Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 45222

Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
18 Oct 2015, 13:12
3
This post received KUDOS
Expert's post
33
This post was BOOKMARKED
Question Stats:
80% (01:36) correct 20% (02:20) wrong based on 1176 sessions
HideShow timer Statistics



Board of Directors
Joined: 17 Jul 2014
Posts: 2736
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
18 Oct 2015, 13:52
3
This post received KUDOS
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?
tough one, let's see... 4 machines do x units in 6 days
we have x/6 => rate of the 4 machines
we know that we need to have 3x units in 4 days therefore, we need to get to 3x/4 rate of the machines.
rate of one machine is x/6*1/4 = x/24.
now, we need to know how many machines need to work simultaneously, to get 3x done in 4 days. 4x/4 work needs to be done by machines that work at x/24 rate.
let's assign a constant Y for the number of machines: (x/24)*y = 3x/4
y = 3x/4 * 24/x cancel 4 with 24, and x with x and get > 18. Answer choice B



Manager
Joined: 01 Jan 2015
Posts: 63

Re: Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
18 Oct 2015, 14:52
15
This post received KUDOS
6
This post was BOOKMARKED
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. If it takes 4 machines 6 days to produce x units then it takes 4 machines 18 days to produce 3x units then it takes \(M\) machines 4 days to produce 3x units There is an inverse relationship between the amount of time and the number of machines required to do the taskSo if the task is 3x units, then (4 machines)*(18 days)=(M machines)*(4 days) > M = 18Correct answer choice is B.



Intern
Joined: 01 Mar 2015
Posts: 49

Re: Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
18 Oct 2015, 22:41
4
This post received KUDOS
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. we have x units by 4 machine in 6 days => x units in 24 machine days => 3x units in 72 machine days therefore machine required = 72 / 4 = 18 Answer choice B



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8064
Location: Pune, India

Re: Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
18 Oct 2015, 23:39
9
This post received KUDOS
Expert's post
7
This post was BOOKMARKED
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 Answer (B)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 1979
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE: Information Technology (Consulting)

Re: Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
19 Oct 2015, 00:09
2
This post received KUDOS
Let work done per machine per day = m Work done by 4 machines in a day, 4m = x/6 Work done by 1 machine in a day , m = x/24 Since work needs to completed in 4 days , work done by 1 machine in 4 days = x/6 Number of machines required = Total work to be completed in 3 days/ Work done by a single machine in 4 days = 3x/(x/6) = 18 Answer B
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it.  Henry Ford The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long +1 Kudos if you find this post helpful



Retired Moderator
Joined: 29 Oct 2013
Posts: 273
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)

Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
11 Dec 2015, 13:44
Since we need to do 3 times as much work (3x vs x) we will need 3 times as many m/cs. so multiply by a factor of 3 Now we need to do this work faster i.e. in 4 days vs 6days, so we will need 6/4 as many more m/cs. so multiply by a factor of 6/4 No of mc/ required= 4*3*(6/4)=18 ans B
_________________
Please contact me for super inexpensive quality private tutoring
My journey V46 and 750 > http://gmatclub.com/forum/myjourneyto46onverbal750overall171722.html#p1367876



Director
Joined: 07 Dec 2014
Posts: 998

Re: Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
13 Dec 2015, 10:50
1
This post was BOOKMARKED
one machine can do x/24 units in one day 3x/(x/24)(4)=18 machines



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8064
Location: Pune, India

Re: Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
18 Dec 2015, 21:31
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 Answer (B) 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.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Joined: 13 Feb 2011
Posts: 95

Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
17 Feb 2016, 19:09
2
This post received KUDOS
2
This post was BOOKMARKED
4 machines take 6 days to complete x amount of work, so 1 machine will take \(6*4=24\) days to complete same work. 3x, i.e. three times of work will require that single machine to work for \(24*3=72\) days. Now in order to do 72 days worth of work in 4 days, we'd need \(72/4=18\) machines. Answer: B



Current Student
Joined: 23 Mar 2016
Posts: 34

Re: Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
02 May 2016, 14:55
given : 4 machines rate = x stuff / 6 days or 4m = x/6
need to find y machines = 3x stuff / 4 days = ym = 3x/4
two equations, two unknowns, solvable now.
4 = x/6 & y = 3x/4 4 = x/6 24 = x (now plug into second equation)
y = 3(24) / 4 y = 3(6) y = 18



