasoning?

Forget "work" here - whether it is more or less. Focus on the relation between the unknown and the variable in question only. So focus on machines and days only.

You have fewer days so you will need more machines to complete the work. So you multiply by 6/4, a quantity greater than 1. This will increase the number of machines.

Let me elaborate on it. The human mind is not good at multi-tasking therefore all the science and maths that mind has invented revolves around finding the relation between one or two things at a time once mind has found the relation it moves on to the rest of the things to discover further relation bout one or two at a time.
Now the purpose of stating is to tell that Krisma's approach is quite near to the calculus-based approach. whenever we have to find the relation between two things we make third thing constant ( since humans can't multi task or have not found any tool to do it yet) so in comparing machines and days we keep work constant and in comparing machines and work we keep days constant.

Hope you enjoyed it.
Quote : Beat the GMAT hard and dispose it off forever.
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Cheers!
Intern  S
Joined: 07 May 2015
Posts: 41
Location: India
Schools: Darden '21
GPA: 4
Re: Working simultaneously and independently at an identical constant rate  [#permalink]

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Bunuel 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

Kudos for a correct solution.

4 machines -> X units/6days
So, 1 machine per day makes -> X/24 units per day
to make 3X/4 we need
X/24 * P = 3X/4
P=18
OA B
Intern  B
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Schools: IIMB EPGP"20 (A)
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Re: Working simultaneously and independently at an identical constant rate  [#permalink]

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Lets say each machine has a rate of k units/day
in six days 6k units per machine were produced
4 machines at the same rate produced 24k units = x
=> k=x/24 units per day per machine

In 4 days one machine can produce = 4*X/24 = X/6 unit s
For 3x units => 3x/(x/6) = 18 machines

The solution is long but emperically derived ,want to know if the approach is correct
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Joined: 31 Oct 2013
Posts: 1464
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: Working simultaneously and independently at an identical constant rate  [#permalink]

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Bunuel 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

Kudos for a correct solution.

(No. of machine)* time * rate = work

4 * 6 * rate = x units

Rate = x / 24 units

Now we are asked to determine the no. of machine

no. of machine * time * rate = work

no of machine * 4 * x / 24 = 3x

No. of machine = 18.

The best answer is B.
Intern  B
Joined: 14 Sep 2018
Posts: 3
Location: Iran (Islamic Republic of)
GPA: 3.8
Re: Working simultaneously and independently at an identical constant rate  [#permalink]

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Golden solution for all of these types of questions: X=Vt
X=Vt --> V(4-machine) = x(unit)/6(day) --> 4*V(1-machine)= x(unit)/6(day) --> V(1-machine)= x(unit)/6(day)/4
--> V(1-machine)= X(unit)/24(day)
THE NUMBER OF Machine needed to produce 3 units in 4 days = T --> X=Vt --> T*V(1-machine)*4(day)=3x -->
T* (x(unit)/24(day))*4(day)=3x --> T= 18
Manager  B
Joined: 19 Jan 2018
Posts: 67
Re: Working simultaneously and independently at an identical constant rate  [#permalink]

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Bunuel 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

Kudos for a correct solution.

Rate Formula:
Rate * Time = Work Done

1.) 4 Machines produce x units in 6 days
Machines: 4
Rate: R
Time: 6 days
Work: X

4R * 6 days = x units (solve for R)
24R = x units
R = x/24
^ This is the rate for 1 machine.

2.) How many machines can produce 3x units in 4 days
Rate: (x/24)*M (M = machines needed)
Time: 4 days
Work: 3x

xM/24 * 4 days = 3x units
4xM/24 = 3x
xM/6 = 3x
M = 3x * (6/x)
M = 18

Intern  Joined: 25 Oct 2018
Posts: 5
Re: Working simultaneously and independently at an identical constant rate  [#permalink]

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Great post and link Karishma - thank you!
Intern  B
Joined: 03 Apr 2018
Posts: 38
Re: Working simultaneously and independently at an identical constant rate  [#permalink]

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work rate = work done / total time takes
work rate of 4 machines = X work done / 6 days taken
work rate of 1 machine (say R) = X / 6*4
X = 24R

Say we need Y machines to do 3X work in 4 days.
So, Work Rate of Y machines = YR (R is our rate as above)
YR = 3X / 4
YR = 3*24*R/4
Y = 18
Intern  B
Joined: 16 Jun 2019
Posts: 1
Re: Working simultaneously and independently at an identical constant rate  [#permalink]

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AMOUNT OF WORK/(TIME*RATE)

#1 4 MACHINES RATE = WORK/TIME = x/6
#1 Y MACHINES RATE = WORK/TIME = 3x/4

4 MACHINES -- X/6
Y MACHINES -- 3X/4 -- CROSS MULTIPLY

Y * x/6 = (3x/4) * 4
Y = 18 Re: Working simultaneously and independently at an identical constant rate   [#permalink] 19 Jun 2019, 14:45

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