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Machines P and Q are two different machines that cover jars in a facto
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27 Feb 2015, 05:04
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82% (02:04) correct 18% (01:59) wrong based on 138 sessions
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Machines P and Q are two different machines that cover jars in a facto
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Updated on: 28 Feb 2015, 15:44
Work in one hour to get 1500 parts covered by P> 1/m by P+Q>1/n by only Q>1/n1/m=(mn)/mn Total time= mn/(mn) answer D
Originally posted by ynaikavde on 27 Feb 2015, 06:00.
Last edited by ynaikavde on 28 Feb 2015, 15:44, edited 1 time in total.



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Machines P and Q are two different machines that cover jars in a facto
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Updated on: 01 Mar 2015, 11:00
Bunuel wrote: Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 1500 jars?
A. m/(m + n) B. n/(m + n) C. mn/(m + n) D. mn/(m – n) E. mn/(n – m)
Kudos for a correct solution. This question seems tricky, but I hope that I have been able to crack it! Here's my solution: Since we are asked to find the number of hours it takes Machine Q to manufacture 1500 jars, we need to first find the rate at which Machine Q operates. So Machine P has a rate of \(\frac{ 1500}{m}\) because it can manufacture 1500 jars in m hours. Together, Machine P and Machine Q's combined rate (when working simultaneously) is \(\frac{ 1500}{n}\), this is because it takes Machine P and Q n hours to manufacture 1500 jars when working together. Therefore Machine Q's rate is \(\frac{ 1500}{n}\) \( \) \(\frac{ 1500}{m}\), which simplifies to \(\frac{ 1500*(m  n)}{mn}\). We need to find the number of hours it takes Machine Q to produce 1500 jars, so that would equal \(\frac{ 1500}{(1500*(m  n))/mn}\), which simplifies to \(\frac{ mn}{(m  n)}\). I think the answer is D! Please consider giving me Kudos, if you found this post helpful. Thanks!
Originally posted by kdatt1991 on 27 Feb 2015, 06:48.
Last edited by kdatt1991 on 01 Mar 2015, 11:00, edited 1 time in total.



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Re: Machines P and Q are two different machines that cover jars in a facto
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27 Feb 2015, 08:49
Time to use SMART numbers.
Rate of p = 1500jars/m hours Let m = 15 hours. Therefore rate of p = 100 jars per hour
Rate of p + rate of q = 1500jars/n hours. Let n = 10 hours. We will assume q has a positive rate of work.
Therefore rate of p + rate of q = 150jars per hour.
Solving for q leads us to rate of q = 50 jars per hour.
1500jars/50jars per hour = 30 hours.
(15*10)/(1510) = 30 hours.
Answer is D.
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Re: Machines P and Q are two different machines that cover jars in a facto
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27 Feb 2015, 08:50
ynaikavde wrote: Work in one hour to get 1500 parts covered by P> 1/m by P+Q>1/n by only Q>1/n1/m=(mn)/mn Total time= mn/(mn) answer E You mean D. But yes, that's the right answer. Posted from my mobile device



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Re: Machines P and Q are two different machines that cover jars in a facto
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28 Feb 2015, 10:56
Answer is D...
with the approach of taking SMART numbers,
lets summarize the given info : Machine p : 1500 jars in M hours
Machine P& Q : 1500 jars in N hours
so lets choose M= 5 and N =3 hours so we have for working rates of p& Q : (1/p + 1/Q ) *3 = 1
so we have : ( 1/5 + 1/Q ) *3 =1 OR : ( 5+Q/5Q ) *3 =1 and : 15 +3Q =5Q so, 2Q= 15 Or : Q =15/2
WE obtain Q =15/2 so we plug in M=5 and N=3 in the answer choices and see which answer choice gives us the result 15/2 :
A ) : m/(m+n) = 5/(5+3) = 5/8 : doesn't match , so reject B ) : n/ (m+n) = 3/ (5+3) = 3/8 : does n't match, so reject
C) : mn/( m+n) = 3*5 /(5+3) = 15/8 : doesn't match, so reject
D) : mn / ( mn) = 3*5 /(53) = 15/2 : THE ANSWER
E) : mn/(nm) = 3*5 / (35) =  15/2 : doesn't match ,so reject
So, answer is D....



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Re: Machines P and Q are two different machines that cover jars in a facto
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02 Mar 2015, 05:42
Bunuel wrote: Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 1500 jars?
A. m/(m + n) B. n/(m + n) C. mn/(m + n) D. mn/(m – n) E. mn/(n – m)
Kudos for a correct solution. MAGOOSH OFFICIAL SOLUTION:This is a particularly challenging, one because we have variables in the answer choices. I will show an algebraic solution, although a numerical solution ( http://magoosh.com/gmat/2012/variables ... approach/) is always possible. “Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 1500 jars? ” Since the number “1500 jars” appears over and over, let’s arbitrarily say 1500 jars = 1 lot, and we’ll use units of lots per hour to simplify our calculations. P’s individual rate is (1 lot)/(m hours) = 1/m. The combined rate of P & Q is (1 lot)/(n hours) = 1/n. We know (P’s rate alone) + (Q’s rate alone) = (P and Q’s combined rate) (Q’s rate alone) = (P and Q’s combined rate) – (P’s rate alone) (Q’s rate alone) = 1/n – 1/m = m/ (nm) – n/ (nm) = (m – n)/(nm) We now know Q’s rate, and we want the amount of 1 lot, so we use the “art” equation. 1 = [(m – n)/ (nm)]*T T = (mn)/(m – n) Answer = D
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Re: Machines P and Q are two different machines that cover jars in a facto
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10 Apr 2015, 06:34
Bunuel wrote: Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 1500 jars?
A. m/(m + n) B. n/(m + n) C. mn/(m + n) D. mn/(m – n) E. mn/(n – m)
Kudos for a correct solution. let 1 jar = 1 unit let m = 5 and n = 3 P does 300 units/hr P & Q together do 500 units/hr so Q does 200 units/hr hence, Q needs 7.5 hrs to produce 1500 jars options D satisfies
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Machines P and Q are two different machines that cover jars in a facto
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10 Apr 2015, 07:42
Bunuel wrote: Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 1500 jars?
A. m/(m + n) B. n/(m + n) C. mn/(m + n) D. mn/(m – n) E. mn/(n – m)
Kudos for a correct solution. \(\frac{1}{Q} = \frac{1}{n} \frac{1}{m}\) \(Q= \frac{m*n}{(mn)}\) answer D



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Re: Machines P and Q are two different machines that cover jars in a facto
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01 Mar 2017, 10:42
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