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2442

Re: Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
03 May 2016, 05:52
4
This post received KUDOS
Expert's post
3
This post was BOOKMARKED
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. We are given that 4 machines can produce a total of x units in 6 days. Since rate = work/time, the rate of the 4 machines is x/6. We need to determine how many machines, working at the same rate, can produce 3x units of product P in 4 days. Thus, we need to determine how many machines are needed for a rate of 3x/4. Since we know that all the machines are working at an identical constant rate, we can create a proportion to determine the number of machines necessary for a rate of 3x/4. The proportion is as follows: “4 machines are to a rate of x/6 as n machines are to a rate of 3x/4." 4/(x/6) = n/(3x/4) 24/x = 4n/(3x) When we cross multiply, we obtain: 72x = 4xn 18 = n Answer: B
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 635
Location: United States (CA)
Age: 38
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42
GRE 1: 337 Q168 V169
WE: Education (Education)

Re: Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
17 May 2016, 19:58
1
This post received KUDOS
Attached is a visual that should help.
Attachments
Screen Shot 20160517 at 7.55.31 PM.png [ 126.58 KiB  Viewed 7990 times ]
_________________
Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching, both inperson (San Diego, CA, USA) and online worldwide, since 2002.
One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong).
You can download my official testtaker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y8zh6qby Date of Birth: 09 December 1979.
GMAT Action Plan and Free EBook  McElroy Tutoring



Manager
Joined: 07 Mar 2016
Posts: 74

Re: Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
24 Aug 2016, 00:29
1
This post received KUDOS
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 individual rate be 'a' therefore, for 4 machines we have: \(\frac{1}{a} +\frac{1}{a} + \frac{1}{a} +\frac{1}{a} = \frac{x}{6}\) >\(\frac{4}{a} = \frac{x}{6}\) > ax = 6 x 4 = 24 ......(eq1) now If Z machines of same rate were used to produce 3x work in 4 days, we would have: Z(\(\frac{1}{a}\)) = \(\frac{3x}{4}\) > Z = \(\frac{3x(a)}{4}\) > Z = \(\frac{3 (24)}{4}\) ......(using eq1) > Z = 18



Manager
Joined: 17 Aug 2015
Posts: 102

Re: Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
28 Aug 2016, 21:52
The problem is not dependent on the rate of each machine. So let us say each machine takes 1 day to produce each product. So 4 machines produce 4 per day. In 6 days they will produce 24 machines. Take 72 machines = 24*3. now the combined rate has to be 72/4 = 18. Since each machine still produces 1 per day we need 18 machines to have a rate of 18 per day.



Manager
Joined: 30 Oct 2012
Posts: 66
Location: India
WE: Marketing (Manufacturing)

Re: Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
29 Aug 2016, 00:16
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 produce x units in 6 days N Machines produce 3x units in 4 days 4/x/6 = N/3x/4 N = 4 * 3x/x * 6/4 N= 72/ 4 = 18
_________________
i am the master of my fate, I am the captain of my soul



Manager
Joined: 30 Dec 2015
Posts: 89
GPA: 3.92
WE: Engineering (Aerospace and Defense)

Re: Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
08 Oct 2016, 21:06
=4*(3x/x)*(6/4) = 18 (3x/x) because no of units went up, so more no of machines are required (6/4) no of days to get work done went down, so more no of machines required
_________________
If you analyze enough data, you can predict the future.....its calculating probability, nothing more!



Manager
Joined: 15 Nov 2016
Posts: 132
Concentration: General Management, Leadership

Re: Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
23 Aug 2017, 07:03
1
This post received KUDOS
No. of men 4M Work X Time 6 Rate of 1 men = x/6 Rate of 4 men= x/24
Apply this rate in the second equation No. of men needed  M Work 3x Time 4
So, Work =Rate x time Apply rate that was calculated above as x/24 3x=x/24 * 4 * (M) no of men
After solving we get
M=18 and that’s the answer.



Intern
Joined: 19 Jun 2017
Posts: 1

Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
17 Dec 2017, 13:39
Let m = number of machine, d = number of days, x = number of units
If \(m = 4\) and \(d = 6\) then \(x = 24\)
Now if \(d = 4\) and \(x = 3x\) or \(72\) then...
\(4m = 72\)
\(m = \frac{72}{4} = 18\)
Thus, the number of machines needed is 18



Intern
Joined: 25 Oct 2017
Posts: 5

Re: Working simultaneously and independently at an identical constant rate [#permalink]
Show Tags
17 Dec 2017, 16:15
1
This post received KUDOS
Let’s say x=600 units of P. Then, there are 100 units produced per day (600/6).
And since there are 4 machines, each machine produces 25 units per day (100/4).
We want to know how many machines it takes to produce 3x. Since we assumed x is 600, 3x is 1800 units of P. There must be 450 units produced per day (1800/4). And because one machine produces 25 units per day we will need 18 machines (450/25).
Sent from my iPhone using GMAT Club Forum




Re: Working simultaneously and independently at an identical constant rate
[#permalink]
17 Dec 2017, 16:15



Go to page
1 2
Next
[ 22 posts ]



